A kinetic theory for internal waves in a randomly stratified fluid

We discuss the transport of energy of internal waves propagating in a stratified unbounded fluid with randomly varying buoyancy frequency N of the form $\text{N}{}^2\text{= N}{}_0{}^2\text{[1 + ?Ξ(}\textcolor{red}{}\text{)]}$. Here N₀ = constant, 0 < ? ? 1 and Ξ is a zero-mean stationary random function of $\textcolor{red}{}\text{= (x,z)}$ where x and z are respectively horizontal and vertical coordinates. In the limit of small ?, a linear kinetic equation (transport equation) is derived which describes the space—time evolution of the mean wave energy density in such a medium. When it is integrated over all wave number space, the kinetic equation implies the total conservation of wave energy. The approach used is reminiscent of the nonlinear wave interaction theories of Phillips (1960), Benny (1962) and Hasselmann (1966) and others, in which the random microstructure Ξ would be regarded as a nonpropagating (zero-frequency) random wave field. Our analysis is based on the Eulerian equations of motion in which no a priori assumptions are made regarding the scattered wave field — on the contrary, it is a deduction of the theory presented here that only the propagating internal wave modes participate in the energy exchange processes. In particular we do not assume that the internal wave field constitutes a homogenous assembly of random wave packets evolving in time alone — unlike much of the earlier work — and this enables us to treat the scattering of individual internal waves by the microstructure.The kinetic equation is used to determine the energy transmitted through and reflected by a horizontally oriented random slab which models a layer of microstructure of finite thickness in the ocean. Specifically, we show that significant reflection can occur when Ψ(2k_0z) is sufficiently large, where Ψ is the vertical wavenumber spectrum of the microstructure fluctuations Ξ(z) and k_0z is the vertical wavenumber of the incident wave. We also show that the reflection coefficient increases monotonically with increasing frequency, which is in qualitative agreement with recent measurements at site D(39°N, 70°W) which indicate that in regions where density inhomogeneities are present, the vertical coherence decreases with increasing frequency. Actual numerical estimates for the reflection coefficient are obtained for vertical microstructure data from station P(50°N, 145°W). It is found that for intermediate wavelengths — 0(10²m) — and a broad band of frequencies (0.6 ? ω/N₀ < 1), the reflection coefficient is greater than 0.5. Finally, the qualitative behaviour of the kinetic equation for two-dimensional microstructure is examined in the geometric optics limit: wavelength much less than (the integral) correlation scale. In this case the integro-differential kinetic equation reduces to a Fokker—Planck diffusion equation. From the latter we infer that at high frequencies, a wave packet becomes incoherent after propagating a distance that is less than a typical correlation scale associated with the fluctuations Ξ.     

Tide,Wind, and River Forcing of the Surface Currents in the Fraser River Plume

A long-term record of surface currents from a high-frequency radar system, along with near-surface hydrographic transects, moored current meter records, and satellite imagery, are analyzed to determine the relative importance of river discharge, wind, and tides in driving the surface flow in the Fraser River plume. The observations show a great deal of oceanographic and instrumental variability. However, averaged quantities yielded robust results. The effect of river flow, which determines buoyancy and inertia near the river mouth, was found by taking a long-term average. The resulting flow field was dominated by a jet with two asymmetric gyres; the anticyclonic gyre to the north had flow speeds consistent with geostrophy. The mean flow speed near the river mouth was 14.3?cm?s^–1, while the flow further afield was 5?cm?s^–1 or less. Wind stress and surface currents were highly coherent in the subtidal frequency band. Northwesterly winds drive a surface flow to the southeast at speeds of nearly 30?cm?s^–1. Southeasterly winds drive a surface flow to the northwest at speeds reaching 20?cm?s^–1; however, there is more spatial variability in speed and direction relative to the northwesterly wind case. A harmonic analysis was used to extract the tidally driven flows. Ellipse parameters for the major tidal constituents varied considerably in both alignment and aspect ratio over the radar domain, in direct contrast to a barotropic model which predicted rectilinear flow along the Strait of Georgia. This is a result of water filling and draining the shallow mud flats north of the Fraser's main channel. The M₂ velocities at the surface were also weaker than their barotropic counterparts. However, the shallow water constituent MK₃ was enhanced at the surface and nearly as strong as the mean flow, implying that non-linear interactions are important to surface dynamics.     

Finite-amplitude, neutral baroclinic eddies and mean flows in an internally heated, rotating fluid: 2. Effects of spatially varying N

The analytical model of finite-amplitude, quasi-geostrophic ‘free mode’ baroclinic eddies and mean zonal flows in a Cartesian channel, presented recently by Read, is extended to take account of vertical variations in the buoyancy frequency N. A series of exact solutions is presented to illustrate the effect of monotonically varying static stability on the structure and properties of the flow. The analytical solutions are then compared with a corresponding series of numerical simulations of steady wave flows in a rotating fluid annulus subject to internal heating and sidewall cooling. By suitable choices of internal heating distributions and boundary conditions, several different forms of N² profile could be obtained in the simulated flows, in which N² was concentrated to a greater or lesser extent towards the upper boundary. The resulting steady flows exhibited strong qualitative similarities in their structure and dependence upon the form of N²(z) to that of the analytical solutions when realistic profiles of N² were included in the latter, especially when an equivalent-barotropic component was included, although the latter component is unable to satisfy the simplest (internal jet) form of horizontal boundary condition as usually applied to Rossby waves.The relatively weak, though crucially important, forcing and dissipation processes in the annulus are examined using approximate quasi-geostrophic diagnostics of the major terms in the budget of potential enstrophy for the numerical simulations. Internal heating is found to be the major source of potential enstrophy for the mean zonal flow, solely by virtue of the variation of N² with height, but has only a minor direct effect upon the eddy flow component. Because of the presence of critical layers in the flow, all non-linear terms (including the third-order potential enstrophy flux divergence) are found to be significant in certain regions. Some implications for the value and applicability of EP flux diagnostics are discussed. Potential enstrophy budgets for horizontal regions enclosed by geostrophic streamlines are used to shed further insight into the maintenance of the flow against ‘friction’, and on the form of the potential vorticity-streamfunction relationship. Some implications of the results for other systems of geophysical interest are also discussed.     

On the validity of layered models of ocean dynamics and thermodynamics with reduced vertical resolution

With the purpose of studying the upper part of the ocean, the shallow water equations (in a `reduced gravity' setting) have been extended in the last decades by allowing for horizontal and temporal variations of the buoyancy field ϑ, while keeping it as well as the velocity field u as depth-independent. In spite of the widespread use of this `slab' model, there has been neither a discussion on the range of validity of the system nor an explanation of points such as the existence of peculiar zero-frequency normal modes, the nature of the instability of a uniform u flow, and the lack of explicit vertical shear associated with horizontal density gradients. These questions are addressed here through the development of a subinertial model with more vertical resolution, i.e., one where the buoyancy ϑ varies linearly with depth. This model describes satisfactorily the problem of baroclinic instability with a free boundary, even for short perturbations and large interface slopes. An enhancement of the instability is found when the planetary β effect is compensated with the topographic one, due to the slope of the free boundary, allowing for a `resonance' of the equivalent barotropic and first baroclinic modes. Other low-frequency models, for which buoyancy stratification does not play a dynamical role, are invalid for short perturbations and have spurious terms in their energy-like integral of motion.     

Buoyancy in tropical cyclones and other rapidly rotating atmospheric vortices

Motivated primarily by its application to understanding tropical-cyclone intensification and maintenance, we re-examine the concept of buoyancy in rapidly rotating vortices, distinguishing between the buoyancy of the symmetric balanced vortex or system buoyancy, and the local buoyancy associated with cloud dynamics. The conventional definition of buoyancy is contrasted with a generalized form applicable to a vortex, which has a radial as well as a vertical component. If, for the special case of axisymmetric motions, the balanced density and pressure distribution of a rapidly rotating vortex are used as the reference state, the buoyancy field then characterizes the unbalanced density perturbations, i.e. the local buoyancy. We show how to determine such a reference state without approximation.The generation of the toroidal circulation of a vortex, which is necessary for vortex amplification, is characterized in the vorticity equation by the baroclinicity vector. This vector depends, inter-alia, on the horizontal (or radial) gradient of buoyancy evaluated along isobaric surfaces. We show that for a tropical-cyclone-scale vortex, the buoyancy so calculated is significantly different from that calculated at constant height or on surfaces of constant σ (σ = (p − p^*)/(p_s − p^*), where p is the actual pressure, p^* some reference pressure and p_s is the surface pressure). Since many tropical-cyclone models are formulated using σ-coordinates, we examine the calculation of buoyancy on σ-surfaces and derive an expression for the baroclinicity vector in σ-coordinates. The baroclinic forcing term in the azimuthal vorticity equation for an axisymmetric vortex is shown to be approximately equal to the azimuthal component of the curl of the generalized buoyancy. A scale analysis indicates that the vertical gradient of the radial component of generalized buoyancy makes a comparatively small contribution to the generation of toroidal vorticity in a tropical cyclone, but may be important in tornadoes and possibly also in dust devils.We derive also a form of the Sawyer–Eliassen equation from which the toroidal (or secondary) circulation of a balanced vortex may be determined. The equation is shown to be the time derivative of the toroidal vorticity equation in which the time rate-of-change of the material derivative of potential toroidal vorticity is set to zero. In analogy with the general case, the diabatic forcing term in the Sawyer–Eliassen equation is shown to be approximately equal to the time rate-of-change of the azimuthal component of the curl of generalized buoyancy.Finally, we discuss the generation of buoyancy in tropical cyclones and contrast the definitions of buoyancy that have been used in recent studies of tropical cyclones. We emphasize the non-uniqueness of the buoyancy force, which depends on the choice of a reference density and pressure, and note that different, but equivalent interpretations of the flow dynamics may be expected to arise if different reference quantities are chosen.     

The role of wave energy accumulation in tropical cyclogenesis over the tropical North Atlantic

A hierarchical modeling approach is used to study the process by which interactions of easterly waves with the background flow can result in a reduction in the longitudinal and vertical scale of the waves. Theory suggests that in flows that possess a negative longitudinal gradient (U _x  < 0) there is a reduction of longitudinal and vertical group speeds and an increase in regional wave action density (or “wave energy”). Relative vorticity increases locally leading to an increase in the likelihood of tropical cyclogenesis near the wave axis. Opposite impacts on the structure of the waves is expected in a U _x  > 0 domain. In the simplified framework of a free-surface and divergent shallow water model, Rossby wave properties are tracked through a range of background flow scenarios to determine the important scales of interaction. The importance of wave energy accumulation for tropical cyclogenesis is then studied in a full physics and dynamics model using a nested regional climate model simulation, at 12 km horizontal grid spacing, over the tropical North Atlantic region for the entire 2005 hurricane season. The dynamical environment within which 70% of easterly waves formed tropical cyclones exhibits coherent regions in which easterly winds increase towards the east, consistent with the occurrence of wave energy accumulation.     

Internal tides in the coastal zone of the Sea of Japan in autumn

The results are presented of hydrological studies in the coastal zone of the Sea of Japan in autumn in different years. It is revealed that the typical density stratification of water is formed there in autumn. The amplitudes are estimated of regular (with the periodicity of tidal harmonic M₂) vertical displacements of isotherms in the intermediate layer and maximum values of flow velocity in the surface and bottom layers. It is demonstrated that temperature perturbations are induced at the shelf edge and propagate to the coastal zone with the velocity that is close to the velocity of the first mode of internal gravity waves with the frequency of the tidal harmonic M₂.     

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.     

A mechanism of deep-ocean mixing due to near-inertial waves generated by flow over bottom topography

This article describes a remarkable effect of the horizontal component of the Coriolis vector, which is traditionally neglected in geophysical fluid wave theory, for the generation of inertio-gravity waves caused by flow over topography. Earlier an initial-value approach was used to calculate the evolutions of internal waves generated by atmospheric forcing in the linear Boussinesq model as done by many investigators for the study of near-inertial waves in the ocean. In this study, however, we focused on the mechanism of generating near-inertial waves by a bottom forcing with various periods. It is shown that the non-traditional Coriolis effects can significantly enhance the generation of near-inertial waves. Moreover, the intensity of generated near-inertial waves increases as the period of bottom forcing approaches to the local inertial period, suggesting the importance of tidal flows for generating near-inertial waves in deep ocean near critical latitudes. It is inferred that such near-inertial waves may contribute to a mechanism of deep-ocean mixing.     

Turbulent characteristics of a shallow convective internal boundary layer

Turbulent characteristics of a 50 to 100 m deep convective internal boundary layer (I.B.L.) have been studied. The data were gathered at a flat coastal site (Näsudden on the island of Gotland, Sweden) during three consecutive days in May 1980 which were characterized by a steady, very stable stratified marine approach flow. The site is situated on a flat area ca. 1500 m from the shoreline. Only daytime runs have been analysed in the present paper. The sensible heat flux at the ground was typically 200 W m^-2 and was found to decrease more or less linearly with height throughout the I.B.L., being slightly negative at greater heights. The momentum flux was also found to decrease with height, but nevertheless shear production of turbulent kinetic energy was found to be large throughout the entire I.B.L. The analysis shows that the turbulent regime has a mixed character. Certain characteristics, such as the rate of growth of the I.B.L., appear to be almost entirely controlled by mechanical turbulence, while others, notably temperature variance and the spectrum of vertical velocity, scale remarkably well with w _* and z _i, in accordance with the results found in fully convective conditions during the experiments at Minnesota and Aschurch. Other turbulent characteristics, such as spectra of the horizontal wind components measured near the top of the I.B.L. tend to adhere to mixed-layer scaling in the high frequency range, exhibiting much increased energy in the lower (reduced) frequency range. Spectra of the velocity components from 10 m are shown to be in general agreement with findings from ‘ideal’, homogeneous sites (Kansas) when properly normalized, although the low frequency part of u- and v-spectra are slightly reduced compared to the case with deep convection.     

Effects of shear and sharp gradients in static stability on two-dimensional flow over an isolated mountain ridge

Summary ?We have investigated the effects of shear and sharp gradients in static stability and demonstrated how a mountain wave and its associated surface winds can be strongly influenced. Linear theory for two-dimensional, nonrotating stratified flow over an isolated mountain ridge with positive shear and constant static stability shows that the horizontal wind speeds on both the lee and upslope surfaces are suppressed by positive shear. The critical F(=U/Nh where U is the basic wind speed, N the Brunt-Vaisala frequency, and h the mountain height) for the occurrence of wave breaking decreases when the strength of the positive shear increases, while the location for the wave-induced critical level is higher in cases with larger positive shear. The linear theory is then verified by a series of systematic nonlinear numerical experiments. Four different flow regimes are found for positive shear flow over a two-dimensional mountain. The values of critical F which separate the flow regimes are lower when the strength of the positive shear is larger. The location of stagnation aloft from numerical simulations is found to be quite consistent with those predicted by linear theory. We calculate the strongest horizontal wind speed on the lee surface (U _max), the smallest horizontal wind speed on the upslope surface (U _min), the reflection (Ref), and the transmission (Tran) coefficients for different combinations of the stability ratio between the upper and lower layers (i.e. and z ₁ (interface height) in a two-layer atmosphere from linear analytical solutions. Both Ref and Tran are found to be functions of log() but not the interface height (z ₁). Ref is larger when is much different from 1, no matter whether it is larger or smaller than 1. However, Tran decreases when log() increases and approaches 0 when log() is large. The magnitude of the largest U _max (smallest U _min) increases (decreases) as the absolute value of log() increases. It is found that the largest U _max occurs when the nondimensional z ₁ is near for cases with a less stable upper layer or when z ₁ is near for cases with a more stable upper layer. These results are confirmed by nonlinear numerical simulations. We find that linear theory is very useful in qualitative analysis of the possibility of high-drag state for different stability profiles. The location of stagnation aloft in a two-layer atmosphere from numerical simulations agrees very well with those predicted by linear theory. The above findings are applied to investigate the Boulder severe downslope windstorm of 11 January 1972. We find that the windstorm cannot develop if the near mountain-top inversion is located at a higher altitude (e.g.,  km). However, if there exists a less stable layer right below the tropopause, the windstorm can develop in the absence of a low-level inversion. These results indicate the importance of partial reflection due to the structured atmosphere in influencing the possibility of severe downslope windstorms, although partial reflection may not be the responsible mechanism for the generation of windstorms. Received September 25, 1999/Revised February 9, 2000     

True gravity in ocean dynamics Part 1 Ekman transport

The direction normal to the Earth spherical (or ellipsoidal) surface is not vertical (called deflected vertical) since the vertical direction is along the true gravity g (= ig_λ+ jg_φ+ kg_z). Here, (λ, φ, z) are (longitude, latitude, depth), and (i, j, k) are the corresponding unit vectors. The spherical (or ellipsoidal) surfaces are not horizontal surfaces (called deflected-horizontal surfaces). The most important body force g (true gravity) has been greatly simplified without justification in oceanography to the standard gravity (-g₀k) with g₀ = 9.81 m/s². Impact of such simplification on ocean dynamics is investigated in this paper using the Ekman layer model. In the classical Ekman layer dynamic equation, the standard gravity (-g₀k) is replaced by the true gravity g(λ, φ, z) with a constant eddy viscosity and a depth-dependent-only density ρ(z) represented by an e-folding near-inertial buoyancy frequency. New Ekman spiral and in turn new formulae for the Ekman transport are obtained for ocean with and without bottom. With the gravity data from the global static gravity model EIGEN-6C4 and the surface wind stress data from the Comprehensive Ocean-Atmosphere Data Set (COADS), large difference is found in the Ekman transport using the true gravity and standard gravity.     

A Hierarchy of Energy- and Flux-Budget (EFB) Turbulence Closure Models for Stably-Stratified Geophysical Flows

Here we advance the physical background of the energy- and flux-budget turbulence closures based on the budget equations for the turbulent kinetic and potential energies and turbulent fluxes of momentum and buoyancy, and a new relaxation equation for the turbulent dissipation time scale. The closure is designed for stratified geophysical flows from neutral to very stable and accounts for the Earth’s rotation. In accordance with modern experimental evidence, the closure implies the maintaining of turbulence by the velocity shear at any gradient Richardson number Ri, and distinguishes between the two principally different regimes: “strong turbulence” at ${Ri \ll 1}$ typical of boundary-layer flows and characterized by the practically constant turbulent Prandtl number Pr _T; and “weak turbulence” at Ri > 1 typical of the free atmosphere or deep ocean, where Pr _T asymptotically linearly increases with increasing Ri (which implies very strong suppression of the heat transfer compared to the momentum transfer). For use in different applications, the closure is formulated at different levels of complexity, from the local algebraic model relevant to the steady-state regime of turbulence to a hierarchy of non-local closures including simpler down-gradient models, presented in terms of the eddy viscosity and eddy conductivity, and a general non-gradient model based on prognostic equations for all the basic parameters of turbulence including turbulent fluxes.     

Instabilities of the tidally induced bottom boundary layer in the rotating frame and their mixing effect

To investigate the stability of the bottom boundary layer induced by tidal flow (oscillating flow) in a rotating frame, numerical experiments have been carried out with a two-dimensional non-hydrostatic model. Under homogeneous conditions three types of instability are found depending on the temporal Rossby number Ro_t, the ratio of the inertial and tidal periods. When Ro_t < 0.9 (subinertial range), the Ekman type I instability occurs because the effect of rotation is dominant though the flow becomes more stable than the steady Ekman flow with increasing Ro_t. When Ro_t > 1.1 (superinertial range), the Stokes layer instability is excited as in the absence of rotation. When 0.9 < Ro_t < 1.1 (near-inertial range), the Ekman type I or type II instability appears as in the steady Ekman layer. Being much thickened (100 m), the boundary layer becomes unstable even if tidal flow is weak (5 cm/s). The large vertical scale enhances the contribution of the Coriolis effect to destabilization, so that the type II instability tends to appear when Ro_t > 1.0. However, when Ro_t < 1.0, the type I instability rather than the type II instability appears because the downward phase change of tidal flow acts to suppress the latter. To evaluate the mixing effect of these instabilities, some experiments have been executed under a weak stratification peculiar to polar oceans (the buoyancy frequency N²  10⁻⁶ s⁻²). Strong mixing occurs in the subinertial and near-inertial ranges such that tracer is well mixed in the boundary layer and an apparent diffusivity there is evaluated at 150–300 cm²/s. This suggests that effective mixing due to these instabilities may play an important role in determining the properties of dense shelf water in the polar regions.     

Vortex shedding behind tapered obstacles in neutral & stratified flow

Results of laboratory and numerical experiments on both homogeneous and density-stratified flow over single, bluff obstacles of various shapes are presented. The obstacle height is in most cases of the same order as the base diameter and the major controlling (flow) parameter is the Froude number, defined here as F_h=U/Nh, where U is the (uniform) upstream velocity, h the obstacle height and N is the buoyancy frequency. Attention is concentrated, firstly, on the case of homogeneous flows over rather weakly tapered obstacles and, secondly, for bodies whose height is similar to their base width, on the case F_h=0.1, representing stratification sufficiently strong that lee-wave motions do not play a significant role in the flow dynamics. For right-circular cones it is shown that the sectional contributions to the total fluctuating side force (lift) show significant phase variations up the height of the obstacle, which are not always reflected in the developed vortex street further downstream. For some obstacle shapes, the vortex lines linking the von Karman eddies at different heights can be significantly tilted, particularly in the upper part of the wake. Vortex convection speeds do not appear generally to vary greatly with height and, as found in previous work, the shedding frequency remains constant with height, despite the strong variation of cross-stream obstacle width. By comparison with the homogeneous results, it is suggested that the stratification enhances the shedding instability, which would otherwise be very weak for squat obstacles, but does not annihilate the ability of the flow at one level to influence that at another.     

Experiments on steady buoyancy transfer through turbulent fluid layers separated by density interfaces

A laboratory experiment was performed to investigate mixing across a density interface which separates two turbulent fluid layers and coexists with a stabilizing buoyancy flux. It was found that the buoyancy flux (q₀) across the interface and through the turbulent layers (of depth D) becomes steady and constant in magnitude in the vertical direction, only when , where u is the horizontal r.m.s. velocity at the base of the mixed layers. The results suggest that mixing across the density interface is controlled by a dynamically important buoyancy gradient induced in the turbulent layers and that parameters such as the bulk Richardson number, , where Δb is the interfacial buoyancy jump, are of secondary importance. Measurements are used to infer the mixing mechanism at the interface, the mixing efficiency of stratified fluids and the entrainment law. Some geophysical applications of the results are also discussed.     

Upstream stagnation points in stratified flow past obstacles

An experimental study has been made of stagnation points and flow splitting on the upstream side of obstacles in uniformly stratified flow. A range from small to large values of Nh/U (where N is the buoyancy frequency, h_m is the maximum obstacle height and U is the undisturbed fluid velocity) has been covered, for three obstacle shapes which are, respectively, axisymmetric, and elongated in the across-stream and in the downstream directions. Upstream stagnation for the first two of these models does not occur until Nh_m/U > 1.05, where it occurs at z ≈ h_m/2. On the central line below this point the flow descends and diverges, and we term this ‘flow splitting’. For the third model (elongated in the downstream direction), stagnation upstream first occurs at Nh_m/U ≈ 1.43, at z ≈ 0. Results for this obstacle are not consistent with the ‘Sheppard criterion’, and this upstream flow stagnation is not apparently related to lee wave overturning, in contrast to flow over two-dimensional obstacles.     

THE EFFECTS OF VERTICAL VARIATION OF BASIC FLOW AND HORIZONTAL GRADIENT OF TEMPERATURE ON LINEAR AND NONLINEAR GRAVITY WAVES

By using two-dimensional dynamical equations in x-z plane with Boussinesq approximation,the effects of the second-order vertical shear of the basic flow u_zz and the horizontal gradient of temperature (M) on the gravity wave and the isolated gravity wave are discussed.The magnitudes of u_zz and M corresponding to the linear and nonlinear stabilities of the gravity waves are worked out,respectively.The results show that amplitude and width of the isolate dgravity wave are closely related to u_zz and M.It is indicated that the isolated gravity wave with a width of about 10 km can be motivated by the disturbance of sub-synoptic scale in the certain ranges of flow field shear and temperature gradient,while the motivated waves may be associated with the cold surge ahead of a cold front and the other mesoscale synoptic systems.