一次暴风雪过程中的中尺度重力波特征及其影响

应用地面自动气象站观测资料、数字化多普勒天气雷达探测资料和WRFV2.2.1中尺度数值模拟资料,分析了中尺度重力波与基本气流的相互作用,以及重力波活动对暴雪和大风天气的重要影响。结果表明,在波导中传播的中尺度重力波能够与基本气流进行动量交换,使得对流层中上层4.5—8 km气层内的水平平均风速趋于均匀,形成斜穿整个对流层的饱和湿空气急流,即"湿急流"。在高空急流出口区激发的垂直向下传播的重力波,使基本气流的水平风速在垂直方向上出现了加速和减速的交替变化,水平风加速的气层,反射率增大;水平风减速的气层,反射率减小。随着波动下传及其随基本气流的移动,反射率回波强度沿高空风的方向(由西南向东北)出现周期性变化,回波带呈西北—东南走向,强回波中心之间为宽约40 km的弱回波区。重力波下传期间,当地面气压迅速下降时,东北风快速增长,风向有明显的改变,反射率强度开始减弱;气压脊线过后,反射率降低到最低点。地面大风中心出现在反射率回波强度周期性变化的地带,沿西南—东北方向间隔着分布。雷达探测表明,对流层低层风速在风向切变层上下边界对称相等,因此推测在重力波与切变层汇合的高度层存在垂直环流,由风切变层上下边界附近的西南气流和东北气流与受重力波影响形成的垂直方向上的上升和下沉气流共同组成。切变层上方的动量通过垂直环流的下沉支到达地面,强风中心对应着下沉气流,出现在降水回波开始减弱之际。     

Properties and stability of a meso-scale line-form disturbance

By using the 3D dynamic equations for small- and meso-scale disturbances, an investigation is performed on the heterotropic instability (including symmetric instability and traversal-type instability) of a zonal line-like disturbance moving at any angle with respect to basic flow, arriving at the following results: (1) with linear shear available, the heterotropic instability of the disturbance will occur only when flow shearing happens in the direction of the line-like disturbance movement or in the direction perpendicular to the disturbance movement, with the heterotropic instability showing the instability of the internal inertial gravity wave; (2) in the presence of second-order non-linear shear, the disturbance of the heterotropic instability includes internal inertial gravity and vortex Rossby waves. For the zonal line-form disturbance under study, the vortex Rossby wave has its source in the second-order shear of meridional basic wind speed in the flow and propagates unidirectionally with respect to the meridional basic flow. As a mesoscale heterotropic instable disturbance, the vortex Rossby wave has its origin from the second shear of the flow in the direction perpendicular to the line-form disturbance and is independent of the condition in the direction parallel to the flow; (3) for general zonal line-like disturbances, if the second-order shear happens in the meridional wind speed, i.e., the second shear of the flow in the direction perpendicular to the line-form disturbance, then the heterotropic instability of the disturbance is likely to be the instability of a mixed Rossby–internal inertial gravity wave; (4) the symmetric instability is actually the instability of the internal inertial gravity wave. The second-order shear in the flow represents an instable factor for a symmetric-type disturbance; (5) the instability of a traversal-type disturbance is the instability of the internal inertial gravity wave when the basic flow is constant or only linearly sheared. With a second or nonlinear vertical shear of the basic flow taken into account, the instability of a traversal-type disturbance may be the instability of a mixed vortex Rossby – gravity wave.     

Kinetic equations and stationary energy spectra of weakly nonlinear internal gravity waves

An ensemble of random-phase internal gravity waves is considered in the dynamical framework of the Euler–Boussinesq equations. For flows with zero mean potential vorticity, a kinetic equation for the mean spectral energy density of the waves is obtained under hypothesis of Gaussian statistics with zero correlation length. Stationary scaling solutions of this equation are found for almost vertically propagating waves. The resulting spectra are anisotropic in vertical and horizontal wave numbers. For flows with small but non-zero mean potential vorticity, under the same statistical hypothesis applied to the wave part of the flow, it is shown that the vortex part and the wave part decouple. The vortex part obeys a limiting slow dynamics equation exhibiting vertical collapse and layering which may contaminate the wave-part spectra. Relation of these results to the in situ atmospheric measurements and previous work on oceanic gravity waves is discussed.     

Wave/wave interaction producing horizontal mean flows in stably stratified fluids

We show that internal wave/wave interactions in stratified fluids are able to produce strong horizontal mean currents. A simple analytical model allows us to estimate the amplitude of the time-periodic horizontal mean flow induced by the interaction of two monochromatic waves. This model shows that in some cases, the mean flow velocity can overgo a threshold beyond which critical layers and intense energy transfers from the waves to the mean flow are expected. This prediction is confirmed by direct pseudo-spectral simulations of the Navier–Stokes equations under the Boussinesq approximation. Such interactions may help to further understand the presence of strong vertical shear observed in the final stage of stratified flows in oceans and atmospheres.     

Atmospheric Disturbances that Generate Intermittent Turbulence in Nocturnal Boundary Layers

Using the unprecedented observational facilities deployed duringthe 1999 Cooperative Atmosphere-Surface Exchange Study (CASES-99),we found three distinct turbulent events on the night of 18October 1999. These events resulted from a density current,solitary wave, and internal gravity wave, respectively. Our studyfocuses on the turbulence intermittency generated by the solitarywave and internal gravity wave, and intermittent turbulenceepisodes associated with pressure change and wind direction shiftsadjacent to the ground. Both the solitary and internal gravitywaves propagated horizontally and downward. During the passage ofboth the solitary and internal gravity waves, local thermal andshear instabilities were generated as cold air was pushed abovewarm air and wind gusts reached to the ground. These thermal andshear instabilities triggered turbulent mixing events. Inaddition, strong vertical acceleration associated with thesolitary wave led to large non-hydrostatic pressure perturbationsthat were positively correlated with temperature. The directionaldifference between the propagation of the internal gravity waveand the ambient flow led to lateral rolls. These episodic studiesdemonstrate that non-local disturbances are responsible for localthermal and shear instabilities, leading to intermittentturbulence in nocturnal boundary layers. The origin of thesenon-local disturbances needs to be understood to improve mesoscalenumerical model performance.     

Energy- and Flux-Budget Turbulence Closure Model for Stably Stratified Flows. Part II: The Role of Internal Gravity Waves

We advance our prior energy- and flux-budget (EFB) turbulence closure model for stably stratified atmospheric flow and extend it to account for an additional vertical flux of momentum and additional productions of turbulent kinetic energy (TKE), turbulent potential energy (TPE) and turbulent flux of potential temperature due to large-scale internal gravity waves (IGW). For the stationary, homogeneous regime, the first version of the EFB model disregarding large-scale IGW yielded universal dependencies of the flux Richardson number, turbulent Prandtl number, energy ratios, and normalised vertical fluxes of momentum and heat on the gradient Richardson number, Ri. Due to the large-scale IGW, these dependencies lose their universality. The maximal value of the flux Richardson number (universal constant ≈0.2–0.25 in the no-IGW regime) becomes strongly variable. In the vertically homogeneous stratification, it increases with increasing wave energy and can even exceed 1. For heterogeneous stratification, when internal gravity waves propagate towards stronger stratification, the maximal flux Richardson number decreases with increasing wave energy, reaches zero and then becomes negative. In other words, the vertical flux of potential temperature becomes counter-gradient. Internal gravity waves also reduce the anisotropy of turbulence: in contrast to the mean wind shear, which generates only horizontal TKE, internal gravity waves generate both horizontal and vertical TKE. Internal gravity waves also increase the share of TPE in the turbulent total energy (TTE = TKE + TPE). A well-known effect of internal gravity waves is their direct contribution to the vertical transport of momentum. Depending on the direction (downward or upward), internal gravity waves either strengthen or weaken the total vertical flux of momentum. Predictions from the proposed model are consistent with available data from atmospheric and laboratory experiments, direct numerical simulations and large-eddy simulations.     

A unified linear theory of wavelike perturbations under general ocean conditions

A linearized instability analysis model with five unknowns was proposed to describe disturbance motions under general oceanic background conditions, including large-scale current shear, density stratification, frontal zone, and arbitrary topography. A unified linear theory of wavelike perturbations for surface gravity waves, internal gravity waves and inertial gravity waves was derived for the adiabatic case, and the solution was then found using Fourier integrals. In this theory, we discarded the assumptions widely accepted in the literature concerning derivations of wave motions such as the irrotationality assumption for surface gravity waves, the rigid-lid approximation for internal gravity waves, and the long-wave approximation for inertial gravity waves. Analytical solutions based on this theory indicate that the complex dispersion relationships between frequency and wave-number describing the propagation and development of the three types of wavelike perturbation motions include three components: complex dispersion relationships at the sea surface; vertical invariance of the complex frequency; and expressions of the vertical wave-number (phase). Classical results of both surface waves and internal waves were reproduced from the unified theory under idealized conditions. The unified wave theory can be applied in the dynamical explanation of the generation and propagation properties of internal waves that are visible in the satellite SAR images in the southern part of the China Seas. It can also serve as the theoretical basis for both a numerical internal-wave model and analytical estimation of the ocean fluxes transported by wavelike perturbations.     

Effect of wind shear on atmospheric wave instabilities revealed by FM/CW radar observations

An FM/CW radar sounding system designed and built by one of us (Richter, 1969) reveals atmospheric wave structure in unparalleled detail.The most outstanding features evident in the record are; internal gravity waves; features resembling Kelvin/Helmholtz instability structures; and multiple layering, often with lamina only a few meters thick.This paper shows a variety of atmospheric structural patterns and compares them with several hypothetical models of internal waves to obtain more insight into the atmospheric processes at work. Special attention is given to the distribution of the Richardson number in trapped and untrapped gravity waves. It is proposed that the multiple layers result from untrapped internal gravity waves whose propagation vector is directed nearly vertically within very stable height regions. It is argued that the layers are caused by dynamic instability resulting from reduction in the Richardson number due to wave induced shear and to some background wind shear when the amplitude-to-wavelength ratio grows during propagation into thermally stable height regions of the atmosphere.     

Particle dispersion and mixing induced by breaking internal gravity waves

The purpose of this paper is to analyze diapycnal mixing induced by the breaking of an internal gravity wave — the primary wave — either standing or propagating. To achieve this aim we apply two different methods. The first method consists of a direct estimate of vertical eddy diffusion from particle dispersion while the second method relies upon potential energy budgets [Winters, K.B., Lombard, P.N., Riley, J.J., D’Asaro, E.A., 1995. J. Fluid Mech. 289, 115–128; Winters, K.B., D’Asaro, E.A., 1996. J. Fluid Mech. 317, 179–193]. The primary wave we consider is of small amplitude and is statically stable, a case for which the breaking process involves two-dimensional instabilities. The dynamics of the waves have been previously analyzed by means of two-dimensional direct numerical simulations [Bouruet-Aubertot, P., Sommeria, J., Staquet, C., 1995. J. Fluid Mech. 285, 265–301; Bouruet-Aubertot, P., Sommeria, J., Staquet, C., 1996. Dyn. Atmos. Oceans 29, 41–63; Koudella, C., Staquet, C., 1998. In: Davis, P. (Ed.), Proceedings of the IMA Conference on Mixing and Dispersion on Stably-stratified Flows, Dundee, September 1996. IMA Publication]. High resolution three-dimensional calculations of the same wave are also reported here [Koudella, C., 1999].A local estimate of mixing is first inferred from the time evolution of sets of particles released in the flow during the breaking regime. We show that, after an early evolution dominated by shear effects, a diffusion law is reached and the dispersion coefficient is fairly independent of the initial seeding location of the particles in the flow.The eddy diffusion coefficient, K, is then estimated from the diapycnal diffusive flux. A good agreement with the value inferred from particle dispersion is obtained. This finding is of particular interest regarding the interpretation of in situ estimates of K inferred either from tracer dispersion or from microstructure measurements. Computation of the Cox number, equal to the ratio of eddy diffusivity to molecular diffusivity, shows that the Cox number varies within the interval [9, 262], which corresponds to the range of vertical eddy diffusivity measured in the interior of the ocean. The Cox number is found to depend on the turbulent Froude number squared.We show eventually that mixing results in a weak distortion of the initial density profile and we relate this result to observations made at small scale in the ocean.Comparisons between the analysis of the two-dimensional and high resolution (256³) three-dimensional direct numerical simulations of the primary wave were also conducted. We show that the energetics and the amount of mixing are very close when the primary wave is of small amplitude. This results from the fact that, for a statically stable wave, the dynamics of the initially two-dimensional primary wave remains mostly two-dimensional even after the onset of wavebreaking.     

Spectral features of the energy transfer between internal waves and a larger-scale shear flow

Internal waves propagating in a larger-scale shear flow slowly change their amplitudes and wavenumbers. For moderate shear flows the secular effect of these changes reduces to a diffusion of wave action in wavenumber space. The diffusion coefficients are derived under the assumption that relaxation processes exist within the internal wave field. Associated with the diffusion of wave action is an energy transfer between the mean flow and the wave field. The wavenumber—frequency dependence of this energy transfer is evaluated for the Garrett and Munk (1975) spectral model. For this spectrum the transfer shows a characteristic +—+ signature with a weak source of internal wave energy at near-inertial frequencies, a weak sink at medium frequencies, and a strong source at high frequencies. The integrated energy transfer is from the mean flow to the internal wave field.     

Internal Gravity Waves Generated by a Local Thermal Source in an Irrotational Zonal－Vertical Plane：Numerical Analysis

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On the low-frequency,planetary-scale motion in the tropical atmosphere and oceans

Scale analyses for long wave, zonal ultralong wave (with zonal scale of disturbance L1~104 km and meridional scale L2~103 km) and meridional ultralong wave (L1~103 km, L2~104 km) are carried out and a set of approximate equations suitable for the study of these waves in a dry tropical atmosphere is obtained. Under the condition of sheared basic current, frequency analyses for the equations are carried out. It is found that Rossby waves and gravity waves may be separated for n ≥ l where n is the meridional wave number, whereas for n = 0 and L1~1000 km, the mixed Rossby-gravity wave will appear. Hence it is confirmed that the above results of scale analyses are correct. The consistency be-tween frequency analysis and scale analysis is established.The effect of shear of basic current on the equatorial waves is to change their frequencies and phase velocities and hence their group velocities. It increases the velocity of westward travelling Rossby waves and inertia-gravity and mixed waves, but decelerates the eastward inertia-gravity waves and the Kelvin wave. The recently observed low-frequency equatorial ocean wave may be interpreted as an eastward Kelvin wave in a basic current with shear.     

中尺度大气波动的波谱和谱函数——数学模型和计算方法

作者得到了准二维Boussinesq方程组，并用其研究了中尺度大气波动的波谱和谱函数。在一定条件下对该方程组线性化并取标准模后，可将其初边值问题转化为矩阵的广义特征值问题来进行数值求解，这样就可知原问题波谱和谱函数的性质。当无基本流且取地转参数、层结参数为常数时，可求得其波谱和谱函数的解析解。此时该模式中仅包含有一对重力惯性内波模态，且各模态均是简谐波；模态越高，垂直波数越大则波动传播得越慢，所有的模态均为离散谱，并存在聚点。对此作者用数值解作了验算，结果表明，该数值求解方案合理可行，对不太高的模态其精度也令人满意。在无基本流然而考虑层结的垂直变化后，则一般无法求取解析解，为此进行了数值求解。这时该模式仍仅包含有一对重力惯性内波的离散谱模态，不过由于层结参数的变化，各模态结构与简谐波出现了偏差。     

An extended Miles' theory for wave generation by wind

Miles' inviscid theory of surface wave generation by wind is (a) modified by replacing the logarithmic shear velocity profile with one which applies right down to the wave surface and which exhibits an explicit dependence on the roughness of the surface, and (b) extended to include the effects of the interaction of wave with air flow turbulence by considering the wave-modified mean flow as the mean of the actual turbulent air flow over water waves and using this in a mixing-length model.The surface pressure is shown to depend significantly on the flow conditions being aerodynamically smooth or rough. Its component in phase with the surface elevation is practically unaffected by the wave-turbulence interaction. However, such interaction tends to increase the rate of energy input ß from wind to waves travelling in the same direction, e.g., the increase is 2gk ² for aerodynamically rough flow, where gk is the Von Karman constant. It also provides damping of waves in an adverse wind which can be about 10% of the growth rate in a favourable wind.     

Unstable modes of a sheared pycnocline above a stratified layer

Internal waves incident on a sheared ocean pycnocline are studied using analytic and numerical methods. Linear analysis of the unstable modes of a sheared ocean pycnocline is used to demonstrate interactions between internal waves and shear instabilities. A new analytic solution for an asymmetric shear layer over a stratified layer is presented, illustrating modes which couple to internal waves, in addition to the well-known Holmboe modes. The robustness of these solutions is demonstrated using numerical methods for realistic shear profiles. Fully nonlinear numerical simulations illustrate the growth of these modes and demonstrate the excitation of shear instabilities by incident internal waves. The results may have implications for internal wave interactions with the ocean pycnocline and the local generation of internal solitary waves.     

风速垂直切变下非均匀层结大气中重力惯性内波的稳定性

本文应用WKB方法研究了在弱非均匀层结大气中,当基本气流具有弱垂直切变时,重力惯性内波的稳定性问题.由导得的波能量方程出发,分析了风速垂直切变及非均匀大气层结对重力惯性内波波能变化率的影响.     

THE SEMI-GEOSTROPHIC ADAPTATION PROCESS WITH TWO-LAYER BAROCLINIC MODEL IN LOW LATITUDE ATMOSPHERE

In this paper, the adaptation process in low latitude atmosphere is discussed by means of a two-layer baroclinic model on the equator β plane, showing that the adaptation process in low latitude is mainly dominated by the internal inertial gravity waves. The initial ageostrophic energy is dispersed by the internal inertial gravity waves, and as a result, the geostrophic motion is obtained in zonal direction while the ageostro-phic motion maintains in meridional direction, which can be called semi-geostrophic balance in barotropic model as well as semi-thermal-wind balance in baroclinic model. The vertical motion is determined both by the distribution of the initial vertical motion and that of the initial vertical motion tendency, but it is unrelated to the initial potential vorticity. Finally, the motion tends to be horizontal. The discussion of the physical mechanism of the semi-thermal-wind balance in low latitude atmosphere shows that the achievement of the semi-thermal-wind balance is due to the adjustment between the stream field and the temperature field through the horizontal convergence and divergence which is related to the vertical motion excited by the internal inertial gravity waves. The terminal adaptation state obtained shows that the adaptation direction between the mean temperature field and the shear flow field is determined by the ratio of the scale of the initial ageostrophic disturbance to the scale of one character scale related to the baroclinic Rossby radius of deformation. The shear stream field adapts to the mean temperature field when the ratio is greater than 1, and the mean temperature field adapts to the shear stream field when the ratio is smaller than 1.     

非均匀层结大气中的重力惯性波及其激发对流的物理机制

本文用WKBJ方法求解Boussinesq近似下的重力波方程,导出非均匀层结大气中重力惯性内波的一个守恒波作用量(称为广义波作用量)。根据广义波作用量守恒原理,着重讨论了重力惯性内波在发展过程中尺度变化的规律;在适当的条件下,重力波随着其尺度的变化而可能崩溃(或破碎),从而激发对流的发展。      

低纬斜压两层模式大气半地转适应过程

利用斜压两层模式研究了赤道平面近似下的低纬热带大气适应过程。指出低纬斜压大气适应过程主要受重力惯性内波控制。通过重力惯性内波对初始非地转能量的频散，使纬向运动达到地转平衡，而经向维持非地转运动，正压模式下称为半地转平衡，斜压模式下称为半热成风平衡。通过对垂直运动方程的求解，可知，垂直运动只与重力惯性内波相联系，其产生与初始斜压位涡度无关，而只与初始时刻的垂直运动和垂直运动倾向有关，半地转适应使运动趋向水平运动。讨论了半热成风平衡的建立及其物理机制，指出由于重力惯性内波激发出垂直运动，与垂直运动相联系的水平辐合辐散调整流场和温度场之间的关系，使温压场最终达到半热成风平衡。通过对适应过程终态的分析，指出平均温度场和切变流场之间的适应方向决定于初始非半地转扰动的尺度与斜压Ｒｏｓｓｂｙ变形半径有关的特征尺度的比值，当比值大于１时，切变流场向平均温度场适应；当比值小于１时，平均温度场向切变流场适应     

Some aspects of internal gravity waves in the multicell-type convective system

Summary Some aspects of internal gravity waves in the multicell-type convective system are examined using a linear theory and a nonlinear numerical model. The basic-state wind is assumed to increase linearly with height and then remain constant.In the theoretical part, the two-dimensional, linear, steady-state response of a stably stratified atmosphere to specified cooling representing the evaporative cooling of falling precipitation in the subcloud layer is analytically considered. It is shown that there exist an updraft on the upstream side of the cooling and a downdraft on the downstream side. As the wind shear increases enough, the magnitude of the updraft decreases. This is because a large portion of the specified cooling is used to compensate for the positive vorticity associated with the positive wind shear and accordingly the effective cooling necessary to produce perturbations is reduced.In the numerical part, a two-dimensional version of the ARPS (Advanced Regional Prediction System) that is a nonhydrostatic, compressible model with detailed physical processes is employed. Results from the dry simulation, in which the steady cooling is specified in the model, show that the simulated quasi-steady field resembles the linear, steady-state solution field because the nonlinearity factor of thermally-induced waves in this case is small. For the moist simulation, the quasi-steady perturbations obtained from the dry simulation are used as initial conditions. It is shown that gravity waces can effectively initiate convection even with small amplitude and that updraft at the head of the density current somewhat resembles the linear, steady-state response of a stably straified flow to the specified cooling. The updraft, that is, forced internal gravity waves, at the head of the density current is responsible for the initiation of consecutive convective cells that move downstream and develop as a main convective cell. This study suggests that internal gravity waves play a major role in the initiation of consecutive convective cells in the multicell-type convective system and hence in its maintenance.