ここでは、科学英語論文を書くさいに、我々を悩ませる「時制」についてまとめる。
なぜ、「時制」が悩ましいかと言うと、これと言ったルールがなく、参考書によって 意見が異なっているからだ。よって、ここではまず、以下の文献にで記述されている 時制の使い分けを記す。
基本は現在形。終わったことは過去形。終わってるけど、今もそれについて考えてることは現在完了形。
以下の論説の4要素によって時制を決める。
具体的な指針は以下の通り。
状況別に使用される時制は以下の通り。
次のように時制を色分けする。
Kaye, N.,Linden, P. (2004). Coalescing axisymmetric turbulent plumes. Journal of Fluid Mechanics, 502, 41–63. doi:10.1017/S0022112003007250
AbstractThe coalescence of two co-flowing axisymmetric turbulent plumes and the resulting single plume flow is modelled and compared to experiments. The point of coalescence is defined as the location at which only a single peak appears in the horizontal buoyancy profile, and a prediction is made for its height. The model takes into account the drawing together of the two plumes due to their respective entrainment fields. Experiments showed that the model tends to overestimate the coalescence height, though this discrepancy may be partly explained by the sensitivity of the prediction to the entrainment coefficient. A model is then developed to describe the resulting single plume and predict its virtual origin. This prediction and subsequent predictions of flow rate above the merge height compare very well with experimental results.
IntroductionThe coalescence of turbulent plumes to form a single plume is a process that occurs in many situations. Ventilated enclosures with multiple heat sources, such as work spaces with electronic equipment or occupied lecture theatres, contain turbulent plumes that rise above heat sources and interact. Their interaction will affect the resulting ventilation flow (Linden 1999). Turbulent plumes rising from smokestacks in close proximity can also interact. In this case the rise height of the plumes into a stratified atmosphere will depend on the nature of the interaction. Despite these numerous applications, very little work has been done on the question of how two turbulent plumes coalesce to form a single plume. This paper describes a model for the merging of two turbulent plumes, and for the resulting single plume.
PeraGebhart (1975) studied the interaction of laminar parallel line plumes, merging to form a single plume. They conducted experiments in which the relative strengths of the two plumes and the ratio of the plume source lengths to their separation were varied. They presented a model for this merging process based on the restriction of the entrainment into each plume by the presence of the other. They observed that for plumes of significantly different strengths, the weaker plume was deflected considerably more than the stronger plume. Some experiments were also done with axisymmetric plumes. Although no model was presented for how the axisymmetric plumes coalesce, they observed that the interaction was weaker than for line plumes.
Moses, ZocchiLibchaber (1993) presented work focused on the starting cap of laminar plumes, but also briefly examined the coalescence height zm of axisymmetric laminar plumes. They found that zm is given by ... where d0 is the source separation, ν the kinematic viscosity, σ the Prandtl number, and F is the buoyancy flux defined in Batchelor (1954) and given by ... where Φ is the heat flux of the plume, Cp is the specific heat, ρ0 is a reference density, g is the gravitational acceleration and T0 in degrees Kelvin is a reference temperature.
The main difference between merging laminar and turbulent plumes is that turbulent plumes are independent of the fluid viscosity. However, there are two key points of similarity: laminar axisymmetric plume interaction results in the plumes coalescing further from their sources than for the case of line plumes, and the weaker plume tends to be deflected significantly more than the stronger plume. As we discuss below, both of these effects are observed in turbulent plume interaction. (略)
Theoritical part(略) Consider first the simplest case of two equal plumes (ψ = 1) with origins at the same height. A simple model, in which the plumes do not interact as they coalesce, provides a limit on λm. The average buoyancy profile of a single turbulent plume can be taken as Gaussian, with a radius given by 6αz/5, where α is the entrainment constant (Morton, TaylorTurner 1956). Allowing the two Gaussians to grow into each other as the height increases, and to have no other effect on each other, leads to a buoyancy profile function of the form ... where r is the radial distance from the plume axis and g′ is the reduced gravity. The model of BjornNielsen (1995) is similar, except that they were concerned with the velocity profiles. Their model is identical to the present case for equal plumes, though when ψ < 1 the ratio of the profile heights will differ. Here the buoyancy rather than the velocity profile is used to judge whether plumes have merged, because the buoyancy is the driving force, and once the driving force can be considered a single entity, it is reasonable to assume that the flow will behave as a single entity. For the case of equal turbulent plumes the choice between buoyancy and velocity profiles will make no difference as they will both merge at the same height. However for unequal plumes the ratio of the peak velocities will be ψ1/3, whereas the ratio of the peak buoyancies will be ψ2/3.
This function (2.4) is plotted in figure 2 for 1 < λ < 8 and χ0 = 1. Clearly the two Gaussians coalesce when λ is large enough, but it is difficult to say where the plumes can be said to have merged. We define the merging height to be the height at which the centreline value first becomes a local maximum – in other words, the height at which there are no longer two distinct peaks. This condition can be written as ... and, for non-interacting plumes, is easily solved to give ... In terms of the non-dimensional height one obtains ... as an upper bound on λm. For an entrainment constant α = 0.09, (2.8) gives λub = 6.5. We will discuss the choice of the numerical value of α in § 4. (略)
Experimental partSections 2 and 3 describe theoretical predictions for the merging height of co-flowing turbulent plumes, and the behaviour of the resulting plume in the far field. Experiments have been performed to test the validity of these models. The experiments were carried out using salt plumes in water. The density of the salt solution and the flow rate determined the buoyancy flux. These were chosen such that the plumes were close to ideal, i.e. with small initial volume and momentum fluxes. Corrections for the non-ideal nature of the sources were made by calculating the virtual origin zv using the method described in HuntKaye (2001). These corrections were typically of the order of 1 cm, which is considerably less that the typical coalescence heights measured of 10–30cm. For the case of unequal plumes, the average of the two virtual origin corrections was used. The difference between the origin corrections for each separate plume was typically less than 0.5cm, or 10% of the plume separation, making the use of the average correction a reasonable approximation.
Typical flow rates used in the experiments were between 0.5 and 2.5 cm3 s−1. The source buoyancy was varied between 30 and 150 cm s−2. The equal plume experiments were run using the dye attenuation technique in a glass tank approximately 60cm square with a depth of 180cm. The unequal plume experiments were run using a light-induced fluorescence (LIF) technique in a 64cm square Perspex tank that was filled to a depth of 15–35 cm. In order to maintain a turbulent plume from the source, a special nozzle was constructed. Figure 10 shows a schematic of the nozzle used. The nozzle allowed the creation of a turbulent outlet that would normally be laminar at the flow rates used. Figure 7 of HuntLinden (2001) shows the outflow from this nozzle compared to a standard cylindrical tube. The use of the Cooper nozzle meant that the plumes rapidly developed into their self-similar form. This can be more clearly seen in figure 13 below, which shows time-averaged buoyancy profiles from an experiment where two equal plumes coalesce. Clearly the profiles are Gaussian in nature well before they coalesce. (略)
ResultsExperiments were conducted with different initial axial separations from 2.5 cm to 7.5 cm to establish the merging height. Figure 13 shows an example of the profiles for two equal plumes. The figure illustrates the fully developed plumes coalescing, with the two plumes merging at λ ≈ 4.5. Figure 14 gives the results of the measurements of the coalescence height. A straight line was fitted through the points. The line is a least-squares fit that was not forced through the origin. The slope of the straight line is the value of λm, see (2.2). The value of λm based on these experiments is λme = 4.1 ± 0.25. For α = 0.09 and the theoretical prediction αλm = 0.44 we obtain λmt = 4.8 which is larger than the measured value, implying that the plumes coalesce closer to the source than predicted. A discussion of possible reasons for this discrepancy is presented later.
The unequal plume experiments were all conducted at a fixed separation of 5cm. The results for this case are plotted in figure 15 as values of λm plotted against ψ. The theoretical predictions for λm and the upper bound λub for α = 0.09, as well as λm for α = 0.1, are also shown in figure 14. It is clear that the theory consistently over-predicts the measured coalescence height. However, the function is very similar to the predictions, with very little variation in λm over the range 0.3 < ψ < 1.
CoclusionsThis paper has examined the coalescence of two axisymmetric plumes rising from two sources separated horizontally. The point of coalescence of two co-flowing plumes is defined as the point at which the mean horizontal buoyancy profile of the combined flow has a single maximum. Assuming that the plumes are only passively advected by the entrainment field of each other, a theoretical prediction of the merging height was made (figure 6). Buoyancy profiles measured using a dye attenuation technique (figure 11) and a light-induced fluorescence (figure 12) showed that the mean buoyancy profiles behaved in a similar manner to that predicted. The prediction of the merging height (λm = 4.8 for equal plumes) was tested experimentally and found to overpredict λm slightly (λm = 4.1 for equal plumes, see figure 15 for unequal plume results). Various reasons for this discrepancy were suggested, particularly the sensitivity of the merging height to the entrainment coefficient. However, the model predicts the qualitative behaviour of the merging height as a function of the buoyancy flux ratio ψ for unequal plumes, that is the merging height decreases only slightly with ψ for ψ > 0.25. The model also accounts for over 80% of the reduction in merging height that results from the approach of the plumes as a result of their mutual entrainment.
Once a point of coalescence was established a calculation was made for the flow in the far field after the plumes had merged. This calculation resulted in a prediction of the virtual origin of the resulting single plume (figure 9) in terms of the buoyancy flux ratio ψ and the horizontal source separation. For equal plumes the virtual origin of the merged plume is found to be a distance below the sources of 1.4 times the source separation. Again this was tested against experimental data (figures 16 to 19), showing very good agreement with theory. This agreement in the prediction of the plume flow rate justifies the selected definition of the merging height, as the transition from two-plume to single-plume behaviour is observed to occur at this height. Measurements of the volume flux show that the two-plume to single-plume transition occurs over a vertical distance of the order of the source separation.
Although the model presented shows good qualitative and quantitative agreement with observations and experiment, it has significant limitations that require further work. The plumes have the same source height, although many examples of vertical as well as radial separation of plume sources exist. For example, two electronic components at different heights on an electronic circuit board will produce plumes with different source heights. A method for adapting this model to account for vertical separation is required.
Scott, R. K.,Polvani, L. M. (2008). Equatorial superrotation in shallow atmospheres. Geophysical Research Letters, 35(24), L24202. doi:10.1029/2008GL036060
AbstractSimple, shallow-water models have been successful in reproducing two key observables in the atmospheres of the giant planets: the formation of robust, and fully turbulent, latitudinal jets and the decrease of the zonal wind amplitude with latitude. However, they have to date consistently failed in reproducing the strong prograde (superrotating) equatorial winds that are often observed on such planets. In this paper we show that shallow water models not only can give rise to superrotating winds, but can do so very robustly, provided that the physical process of large-scale energy dissipation by radiative relaxation is taken into account. When energy is removed by linear friction, equatorial superrotation does not develop; when energy is removed by radiative relaxation, superrotation develops at apparently any deformation radius.
ItroductionThe pronounced latitudinally aligned bands observed on the giant gas planets are the cloud-top signatures of strong alternating zonal jet streams in the so-called ‘‘weather layer’’, the shallow layer of stably-stratified atmosphere overlying the deeper convective region. Despite much attention over several decades, the actual dynamical processes involved in the maintenance of these jets remain controversial, to the extent that there is still debate over whether their origins lie in deep convection throughout the planetary interior [Busse, 1976], or rather in shallow turbulent motions within the thin atmospheric layer itself [Williams, 1978]. Somewhere between these two paradigms lies recent three-dimensional general circulation model studies [Schneider and Lui, 2008; Yamazaki et al., 2005]. Quantitative predictions based on the former paradigm have been difficult to make, in part because very little is known about the planets’ interior [Guillot, 1999], and in part because of the high cost of three-dimensional numerical integrations of convective turbulent flow. The latter paradigm is both conceptually and computationally simpler and is based upon well-known and fundamental properties of rotating, stratified flows.
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As we demonstrate below, the form of the large-scale energy dissipation is a determining factor in the direction of equatorial jets. In forced-dissipative calculations with simple models, linear momentum damping is commonly employed because it provides a convenient closure for the total energy in two-dimensional flow. The atmospheres of the gas giants, however, dissipate energy primarily through radiation to space [e.g., Ingersoll et al., 2004; Showman, 2007]; the absence of a solid ground underlying the atmospheres of the giant planets obviates the usual motivation of linear momentum damping as a model for Ekman drag. Here, we focus on the effect of radiative or thermal damping and demonstrate that it leads to the spontaneous emergence of equatorial superrotation, even though the small-scale forcing is completely isotropic.
MethodsOur model consists of the shallow water equations for a fluid of mean depth H, on the surface of a sphere of radius a, rotating at constant angular velocity W, and with gravity g. In terms of vorticity, z, divergence, d and height h = H + h0, the governing equations are: ... where za = f + z is the absolute vorticity, f = 2Wsinf is the Coriolis parameter, u = (u, v) is the velocity, and E = juj2/2. The shallow water equations can be viewed as describing the motion of a shallow layer of rotating fluid, or, alternatively, as describing an internal vertical mode of equivalent depth H in a continuously stratified fluid. The relevant nondimensional parameters are the Rossby number Ro = U/2aW and Froude number Fr = U/ gH, where U is a typical velocity scale. In place of the latter we use LD/a = Ro/Fr, where LD = gH/2W is the deformation radius, since it can be determined entirely in terms of physical parameters.
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Equations (1a)–(1c) are integrated numerically using a standard pseudo-spectral method [Scott and Polvani, 2007] with a resolution of T682 (equivalent to a 2048 x 1024 longitude-latitude grid). Small-scale hyperdiffusion, nr8x, is included to control the enstrophy at small scales. The equations are integrated for 104 planetary rotations.
Our choice of physical parameters is dictated by values typical of the giant planets. In particular, we are interested in the small Ro regime and we verify a posteriori that the zonal jet speeds that arise in our model are comparable to those of the planets (O(100) ms1). For a given forcing strength 0 the final Ro is determined by trad. This leaves LD as the main free parameter. While we are interested in how the nature of the equatorial flow changes with LD, we are again primarily concerned with cases relevant to the giant planets, for which LD/a is usually put in the range 0.025 – 0.03 [e.g., Cho et al., 2001; Ingersoll et al., 2004].
ResultsFigure 1 shows the instantaneous zonal mean zonal velocity u at t = 10000 days for a series of three numerical integrations with decreasing LD/a = 1.0, 0.1, 0.025, and with radiative damping timescale trad = 0.25(LD/a)2 (in all cases 1/tfr = 0). The prominent feature, and the main result of the paper, is the strong superrotating (positive) equatorial jet, clearly visible in all cases. In contrast, when purely frictional damping is used (the case 1/trad = 0 and tfr = 10000 is shown bold dashed) the equatorial jet is subrotating. In all cases, an alternating pattern of weaker jets is also apparent, and extends through the midlatitudes. We emphasize that these zonal jets and their structure arise spontaneously and despite the fact that the forcing is purely isotropic in space and time: there is no forcing in the zonal mean and there is no asymmetry in the forcing that might fix the sign of the jet at the equator.
While our model is highly idealized, we have nevertheless selected parameters that correspond, approximately, to the Jovian atmosphere. Rossby numbers are similar to Jovian values, with resulting equatorial jet speeds of approximately 200 ms1, and LD/a ranges down to 0.025. As far as we are aware, this is the first numerical integration with physically relevant parameters in rotating shallow water to produce the observed sign of the equatorial jet. (In a two-dimensional barotropic model, that is, the shallow water model in the limit LD/a ! 1, Dunkerton and Scott [2008] showed that superrotating and subrotating equatorial jets emerged with roughly equal probability in an ensemble of numerical calculations with identical physical parameters. Similar behavior also emerges in the shallow water equations with linear friction for LD/a 1, but has until now not been found for LD/a 1, the regime of relevance for the giant planets.) (略)
DiscussionIn conclusion, we have shown that a simple shallow water model, with random isotropic forcing and a large-scale energy dissipation that crudely represents energy loss through radiation, is able to capture several of the main features of the atmospheres of the giant gas planets, specifically: (i) a turbulent flow dominated by strong, steady zonal jets; (ii) a decrease in jet amplitude with latitude; (iii) small scale filaments and vortices similar to observed cloud top features; and, most importantly, (iv) an equatorial jet that is superrotating. Further, we note that equatorial super-rotation is a stable feature of this model, whose persistence does not require continued thermal damping: when the thermal damping is turned off, the equatorial jets continue to intensify (in cases where the forcing remains present) or remain steady (in cases where the forcing is also turned off).
Given that they are so robust, why then have super-rotating equatorial jets not been previously obtained in shallow water models? One possible reason is that in rotating shallow water anticyclones are in general more stable than cyclones [Polvani et al., 1994; Stegner and Dritschel, 2000], an asymmetry which grows with decreasing LD/a. Although difficult to diagnose in a fully turbulent flow, this asymmetry, coupled with the b-drift of anticyclones toward low latitudes, may account for an accumulation of anticyclonic shear, and hence a subrotating jet at the equator. Linear friction acts equally on both cyclonic and anticyclonic vorticity and so does not alter this asymmetry. In contrast it can be shown that, under certain conditions, radiative relaxation can damp anticyclones at a faster rate than cyclones (full details will be presented in a longer article), and may therefore offset the asymmetry. However, other mechanisms may also be relevant in the selection of equatorial superrotation, including the latitudinal dependence of the angular momentum changes arising from thermal damping, and the relative effects of thermal and frictional damping on mean flow changes induced by momentum flux convergences due to equatorial waves [Andrews and McIntyre, 1976]. Work is currently underway towards a deeper understanding of the precise mechanisms whereby the superrotation is generated.
Bordoni, S.,Schneider, T. (2010). Regime Transitions of Steady and Time-Dependent Hadley Circulations: Comparison of Axisymmetric and Eddy-Permitting Simulations. Journal Of The Atmospheric Sciences, 67(5), 1643–1654. doi:10.1175/2009JAS3294.1
AbstractSteady-state and time-dependent Hadley circulations are investigated with an idealized dry GCM, in which thermal forcing is represented as relaxation of temperatures toward a radiative-equilibrium state. The latitude f0 of maximum radiative-equilibrium temperature is progressively displaced off the equator or varied in time to study how the Hadley circulation responds to seasonally varying forcing; axisymmetric simulations are compared with eddy-permitting simulations. In axisymmetric steady-state simulations, the Hadley circulations for all f0 approach the nearly inviscid, angular-momentum-conserving limit, despite the presence of finite vertical diffusion of momentum and dry static energy. In contrast, in corresponding eddy-permitting simulations, the Hadley circulations undergo a regime transition as f0 is increased, from an equinox regime (small f0) in which eddy momentum fluxes strongly influence both Hadley cells to a solstice regime (large f0) in which the cross-equatorial winter Hadley cell more closely approaches the angular-momentum-conserving limit. In axisymmetric time-dependent simulations, the Hadley cells undergo transitions between a linear equinox regime and a nonlinear, nearly angular-momentum-conserving solstice regime. Unlike in the eddy- permitting simulations, time tendencies of the zonal wind play a role in the dynamics of the transitions in the axisymmetric simulation. Nonetheless, the axisymmetric transitions are similar to those in the eddy-permitting simulations in that the role of the nonlinear mean momentum flux divergence in the zonal momentum budget shifts from marginal in the equinox regime to dominant in the solstice regime. As in the eddy-permitting simulations, a mean-flow feedback—involving the upper-level zonal winds, the lower-level temperature gradient, and the poleward boundary of the cross-equatorial Hadley cell—makes it possible for the circulation fields to change at the transition more rapidly than can be explained by the steady-state response to the thermal forcing. However, the regime transitions in the axisymmetric simulations are less sharp than those in the eddy-permitting simulations because eddy–mean flow feedbacks in the eddy-permitting simulations additionally sharpen the transitions.
IntroductionMonsoons are generally viewed as regionally concentrated, thermally direct overturning circulations in the latitude–height plane, with ascending motion in the summer hemisphere subtropics and descending motion in the winter hemisphere (Newell et al. 1972; Gadgil 2003; Bordoni and Schneider 2008). These monsoonal circulations dominate the solstitial zonally averaged Hadley circulation, which is characterized by a strong and broad cross-equatorial winter cell and a very weak and narrow summer cell. Most theories of the dynamics of these circulations have been developed in the context of axisymmetric models of the Hadley circulation in which the upper branches of the circulation are assumed to be nearly inviscid and angular-momentum-conserving (e.g., Schneider 1977; Held and Hou 1980; Lindzen and Hou 1988; Satoh 1994; Caballero et al. 2008). For instance, Plumb and Hou (1992) showed that axisymmetriccirculations driven by a localized off-equatorial thermal forcing undergo transitions from a linear, viscous regime to a nonlinear, angular-momentum-conserving regime beyond a threshold forcing value; they suggested that this threshold behavior may account for the rapid onset of monsoons.
The nonlinear axisymmetric theory of Plumb and Hou (1992) has been extended in several studies to account for the influences of moist convection (Emanuel 1995; Zheng 1998), of a subtropical continent (Prive ́ and Plumb 2007a,b), and of moisture–dynamics feedbacks such as wind-induced surface heat exchange (Boos and Emanuel 2008a,b). All of these studies, however, have postulated the existence of a localized subtropical heating (either provided by imposed surface temperature anomalies or a subtropical continent) as necessary for monsoon development and have neglected the interaction between large-scale eddies and tropical circulations.
But, large-scale eddies of midlatitude origin may in fact play an important role in the dynamics of Hadley and monsoonal circulations. Through idealized GCM experiments, Walker and Schneider (2006) found that over a wide range of climates, including earthlike climates, the strength of a Hadley cell driven by hemispherically symmetric thermal forcing is strongly influenced by eddy momentum fluxes of extratropical origin, so the scalings that nearly inviscid axisymmetric theory gives for the extent and strength do not apply.
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Model description and experimetsThe idealized GCM is the same hydrostatic primitive-equation model as in SB08, where more details can be found. The model is a spectral-transform model, run in axisymmetric configuration (truncated at zonal wave-number zero) with T42 horizontal resolution and 30 unequally spaced sigma levels in the vertical. Radiative forcing is provided by Newtonian relaxation toward a radiative-equilibrium state of a semigray atmosphere, which is axisymmetric and statically unstable in the lower troposphere. The radiative-equilibrium surface temperature varies with latitude as ... where f0 is the latitude at which Tse is maximal, and Dh 5 112.5 K is the pole-to-equator temperature difference for f0 5 0. In the steady-state simulations, f0 is a fixed parameter; in the time-dependent simulations, it varies with time according to This thermal forcing fundamentally differs from that used in Plumb and Hou (1992) in that it is not localized in the subtropics and in that the radiative-equilibrium temperature has nonzero curvature and (for f0 61⁄4 0) a nonzero gradient at the equator. This implies that a meridional circulation is to be expected for all values of f0 (Plumb and Hou 1992). It also differs from that used in Fang and Tung (1999) in that it features larger seasonal excursions of the Tse maximum away from the equator.
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Steady-state simulations were conducted with fixed values of f ranging from 08 (vernal equinox) to 23.58N (boreal summer solstice). For comparison with the results from these steady-state axisymmetric simulations, in section 3 we also show results from the statistically steady states of the eddy-permitting simulations in SB08. The averages shown are surface-pressure-weighted sigma-coordinate averages over longitude and time (over 100 simulated days) in the axisymmetric and eddy-permitting simulations. The time-dependent simulation of seasonal cycles was started from the equinox steady state (f0 5 08) and was run for five years. The results shown in section 4 are from the equilibrated response, which is reached three years into the simulation. Our discussion mostly focuses on the comparison of the axisymmetric time-dependent simulations with the eddy-permitting simulations in SB08 (control). We also discuss how the longer convective time scale and the nonzero vertical diffusivities used in the axisymmetric simulations impact our results, by comparing the control eddy-permitting simulation with eddy-permitting simulations in which the longer convective time scale and the vertical diffusivities are separately or simultaneously introduced.
Numerical resultsFigure 1 shows the strength of the cross-equatorial Hadley cell in the axisymmetric steady-state simulations for different values of the latitude f0 of maximum radiative-equilibrium surface temperature, together with the corresponding values from the eddy-permitting simulations in SB08. In the eddy-permitting simulations, the scaling of the cross-equatorial Hadley cell strength as a function of f0 is in two different regimes: a weaker dependence on f for f98 (roughly f1/5) and a stronger dependence for f for f * 98 (roughly f3/4). In contrast, in the axisymmetric simulations, the cross-equatorial Hadley cell strength increases almost linearly with f0 throughout the parameter space. For the largest f0 values, the Hadley cell strengths in the eddy-permitting and axisymmetric simulations converge. In Fig. 1, we also show the strength of the cross-equatorial Hadley cell from numerical calculations analogous to those of Lindzen and Hou (1988) but with the radiative–convective equilibrium state of our simulations. Similarly to what is seen in the axisymmetric simulations, the nearly inviscid axisymmetric theory for our simulations does not exhibit a transition in scaling regimes at f0 ; 98, but it predicts a somewhat stronger power-law dependence of the circulation strength on f (roughly f4/3). The axisymmetric cross-equatorial circulations do not exhibit a transition in scaling regimes in the parameter space because they tend to approach the angular-momentum-conserving limit for all values of f0, despite the finite vertical diffusion of momentum and dry static energy.
ConclusionsTo explore if and to what extent the rapid regime transitions of the Hadley cells in the eddy-permitting simulations in SB08 and Bordoni and Schneider (2008) can still occur when large-scale eddies are suppressed, we have performed steady-state and time-dependent axisymmetric simulations. Although finite vertical diffusion of momentum and dry static energy needs to be used to achieve approximately steady states, the Hadley cells in the axisymmetric steady-state simulations generally approach the nearly inviscid limit. As the latitude of maximum radiative-equilibrium temperature is progressively displaced off the equator, they do not undergo regime transitions. The marked shifts in circulation fields that occur at the transitions from the eddy-dominated regime to the nearly angular-momentum-conserving regime in the eddy-permitting steady-state simulations do not occur in the axisymmetric steady-state simulations. As a consequence, in the axisymmetric steady-state simulations, the strength of the cross-equatorial Hadley cell, the location and intensity of the main convergence zone, and the upper- and lower-level winds in the summer subtropics do not change as rapidly as in the corresponding eddy-permitting simulations.
Bird, M. K., Allison, M., Asmar, S. W., Atkinson, D. H., Avruch, I. M., Dutta-Roy, R., Dzierma, Y., et al. (2005). The vertical profile of winds on Titan. Nature, 438(7069), 800–802. doi:10.1038/nature04060
AbstractOne of Titan’s most intriguing attributes is its copious but featureless atmosphere. The Voyager 1 fly-by and occultation in 1980 provided the first radial survey of Titan’s atmospheric pressure and temperature1,2 and evidence for the presence of strong zonal winds3. It was realized that the motion of an atmospheric probe could be used to study the winds, which led to the inclusion of the Doppler Wind Experiment4 on the Huygens probe5. Here we report a high resolution vertical profile of Titan’s winds, with an estimated accuracy of better than 1 m s21. The zonal winds were prograde during most of the atmospheric descent, providing in situ confirmation of superrotation on Titan. A layer with surprisingly slow wind, where the velocity decreased to near zero, was detected at altitudes between 60 and 100 km. Generally weak winds (,1 m s21) were seen in the lowest 5 km of descent.
IntroductionTitan’s winds have been the subject of many investigations since that first close-up look from Voyager nearly 25years ago. The infrared observations revealed a distinct pole-to-equator latitudinal contrast in temperature, varying from DT < 3 K at the surface to DT < 20 K in the stratosphere, implying a superrotational, global cyclostrophic circulation analogous to that observed on Venus3. Scaling for a hydrostatic, gradient-balanced flow suggested that the meridional and vertical winds should be much weaker than the zonal motion. Titan-specific general circulation models (GCMs) have since been introduced to study the conditions necessary for generation of atmospheric superrotation6–9.
Observational evidence for winds on Titan has also been inferred from the finite oblateness of surfaces of constant pressure determined from precise ground-based astrometry during stellar occultations in 1989 and 200110,11. These occultation experiments, as well as the thermal gradient observations, cannot be used to determine the sense of the zonal winds (that is, prograde or retrograde). A technique offering a direct determination of the wind velocity is to measure the differential Doppler shift of atmospheric spectral features as the field-of-view moves from east limb to west limb. Infrared heterodyne observations of Titan’s ethane emission at 12 mm have yielded evidence for prograde winds with velocities exceeding 200ms21 but with a relatively large uncertainty of 150 m s21 (ref. 12). These results assume a global-average zonal wind field and apply to only a limited range in height near the 1 hPa level (200 km altitude). More traditional cloud-tracking techniques using Voyager 1 and ground-based images of Titan have been largely stymied by the ubiquitously poor image contrast. The success of such efforts has improved with the extended capabilities of the imaging system on Cassini, from which a number of atmospheric features have been identified as middle- to lower- tropospheric clouds, particularly near Titan’s southern pole13.
MethodsThe Huygens probe entered and descended for nearly 150 min through the atmosphere of Titan, survived impact on the surface, and continued its telemetry broadcast to the Cassini spacecraft on two separate radio links, denoted channels A and B, for an additional 193 min (ref. 5). The Doppler Wind Experiment (DWE) instrumen- tation—consisting of an atomic rubidium oscillator in the probe transmitter to assure adequate frequency stability of the radiated signal and a similar device in the orbiter receiver to maintain the high frequency stability—was implemented only in channel A (2,040 MHz)4. Whereas channel B (2,098 MHz) functioned flawlessly during the entire mission, the channel A receiver was not properly configured during the probe relay sequence. All data on channel A, including the probe telemetry and the planned DWE measurements, were thus lost.
The channel A signal was monitored on Earth during the Huygens mission at fifteen radio telescopes, six of which recorded ground- based DWE measurements of the carrier frequency. Details on the participants in the radio astronomy segment of the Huygens mission, the observation campaign, and plots of the raw data are given in Supplementary Information. Only the data sets from the NRAO Robert C. Byrd Green Bank Telescope (GBT) in West Virginia and the CSIRO Parkes Radio Telescope in Australia have been processed for this initial report.
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ResultsThe zonal wind derived from the ground-based Doppler data is shown in Fig. 1 as a function of time. More precisely, this quantity is the horizontal eastward velocity of Huygens with respect to the surface of Titan (with a positive value indicating the prograde direction). The time-integrated wind measurement from t0 yields an estimate for the longitude of the Huygens landing site on Titan, 192.33 0.318 W, which corresponds to an eastward drift of 3.75 0.068 (165.8 2.7 km) over the duration of the descent. Unfortunately, because of the slow rotation of Titan and the fact that the Earth was near zenith as viewed by Huygens, the Doppler data recorded after landing are not considered suitable for a more precise determination of the Huygens longitude.
The variation of the zonal wind with altitude and pressure level is shown in Fig. 2. The measured profile roughly agrees with the upper level wind speeds anticipated by the engineering model, and is generally prograde above 14 km altitude. Assuming this local observation is representative of conditions at this latitude, the large prograde wind speed measured between 45 and 70 km altitude and above 85km is much larger than Titan’s equatorial rotation speed (Qa < 11.74 m s21, where Q 1⁄4 4.56 £ 1026 rad s21 and a 1⁄4 2,575 km are Titan’s rotation rate and radius, respectively), and thus represents the first in situ confirmation of the inferred superrotation of the atmosphere at these levels, as anticipated from the Voyager temperature data3. Moreover, the measured winds are consistent with the strong winds inferred from ground-based data under the assumption of cyclostrophic balance
Sura, P.,Perron, M. (2010). Extreme Events and the General Circulation: Observations and Stochastic Model Dynamics. Journal Of The Atmospheric Sciences, 67(9), 2785–2804. doi:10.1175/2010JAS3369.1
AbstractThis study explores the dynamical role of non-Gaussian potential vorticity variability (extreme events) in the zonally averaged circulation of the atmosphere within a stochastic framework. First the zonally averaged skewness and kurtosis patterns of relative and potential vorticity anomalies from NCEP–NCAR reanalysis data are presented. In the troposphere, midlatitude regions of near-zero skewness coincide with regions of maximum variability. Equatorward of the Northern Hemisphere storm track positive relative/potential vorticity skewness is observed. Poleward of the same storm track the vorticity skewness is negative. In the Southern Hemisphere the relation is reversed, resulting in negative relative/potential vorticity skewness equatorward, and positive skewness poleward of the storm track. The dynamical role of extreme events in the zonally averaged general circulation is then explored in terms of the potential enstrophy budget by linking eddy enstrophy fluxes to a stochastic representation of non-Gaussian potential vorticity anomalies. The stochastic model assumes that potential vorticity anomalies are advected by a random velocity field. The assumption of stochastic advection allows for a closed expression of the meridional enstrophy flux: the potential enstrophy flux is proportional to the potential vorticity skewness. There is some evidence of this relationship in the observations. That is, potential enstrophy fluxes might be linked to non-Gaussian potential vorticity variability. Thus, extreme events may presumably play an important role in the potential enstrophy budget and the related general circulation of the atmosphere.
Introduction
The empirical and dynamical study of the general circulation of the atmosphere can be rightfully considered to provide the foundations of modern meteorology, climatology, and related fields. In its broadest sense the atmospheric general circulation may be regarded to encompass all motions that are needed to characterize the large and global-scale atmospheric flow (e.g., Holton 1992; James 1994; Vallis 2006). The time-mean circulation is the most relevant, first-order property we are interested in (zeroth order being a resting atmosphere). It is, of course, well known that the mean atmospheric circulation cannot be understood without knowing some statistics of fluctuations (eddies) around the mean. The mean and fluctuations of the general circulation are intricately linked through eddy fluxes of primarily heat, momentum, and vorticity (or enstrophy). The zonal eddy flux of temperature, for example, is the dominating mechanism redistributing heat from the tropics to the poles. In other words, to dynamically describe the mean circulation we need to know some second-order statistics (variances, correlations) of relevant quantities. For example, the zonally averaged poleward eddy flux by transient waves is given by the covariance [y9T9], where y9 and T9 denote transient fluctuations of meridional velocity and temperature, respectively; [x9] denotes the zonal and x9 the temporal averages of the quantity x9.
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Sura and Sardeshmukh (2008) and Sardeshmukh and Sura (2009) tried to fill this gap by analyzing local non-Gaussian oceanic and atmospheric variability in a stochastic–dynamical framework. Their theory attributes extreme anomalies to stochastically forced linear dynamics, where the strength of the stochastic forcing depends on the flow itself (multiplicative noise). Because stochastic theory makes clear and testable predictions about non-Gaussian variability, the multiplicative noise hypothesis can be verified by analyzing the detailed non-Gaussian statistics of oceanic and atmospheric variability. In fact, Sura and Sardeshmukh (2008) and Sardeshmukh and Sura (2009) did just that for sea surface temperature and atmospheric geopotential height and vorticity anomalies, thereby confirming the multiplicative noise hypothesis of extreme events for the respective variables.
This paper studies the role of higher-order (non-Gaussian) statistics in the dynamics of the general circulation. Section 2 discusses the non-Gaussianity of the atmospheric general circulation using daily National Centers for Environmental Prediction (NCEP)–National Center for Atmospheric Research (NCAR) reanalysis data, focusing on zonally averaged relative and potential vorticity (PV) statistics. In section 3 we discuss the zonally averaged circulation in terms of the potential enstrophy budget. In particular, we elucidate the dynamical role of extreme atmospheric events in the zonally averaged general circulation by linking eddy enstrophy fluxes to a stochastic representation of potential vorticity anomalies. Finally, section 4 provides a summary and discussion.
Observations
In this section we will present non-Gaussian attributes of the atmospheric general circulation from daily NCEP– NCAR reanalysis data. Because most of the previous studies focused on the horizontal distribution of extreme events and higher-order statistics (skewness and kurtosis), we will pay particular attention to the height dependence of non-Gaussian statistics. That is, here the focus will be on the zonally averaged non-Gaussian statistics of the general circulation.
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We use the full 60-yr record because the reliable estimation of higher-order statistics needs rather long time series to reduce the standard errors as much as possible. However, it is known that the reanalysis data are not very reliable in the Northern Hemisphere before 1958 or before the mainstream meteorological satellite era (1979) in the Southern Hemisphere (Kistler et al. 2001). Thus, the reanalyses more reflect the model than the actual atmosphere in the mentioned periods and regions. Given that today’s models are very reliable on synoptic and large scales, and we are primarily looking at the statistics of large-scale flows, we are not expecting major biases in the troposphere by using the full record. In the troposphere we might observe biases, however. To make sure that our findings are stable, we will later also present the main results of our analysis for the periods 1958–2007 and 1979–2007.
Grant van Riessen et al 2010 J. Phys.: Condens. Matter 22 092201 doi: 10.1088/0953-8984/22/9/092201
AbstractWe have measured the correlated electron pair emission from a Cu(001) surface by both direct and core-resonant channels upon excitation with linearly polarized photons of energy far above the 3p threshold. As expected for a single-step process mediated by electron correlation in the initial and final states, the two electrons emitted by the direct channel continuously share the sum of the energy available to them. The core-resonant channel is often considered in terms of successive and independent steps of photoexcitation and Auger decay. However, electron pairs emitted by the core-resonant channel also share their energy continuously to jointly conserve the energy of the complete process. By detecting the electron pairs in parallel over a wide range of energy, evidence of the core-resonant double photoemission proceeding by a coherent single-step process is most strikingly manifested by a continuum of correlated electron pairs with a sum energy characteristic of the process but for which the individual electrons have arbitrary energies and cannot meaningfully be distinguished as electron.
IntroductionThe emission of two electrons from a solid surface upon the absorption of a single photon has become of much current interest due to the decisive role played by electron–electron correlation in such processes. Because of the single-particle nature of the dipole interaction, the electric field of the photon directly interacts with only a single electron. However, if the photon energy exceeds the double photoemission (DPE) threshold, two interacting electrons may be directly emitted from the valence band, sharing the photon energy in excess of that needed to eject both of them [1]. Detecting the emitted pair in coincidence with energy and momentum discrimination yields observables relevant to the electron–electron interaction in the solid [1–7]. When the energy of the incident photon exceeds the binding energy of a core-level electron, the electron is excited to the continuum above the vacuum level. A second electron may be excited to the continuum by an Auger (autoionization) transition in which the core–hole is annihilated, leaving two holes in the valence band. Auger photoelectron coincidence spectroscopy (APECS) has been developed to study this process, motivated also by the ability to yield information not directly accessible by single-electron spectroscopy [8–16]. (略)
Experimental detailsA new two-electron coincidence spectrometer for surfaces was implemented by combining two hemispherical energy analysers (Scienta R4000, Sweden) with wide-angle transfer lenses. The analysers were modified by the installation of two-dimensional detectors (microchannel plates (MCP) and resistive anodes) and the lenses are operated in customized modes optimized for the requirements of high transmission with large pass energy, low mean kinetic energy and small temporal dispersion. Angular dispersion characteristics are compromised to achieve these requirements and only energy information was recorded. Constant energy resolution can be preserved independently of the electron kinetic energy, which allows DPE experiments to be extended to photon energies previously inaccessible with time-of-flight spectrometers which presently cannot achieve comparable energy resolution beyond energies 50 eV [2, 6].
The spectrometer was installed at the UE56/2-PGM-2 beamline at the BESSY II storage ring [19]. Figure 1 schematically illustrates the geometry of the experiment. Linearly polarized radiation of energy 125 eV was incident upon a Cu(001) surface at a grazing angle of 10◦. Electrons emitted within the solid angle of collection of the lenses are transported to hemispherical analysers that energetically disperse the electrons onto the detectors. The optical axes of the lenses define the scattering plane and are separated by 90◦ with one axis in the plane of the storage ring and the other perpendicular to it. The sample was oriented such that the mean take-off angles for the horizontal and vertical analyser with respect to the surface normal were 15◦ and 75◦, respectively.
Each analyser was operated in a mode that allowed the collection of electrons within an angular range of ≈30◦ within the xy plane (figure 1) and, simultaneously, within a 30 eV energy range centred at 50 eV. The energy range recorded in parallel by each analyser is partitioned respectively into discrete values E1 and E2 for the vertical and horizontal analysers in order to represent two-dimensional (2D) electron pair energy distributions. The total energy resolution for each analyser was ≈0.8 eV. Consequently the total energy resolution for electron pairs was ≈1.1 eV. All kinetic energies were measured with respect to the vacuum level of the Cu(001) surface. (略)
Experimental resultsFigure 2(a) shows a histogram of arrival time differences t for all detected pairs from a Cu(001) surface upon excitation with linearly polarized photons of energy 125 eV. The area of the prominent peak (shaded) at t = 0 ns that lies above the flat background is a measure of the total number of true coincidences. Its width tc is consistent with an estimation of the temporal resolution by simulating the dominant contribution of time dispersion through the electron optics. The number of correlated events (true coincidences) Nt is found from the total number of counts within a region of width tc centred on the peak minus the number of random coincidence events in the same area which is estimated from the average intensity away from the peak.
The 2D energy distribution of correlated electron pairs (true coincidences) detected from the Cu(001) surface upon excitation with 125 eV photons is presented in figure 2(b). This data is obtained by determining the number of true coincidences at each locus (E1, E2) by the method described above. Several distinctive spectral features appear that have not previously been observed together in a single spectrum from a solid surface. The highest energy structure is related to the onset of direct DPE. Below that there are three regions of interest labelled as A, B and C which are situated around (E1,E2) = (56 eV,46 eV), (46 eV, 56 eV) and (46 eV, 58 eV), respectively. These regions correspond to the nominal energy of 3p photoelectrons and M2,3–M45M45 Auger electron pairs, i.e. the process studied by APECS. Their structure in and between these regions is considered in more detail below. The difference in the sum energy of the detected pairs emitted by these processes will be discussed elsewhere. (略)
ConclusionsWe have presented the two-particle emission spectra from a Cu(001) surface upon excitation with linearly polarized photons with sufficiently high energy to excite the 3p core level. We observe both direct DPE and core-resonant DPE in the same spectrum. The final state of both processes contain two holes in the d-band but is distinguished on the basis of the total energy available to the pair. In the energy sharing distribution of electron pairs, the direct DPE manifests as a continuum without discrete structure. Pairs emitted by core-resonant double photoemission are also clearly shown to share their total energy continuously while jointly conserving the energy of the complete process. The energy of both electrons is not constrained to the energy they are observed to have when detected independently. These results confirm that core-resonant double photoemission must be described by a coherent single-step process in which the emitted electrons represent a correlated two-particle state. Detailed comparison of the dynamics of direct double photoemission and core- resonant double photoemission is currently being investigated for different scattering geometries and photon energies and is expected to yield further insight into the role of correlation in these processes.
実際の論文を見てみると、参考文献で述べられているように「先行研究 = 現在形」「自分の今の研究 = 過去形」という関係は、自分の周辺分野(大気力学)では成り立っていないようである。
そこで、be動詞 を抽出し be動詞全体に対する現在形(is, are)、 過去形(was, were)と完了形(been)の比率を調べてみた。
まず、数値実験と理論の論文
・Vallis, G. K. and Farneti, R. 2009. Meridional Energy Transport in the Atmosphere-Ocean System. Scaling and Numerical Experiments. Quart. J. Roy. Meteor. Soc., 135, 1643-1660, doi:10.1002/qj.498
では
現在形: 97%、過去形: 3%、完了形: 0%
で現在形が大半を占める。
次に、室内実験の論文
・Thomas, P.J.Linden, P.F. 2010 Laboratory modelling of the effects of temporal changes of estuarine-fresh-water discharge rates on the propagation speed of oceanographic coastal currents. J. Fluid Mech., 664, 337-347
では
現在形: 58%、過去形: 40%、完了形: 2%
で過去形が4割を占める。
そして、化学実験の論文
・Synthesis of Heterocyclic Homotriptycenes. (2011). Synthesis of Heterocyclic Homotriptycenes, 76(14), 5531–5538. doi:10.1021/jo200110w
では
現在形: 24%、過去形: 72%、完了形: 4%
で過去形は7割を占める。
ここには記さないが、同様の手法の他の論文もおおよそ、同じような割合で現在形と過去形が使用されている。
結局、自分の周辺分野 (大気力学・地球流体力学) では、多くの参考書で挙げられている、時制の区別 「先行研究 = 認められた一般的な知識 = 現在形」「自分の今の研究 = まだ認められていない知識 = 過去形」 にそっていないようだ。
自分の今の研究も現在形で書くかどうかは、おそらく、「再現性が自明かどうか」によるのではなかろうか。
たとえば、「紙と鉛筆」でおえるような、数学の論文は、現在形で書かれてて不自然ではない。逆に、 “Adding 1 to 2, we obtained 3” なんて書いたら、「(一般にはどうか分からないが) そのときは２に１を足したら3を得た。」という文意になってしまう。
数学の論文と同様に、主に数学を用いて記述される力学などの理論も、 現在形が相応しいように思う。
一方、実験室で行うような、(実在するものを用いて行う)実験結果に関する論文は、 自分の実験結果が、再現性を有しているかが自明ではないので、 「(少なくとも自分がやったら、そのときは)こうなった。」という意味で、過去形が相応しいように思う。 これは、化学実験や実験流体を用いた室内実験などは、著者が全く気づいていない未知のファクター によって結果が変わる、という可能性があるからだろう。
同様に、自然現象の観測結果に関する記述をする際も、「自分が観測したときは、そうだった。」 という意味で過去形が適切だろう。
しかし、JRA-25のように公開されている、再解析データセットを利用した「データ解析」の場合は、 同じデータを用いれば、同じ結果が得られるのは自明なので、現在形なのだろう。 (逆にそのような研究は、そのデータセットに関する研究であることを意識する必要がある。)
では、数値実験がどうか。数値実験の場合、自分で制御できないファクターは普通ないので、 (計算機のソフト・ハードに未知のバグはないという前提で) 計算方法、設定条件の説明を尽くせば、数値実験の結果は「再現性が保証されている」ような気がする。
なら、数値実験に関する計算方法や設定条件の説明は現在形か？過去形か？ いろいろと論文を見て回ると、現在形が多いように感じる。 でも過去形や現在完了形で書かれている論文もある。