On deep mean flow generation mechanisms and the abyssal circulation of numerical model gyres

Mesoscale resolution ocean general circulation model (EGCM) experiments have been carried out under a variety of different model physical assumptions, and the different model systems often produce very different deep mean flow fields. The flat bottom, rectangular basin experiments exhibit two distinct types of deep mean flow, which are here called “corotating” and “counterrotating”. Counterrotating deep flow, in which two adjacent deep gyres, with circulation of opposite senses, underlie the upper ocean eastward jet and its recirculation, has been found only in models with adiabetic two-layer model physics. None of the more complex model systems exhibit counterrotating deep flows; this type of flow is apparently restricted to a particular range of forcing/dissipation parameter space and/or particular model physical assumptions.Since the deep flow in these EGCM systems is generally weak, geostrophic dynamics provides the basic deep flow interior balance and the mean vertical velocity field, through the lower layer vorticity equation, largely determines the deep interior flow. The dynamical constraints on the mean vertical velocity field introduced by different model physical equations are reviewed and the adiabatic quasi-geostrophic (QG) two-layer model system is shown to be strongly constrained in several respects. In particular, the idea that eddy and mean heat flux divergence (or “layer thickness flux divergence”) drive the mean vertical velocity does not generalize to more complicated dynamical systems in which there is the possibility of altering the mean vertical density profile and/or in which the horizontal flow can be divergent. As a consequence of the constraints, there can be no basin net vorticity input to the lower layer via vortex stretching in the QG system.Because of the adiabatic QG constraints and the particular parametric regime in which the published adiabatic QG EGCM experiments exist, a very plausible explanation can be found for the existence of the deep cyclonic circulation of the model subtropical gyre. It is this cyclonic circulation that causes these deep flows to differ so dramatically from those of the more physically complex model systems. Because all the published adiabatic QG experiments that have non-trivial deep flows exhibit the counterrotating behavior, and because available ocean data do not support the existence of such a gyre in the North Atlantic, it seems important to thoroughly understand the reasons for the existence or absence of the deep cyclonic circulations. If they are an invitable feature of adiabatic QG systems, these models may need to be treated with caution as tools for understanding the mean ocean circulation.     

二维波状地形上的流场

在一个简化的二层模式中，求解大气波动方程，得到了二维波状起伏地形上扰动流线的分析解。研究了在上、下两层大气中，不同的温度廓线和风速廓线情况下，地形引起扰动的流场形式，同时讨论了支配扰动振幅的大气因子和地形特征。分析解的结果表明:若大气低层为深厚的不稳定层，地形引起的波动很微弱;如低层大气强稳定，上层大气弱稳定，则可能产生较强的波动;而当上层稳定度增加时，可产生非陷波，有利于高层动量下传，造成较大的地面风速。     

大气中孤立波的相互作用

本文讨论无限深上层流体和有限深下层流体的两层流体系统，该系统是大气的一种近似模型。采用拉格朗日坐标系，从无粘不可压流体力学方程式出发，利用摄动方法获得了所讨论系统中界面孤立波迎撞的摄动解。结果表明，在迎撞前后每个波独立地由Benjamin-Ono方程所描述，即波的形状不发生变化，迎撞的效应由相移来体现。     

Dissipative effects on inertial flows over a sill

A systematic investigation of the effects of various parametrizations of dissipation, e.g. quadratic and linear frictional drag, harmonic lateral viscosity, and harmonic lateral diffusion on inertial flow over a sill and possible hydraulic control is presented. Rotation effects are ignored and the geometry is assumed to vary only slowly with downstream distance so that the flow may be considered one-dimensional. Results are given both for a single-active layer and for two-active layers with a rigid lid.If the parametrization is only a function of the dependent variables and not of their spatial derivatives, then it may be possible to hydraulically control the flow. A general expression is derived for the possible control point and the two gradients there, which are functions of the slope and possibly of flow rate. Specific energy is irreversibly removed from the flow and non-controlled as well as controlled flows can exhibit significant asymmetry in fluid depth over a sill. The upstream specific energy, and hence depth of the lower layer, of the controlled flow is greater than for an ideal fluid. Frictional effects modify the behaviour of long gravity waves, such that they are dispersive and damped with time. The system will only exhibit hydraulic control if these effects are small.For a viscous single layer of fluid, the gradient in surface elevation is always uniquely defined, so classically defined hydraulic control, as such, cannot exist. However, for values of non-dimensional lateral eddy viscosity coefficient, , where q is the flow rate, there is a narrow band of specific energies centred around that for the control solution in an ideal fluid, E_crit, for which the surface elevation, h is very asymmetric over the sill; the solutions resemble the inviscid, hydraulically controlled solutions. Outside this range, either the fluid depth tends to zero, or the surface elevation is almost uniform over the sill. A ‘control’-type solution exists which has the conjugate values of the inviscid equation up- and downstream of the sill, where the gradient in fluid depth, and hence the viscous term, is zero. For larger values of A_M, the band of specific energies is much wider, and the upstream specific energy of the ‘control’-type solution is much lower than that for an inviscid fluid. Long gravity waves are dispersive and damped with time. There is a short-wave cut-off, k² > h/(4A_M²), above which waves are stationary in the flow. Longer waves, k² h/(4A_M²), are critical if , as for an ideal fluid. If these waves can propagate significant distances, then any observed asymmetry in h will be due to inertial and not to viscous effects. The behaviour of unidirectional, two-layer flow is similar. The governing equation for viscous, two-layer exchange flow is singular, and typically excludes the ‘control’-type solutions found for unidirectional flows.Establishing the existence and behaviour of steady inertial flows in the presence of lateral diffusion between layers is more difficult. It significantly alters the single-layer solutions once the non-dimensional coefficient A_H is large, i.e. . The flow rate may become zero on the downslope as all the fluid diffuses into the inert, infinitely deep, overlaying layer. The fluid depth is maintained by reverse flow from downstream. In this case, the depth of the active layer tends to zero downstream for all values of specific energy. For two-layer flow, both unidirectional and exchange, the governing equation is such that the lower-layer flow rate and interfacial height return to their upstream values.Motivation for the study is provided by the increasingly fine spatial resolution achievable in large-scale numerical models of the ocean general circulation, and the question of whether they are capable of simulating some form of hydraulic control. Application to modelling oceanic flows over a sill is discussed.     

包含超梯度力作用的台风次级环流诊断方程

次级环流在台风的发展和维持中起着重要作用,基于梯度风平衡的Sawyer Eliassen（SE）方程常用于台风次级环流的诊断。然而梯度风平衡关系在台风边界层及边界附近有较大误差,这导致SE方程求解出的次级环流在边界层也会有较大误差。本文在梯度风平衡方程中保留包含径向摩擦力项在内的超梯度力项,得到包含超梯度力作用的SE方程,从方程形式上看超梯度力主要是通过调节与斜压性相关的系数来影响次级环流的。对“森拉克”（2008）台风次级环流的诊断结果显示,在不人为改变边界层流场结构的情况下,新的SE方程能显著改善次级环流的求解效果,避免眼墙外侧边界层附近的虚假对流并且减小虚假入流。     

A model of atmospheric boundary-layer flow above an isolated two-dimensional ‘hill’; an example of flow above ‘gentle topography’

A numerical model is developed for two-dimensional turbulent boundary-layer flow above gentle topography — defined as not giving rise to mean flow separation. Although the model is formulated in a framework of mixing length and turbulent energy equation models for the surface layer of the atmospheric boundary layer, it could be modified to include higher-order closure hypotheses and/or extended to model gentle topography for the planetary boundary layer or on the sea bed. Results are presented for flow above a specific shape of hill and the effects of surface roughness and hill height are investigated.     

Wind-Tunnel Simulation of Weakly and Moderately Stable Atmospheric Boundary Layers

The simulation of horizontally homogeneous boundary layers that have characteristics of weakly and moderately stable atmospheric flow is investigated, where the well-established wind engineering practice of using ‘flow generators’ to provide a deep boundary layer is employed. Primary attention is given to the flow above the surface layer, in the absence of an overlying inversion, as assessed from first- and second-order moments of velocity and temperature. A uniform inlet temperature profile ahead of a deep layer, allowing initially neutral flow, results in the upper part of the boundary layer remaining neutral. A non-uniform inlet temperature profile is required but needs careful specification if odd characteristics are to be avoided, attributed to long-lasting effects inherent of stability, and to a reduced level of turbulent mixing. The first part of the wind-tunnel floor must not be cooled if turbulence quantities are to vary smoothly with height. Closely horizontally homogeneous flow is demonstrated, where profiles are comparable or closely comparable with atmospheric data in terms of local similarity and functions of normalized height. The ratio of boundary-layer height to surface Obukhov length, and the surface heat flux, are functions of the bulk Richardson number, independent of horizontal homogeneity. Surface heat flux rises to a maximum and then decreases.     

多层土壤温度模拟及其检验

对陆面过程模式(BATS)土壤温度模拟进行了改进,提出了一个利用气象站资料模拟土壤温度的模式。研究结果表明：采用热扩散方程模拟多层土壤温度,可与观测站的资料直接比较;模式能很好地模拟各层土壤温度的年变化、季变化、日变化。冬季下层土壤温度高于上层土壤温度,夏季上层土壤温度高于下层土壤温度,上下层温度的转换时间大约在3月份和10月份,这与实测土壤温度的年变化非常一致;模式较准确地模拟了各层土壤温度垂直方向变化的时滞效应。     

Principles for capturing the upstream effects of deep sills in low resolution ocean models

Principles for incorporating the upstream effects of deep sills into numerical ocean circulation models using nonlinear analytical hydraulic models are discussed within the context of reduced gravity flow. A method is developed allowing the upstream influence of a numerically unresolvable deep sill or width contraction to be reproduced. The method consists of placing an artificial boundary in the numerical model's overflowing layer at some distance upstream of the actual sill or width contraction of the deep strait. Given the model state at time t, the dependent flow variables are then predicted at the artificial boundary at time t + Δt by using the method of characteristics in combination with quasi-steady hydraulic laws. The calculation requires the use of Riemann invariants and examples are given for a simple nonrotating flow and for rotating channel flow with uniform potential vorticity. The computation is considerably simplified by linearizing the relevant equations in the vicinity of the artificial boundary, resulting in a linear wave reflection problem. The reflection coefficients for the two cases are calculated and these can be used directly to numerically satisfy the boundary condition in a straightforward way.     

Applied model for the growth of the daytime mixed layer

A slab model is proposed for developing the height of the mixed layer capped by stable air aloft. The model equations are closed by relating the consumption of energy (potential and kinetic) at the top of the mixed layer to the production of convective and mechanical turbulent kinetic energy within the mixed layer. By assuming that the temperature difference at the top of the mixed layer instantaneously adjusts to the actual meteorological conditions without regard to the initial temperature difference that prevailed, the model is reduced to a single differential equation which easily can be solved numerically. When the mixed layer is shallow or the atmosphere nearly neutrally stratified, the growth is controlled mainly by mechanical turbulence. When the layer is deep, its growth is controlled mainly by convective turbulence. The model is applied on a data set of the evolution of the height of the mixed layer in the morning hours, when both mechanical and convective turbulence contribute to the growth process. Realistic mixed-layer developments are obtained.     

Towards closing the vertical water balance in Canadian atmospheric models: Coupling of the land surface scheme class with the distributed hydrological model watflood

Abstract

Second generation land surface schemes are the subject of much development activity among atmospheric modellers. This work is aimed at, among other things, improving the representation of the soil water balance in order to simulate, more properly, exchanges with the atmosphere and to permit the use of model output to generate streamflow for model validation. The Canadian development program is centred on CLASS, the Canadian Land Surface Scheme, developed at Environment Canada. This paper focuses on the improvement of hydrology in CLASS. This was accomplished by designing a two‐way interface to WATFLOOD, a distributed hydrologic model developed at the University of Waterloo. The two models share many features, which facilitated the coupling procedure.

The interface retains the three‐layer vertical moisture budget representation in CLASS but adds three horizontal runoff possibilities. Runoff from the surface water follows Manning's equation for overland flow. Interflow is generated from the near‐surface soil layer using a parametrization of Richard's equation and base flow is produced by Darcian flow from the bottom of layer 3. An approximation of the internal topography of grid elements is used to supply horizontal gradients for the runoff components.

Tests are in progress in four Canadian study areas. Initial results are presented for the summer of 1993 for the Saugeen River in southwestern Ontario. The new scheme produces realistic hydrographs, whereas the old scheme did not. Bare ground evaporation is reduced by about 17% as a consequence of reduced water availability in layer 1. Evapotranspiration is not affected because the rooting depth extends into layer 3, in which soil moisture does not change appreciably with the new scheme. These results suggest that the new scheme improves the representation of streamflow in WATFLOOD/CLASS and of the soil moisture budget in CLASS. Work is in progress to validate this result over basins, such as the BOREAS study watersheds, where both runoff and evapotranspiration measurements are available.     

Turbulent dispersion of pollutant over complex terrain

A two-dimensional turbulent diffusion equation is derived in a streamline coordinate system, defined for rotational flow over complex terrain and limited aloft by an elevated, impenetrable inversion. In the first instance, the steady-state equation is solved for an inner region of the boundary layer, in which the effect of curvature is negligible and, for simplicity, it is assumed that vorticity has a power-law dependence upon stream function. A variational method of solution is also discussed, in which vorticity may have a more general representation. A numerical calculation is performed for a special case of symmetrical flow over an isolated hill. The dependence of pollutant concentration upon the flow field, downwind distance and source is examined and the effect of wind acceleration in the neighbourhood of the top of the hill is discussed. It is pointed out that the diffusion model can be applied to any realistic flow field, provided that the streamlines are specified.     

Chanchu台风(0601)精细结构中的熵流特征分析

在耗散结构理论的基础上,根据热力学第二定律推导出了熵平衡方程。利用高分辨率模式输出资料通过对比Chanchu台风(0601)螺旋雨带上游、中游和下游及眼壁附近不同区域对流单体和熵流分布情况,揭示出负熵流值与台风的强对流单体有密切联系。基于负熵流与台风精细结构的配置分析,研究中尺度范围内熵流随Chanchu台风发生、发展、消亡各阶段的演变特征。分析表明,对流单体在从雨带上游至下游的演变过程中,熵流分布特征也会发生相应的变化,强对流单体与负熵流大值区相对应;当对流单体减弱,负熵流也随之减弱;当单体最后合并并汇入眼墙时,负熵流彼此合并旋入眼墙,有助于眼墙中深厚对流的维持和发展;此外,负熵流对于Chanchu台风在各发展阶段的强度变化也有一定的指示意义,揭示了负熵流对大气系统的组织化作用。      

甘肃省倒槽暴雨的个例分析

1976年8月2日,甘肃省中部地区发生了一次暴雨。在热带东风带中,当西移的倒槽和高原北部东移的低涡相结合时,就会使倒槽强烈发展并伸入内陆。倒槽东侧深厚的东南气流,造成该区深厚的位势不稳定,并使水汽输入到西北区东部,它与冷锋后部的西北气流相遇后,产生大范围水汽通量的辐合,这是本次暴雨的大尺度条件。 次天气尺度的低涡是产生这次暴雨的直接影响系统。当对流层上部的扰动与低层扰动上下叠置,形成一个深厚的次天气尺度低涡时,易产生对流性暴雨。 次天气尺度的低涡,是雨团迅猛加强的背景,南移的低层切变线起触发作用,而该地早先存在的一个暖湿的地方性中低压,则是合适的局地环境场。当低层切变线移入此中低压时,往往造成中尺度雨团的合併,出现急骤加强,形成暴雨。     

A Three-Dimensional Correlation/Spectral Model for Turbulent Velocities in a Convective Boundary Layer

A three-dimensional model for correlation functions and spectra in theatmospheric, convective boundary layer (CBL) is presented. The modelincludes vertical inhomogeneities introduced by eddy-blocking at the ground.By assuming the disturbance to the turbulent flow resulting from the groundblocking is irrotational, an equation is developed which allows one to writethe inhomogeneous, two-dimensional (2D) cross spectra for the blocked flowin terms of the 2D cross spectra for a homogeneous flow. VonKármán's energy spectrum then is used to determine thehomogeneous, 2D cross spectra. Although there are only two adjustableparameters in the model, the variance and a length scale, the model is shownto agree quite well with a diversity of previous results for the CBL.     

A study of hurricane dynamics using a two-fluid axisymmetric model

Summary A model of a frictionless rotating axisymmetric flow in an incompressible fluid is extended to the spun-up flow in the lower of two incompressible fluids, the upper fluid remaining at rest. It is shown that a steady state can be maintained only if the upper fluid extends to the surface in an inner core (the eye), the surface radius of which is determined by the strength of the tangential flow, as is the configuration of the eye wall. A secondary (meridional) circulation may also be present provided that the tangential flow has its maximum strength at middle levels.In order to relate this idealised model of a mature hurricane to the physical processes involved in its evolution, the eye wall, treated as a flow separation discontinuity in the idealised case, is considered as a transition zone between the fluids. The physical processes involved in the creation of this zone from a pre-existing ring of deep moist convection are proposed. Finally, the dynamics of the inflow layer, taking account of momentum transfer by small-scale eddies, is considered using a boundary layer model based on a modification of the classical Ekman-Taylor spiral.With 7 Figures     

A comparison of parameterized vs. measured transilient mixing coefficients for a convective mixed layer

The parameterization for transilient turbulence coefficients suggested by Stull and Driedonks (SD. 1987) is tested against the large-eddy simulations (LES) of Ebert et al. (ESS, 1989) for the special case of an idealized convective boundary layer. The SD parameterization is based on a nonlocal approximation to the turbulence kinetic energy (TKE) equation, and requires turbulent exchange (i.e., the matrix of transilient mixing coefficients is assumed to be symmetric) and dominance of the smaller eddies (i.e., elements closer to the main diagonal of the matrix are greater). Measurements from the LES model, however, show that the transilient matrix is asymmetric in convective situations, with larger eddies dominating.Mean-state conditions such as the deep convective mixing and mixed-layer growth are satisfactorily described by the parameterization, but the surface layer is too deep and the entrainment zone thickness is poorly defined. Turbulence properties such as skewed vertical velocity distributions are not possible within the constraint of a symmetric matrix, and partial convective overturning is also not possible because of the restriction that small eddies dominate. Future improved parametcrizations might continue to be based on the TKE equation, but should allow transilient matrix asymmetry.Research was performed while the author worked at the Institute of Atmospheric Physics, German Aerospace Research Establishment (DLR), D-8031 Weling. Germany.     

Influence of canyon-induced flows on flow and dispersion over adjacent plains

Summary The study investigates two effects that a valley or canyon opening onto a plain can have on flow and contaminant dispersion over the downwind plain. The first effect is the channeling of strong ambient flow by the canyon when the wind is nearly aligned with the canyon axis. Two cases showed that these conditions produced a region of focused flow downwind of the canyon mouth. The second effect is the formation of canyon exit jets on nights with weaker ambient flow. In two case studies under these conditions strong exit jets formed that were several hundred meters deep. The jets remained narrow and strong at least 10 km onto the plains, and in one of the cases the jet extended more than 20 km over the plains. These deep jets only lasted 2–3 h, and they had a small but significant effect on surface-released tracer transport as indicated by surface sampling. We hypothesize that the near-surface advection of tracer was accomplished by a thin katabatic layer of flow, and that an elevated release or elevated sampling would have indicated a greater effect of the exit jet on tracer transport.With 18 Figures     

The subcloud-layer eddy kinetic energy budget of a microburst-producing thunderstorm determined from jaws dual-Doppler measurements

Dual-Doppler data collected from 1646 to 1648 MDT on 14 July, 1982 in Colorado were employed to study the eddy kinetic energy budget in the subcloud layer of a microburst-producing thunderstorm during its mature stage. Each term in the budget equation was computed from the Doppler-derived winds and retrieved thermodynamic fields within the 10 by 10 km horizontal domain. Results show that in the atmospheric boundary layer (ABL) where the microburst dominates, the turbulent flow extracts energy from the mean flow in order for the microburst to maintain its strong diverging outflow at low levels. The vertical transport of eddy kinetic energy is predominantly downward in the low layer due to the organized downdrafts in the microburst area. The horizontal flux convergence (divergence) of eddy kinetic energy by the mean and eddying motions is approximately balanced by that of the vertical flux divergence (convergence). Similarly, the contributions from the pressure and buoyancy production terms are nearly in balance. As a result, a net change of the eddy kinetic energy generation in the subcloud layer is relatively small in comparison with the individual term in the budget equation.     

Structures of dynamically unstable shear flows and their implications for shallow internal gravity waves

Summary In this study, the response of a dynamically unstable shear flow with a critical level to periodic forcing is presented. An energy argument is proposed to explain the upshear tilt of updrafts associated with disturbances in two-dimensional stably stratified flows. In a dynamically unstable flow, the energy equation requires an upshear tilt of the perturbation streamfunction and vertical velocity whereU _z is positive. A stability model is constructed using an iteration method. An upshear tilt of the vertical velocity and the streamfunction fields is evident in a dynamically unstable flow, which is required by energy conversion from the basic shear to the growing perturbation wave energy according to the energy argument. The momentum flux profile indicates that the basic flow is decreased (increased) above (below) the critical level. Thus, the shear instability tends to smooth the shear layer. Following the energy argument, a downshear tilt of the updraft is produced in an unstably stratified flow since the perturbation wave energy is negative. The wave energy budget indicates that the disturbance is caused by a thermal instability modified by a shear flow since the potential energy grows faster than the kinetic energy.With 4 Figures