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1.
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.  相似文献   

2.
We consider the three-dimensional reflection and diffraction properties of internal waves in a continuously stratified rotating fluid which are incident on the junction of a vertical slit and a half-space. This geometry is a model for submarine canyons on continental slopes in the ocean, where various physical phenomena embodying reflection and diffraction effects have been observed. Three types of incident wave are considered: (1) Kelvin waves in the slit (canyon); (2) Kelvin waves on the slope; and (3) plane internal waves incident from the half-space (ocean). These are scattered into Kelvin and Poincaré waves in the slit, a Kelvin wave on the slope and Poincaré waves in the half-space. Most of the discussion is centered around case (1). Various properties of the wave field are calculated for ranges of the parameters c/cot θ, γα and ƒ/ω where cot θ is the topographic slope, c is the internal wave ray slope, α is the canyon half-width, γ is the down-slope wave-number, ƒ is the Coriolis parameter and ω is the wave frequency. Analytical results are obtained for small γα and some approximate results for larger values of γα. The results show that significant wave trapping may occur in oceanic situations, and that submarine canyons may act as source regions for internal Kelvin waves on the continental slope.  相似文献   

3.
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.  相似文献   

4.
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.  相似文献   

5.
Within the framework of the semiempirical theory of turbulence for stratified fluids some aspects of the problem of internal wave-turbulence interaction in the upper layer of the ocean are discussed. The conditions of amplification and sustaining of turbulence by internal waves are investigated. Stationary distributions of turbulent energy are found for a stratified fluid with a shear flow produced, for example, by a low-frequency internal wave. The internal wave damping due to both turbulent viscosity and turbulent diffusion in the thermocline is studied. For a two-layer model damping constant is determined as a function of the wave number. The variation of surface turbulence by internal waves is estimated and the role of this process in slick formation is considered.  相似文献   

6.
Tidal processes are examined that control the water exchange between two basins of the Trondheimsfjord through a narrow channel with sills. For this purpose, a non-hydrostatic numerical model based on the laterally averaged Reynolds equations in the Boussinesq approximation was developed. The model takes into account the real vertical fluid stratification, variable bottom topography and variable cross-section of the fjord. Numerical experiments were performed to investigate tidally generated internal waves and their influence on the water exchange.The model produces both baroclinic tides and tidally generated lee waves. It was found that, for the Skarnsund strait which connects the Middle Fjord and the Beitstadfjord, the internal tides generated over the Skarnsund sills are very weak. Their amplitudes do not exceed 1 m.The intense short internal waves, which are identified as unsteady lee waves, comprise the basic input of the total internal wave field. These waves are generated by tidal currents at sill breaks, are trapped by topography in the generation area and grow by continuing feedback into large-amplitude waves. As the tidal flow slackens, they move upstream as freely propagating waves.As essentially nonlinear responses, the lee waves cause a nonlinear water transport. The detailed analysis of the residual currents produced by unsteady lee waves (which are propagating in both directions from the Scarnsund sills) has shown, in particular, that the residual currents can reach values as high as 0.27 m s−1.It was also found that such currents exert a considerable effect on the water exchange through the Skarnsund strait between the adjacent basins. This mechanism can play an important role in water renewal and formation of the Beitasdfjord waters.  相似文献   

7.
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, hm 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 Nhm/U > 1.05, where it occurs at z ≈ hm/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 Nhm/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.  相似文献   

8.
The quasi-geostrophic response of a stratified stream incident upon isolated finite amplitude topography on a f-plane is examined in the limit of a Boussinesq, incompressible, inviscid fluid. Compact solutions are derived subject to the following stipulations: uniform upstream velocity and stratification, a circular obstacle and an entirely isentropic/isopycnic lower surface.It is shown that for a semi-infinite flow domain the criterion for Taylor cap formation (i.e., a region of closed streamlines) is . However, for the isentropic lower boundary condition the solutions exist (i.e., have physical validity) only if R0F−1 < 0.5. (Here R0 and F refer to the Rossby and Froude numbers defined respectively in terms of the mountain half-width and height.) Also considered are the modifications both to the flow response and to the foregoing existence criterion that are induced by the introduction of an upstream profile comprising two layers of uniform but different stratification. In addition, the relationship of the derived solutions to the results obtained in previous studies is explored, and in particular an outline is given of the impact of adopting the ‘traditional’ simplified lower boundary condition.  相似文献   

9.
An exact model to describe submesoscale, coherent vortices in a uniformly stratified fluid is presented. The model allows for stratification of the eddy interior, so as to agree with observations. The closed set of equations governing the evolution of the eddy on the F-plane is derived. In the case that the interior isopycnal surfaces remain horizontal the stratified analogue of the ‘rodon’, a special solution of the ‘lens equations’ that govern the evolution of uniform-density, warm-core surface eddies, is obtained.  相似文献   

10.
Interaction of a zonal jet and small-amplitude Rossby-wave turbulence is studied within the framework of the barotropic β-plane model. It is demonstrated that turbulent-laminar interaction in this case transfers energy from the wave turbulence to the laminar flow (the effect of negative friction). We derive a conclusion that, as the geophysical turbulence is determined partly by wave turbulence and none of the traditional heuristic models can adequately describe the effect of negative friction associated with wave turbulence, the application of these models to the ‘real’ ocean and atmosphere is unreliable.It is also demonstrated that, as they are affected by the turbulence, all westward jets slowly expand without strengthening. Each jet has a core, within the limits of which the velocity of the fluid is constant. In some cases, the core expands faster than the jet periphery, resulting in jumps on the profile of the flow. All eastward jets are steady irrespective of their profiles.  相似文献   

11.
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.  相似文献   

12.
切变流场中惯性重力内波的发展   总被引：2，自引：1，他引：1  
假定背景流场为缓变的平行切变流,扰动沿基本流方向是均匀的;用WKBJ方法求解Boussinesg近似下的线性化重力波方程组,根据波作用量守恒原理,研究了流场非均匀性对重力波发展的影响。   相似文献   

13.
Over a range of incidence angles the energy of an internal wave propagating onto a sloping boundary is concentrated in a boundary layer on the slope. As a wave propagates upslope the change in its amplitude and interaction with the downslope flow remaining from previous waves results in the wave breaking and the generation of turbulence and mixing in the boundary layer. Measurements of the overturning and buoyancy scales on the slope show that turbulence is generated and decays during each wave cycle and that much of the energy input to mixing scales is extracted from density inversions generated by the wave-induced mean flow. A comparison with decaying turbulence behind a grid in a stratified water tunnel suggests that the criterion for the extinction of the buoyancy flux is similar in the two cases.  相似文献   

14.
The amplitude, wavelength, and frequency of short waves in the presence of waves of a longer scale vary in a manner that is related in phase to the long-wave profile. The purpose of this study is to observe and quantify the change in the variance of short-wave slope that occurs as a result of the change in short-wave position along a coincident long wave, during the active generation of the short-wave field by wind. To this end, measurements of wave-slope time series are made in a laboratory environment where the long-scale waves are generated mechanically and the short scale are generated primarily by air flow. The frequency variation of the short waves, as measured along the long-wave profile, is described by considering the waves to be linearly advected by the longer waves. The peak-to-peak variation along the long-wave profile of the short-wave slope variance for a given frequency band is commonly found to be 10% of its mean value. The magnitude of the excursions become smaller as short-wave frequency increases, and larger as wind speed increases. The maximum value of the short-wave slope variance generally leads the long-wave profile curve by 45 ° to 180 °.  相似文献   

15.
Trapped Kelvin–Helmholtz (K–H) waves and vortices were monitored as they were generated immediately upwind of a mountain and driven into the barrier by a low-level jet. A stratus cloud visually revealed the embedded, propagating, gravity-shear waves. Interactions of the waves with the mountain were deciphered using remote sensing measurements of the structure, motions, and microphysics within the cloud and conceptual models based on existing theories. The observations show that the mountain acted as a dam to the flow that was primed for, but did not spontaneously induce, the waves. In response to the blocking, the waves spatially developed a pattern of formation, amplification, and breakdown between the upstream flow and the barrier, and altered the associated clouds in the process. Notably, radar signatures of velocity variance depicted organized, intertwined ribbons of relatively large vorticity within the wave layer. These provided measured evidence of the vortex sheet and streamwise vortex tubes predicted by advanced K–Hinstability theory, the three-dimensional version of Scorer's `stripe', the layer of rotational fluid between opposed flows that led to the wave generation. A theory of resonant interaction of wave trains, but with blocking imposed, appears to explain the internal structure of the pile-up of the flow and wave amplification approaching the barrier. Evolution of the supporting atmospheric thermal structure and introduction of a boundary-layer flow reversal follow a current model of blocking, although some features may have developed more directly from wave-driven mixing. The remote sensors also measured the influence of the waves on the cloud liquid water, including a cumulative enlargement of droplets as they were carried through a series of waves.  相似文献   

16.
Summary The stability characteristics of trapped gravity waves, generated by an isothermal bounded tanh (z) velocity profile in the presence of a saturated finite layer, are studied. The saturated layer is introduced at different levels above the inlection point and the variations of moisture content, layer thickness and distance from the origin are examined. The growthyrates and phase speeds of the unstable modes are obtained by solving numerically the equations of motion in the linear, inviscid, Boussinesq limit, via the technique of Lalas and Einaudi (1976).It is shown that the presence of the saturated layer can significantly affect the stability characteristics of the waves. inereases in moisture, layer thickness and distance of the layer from the inflection point are found to amplify the wave response because the saturated layer behaves as a top boundtry to the shear flow. The presence of such effective boundaries is found to stabilize short wavelengths and destabilize longer wavelengths. Finally, an application of the results to a rainband case produces values of the wave parameters in good agreement with the observed ones.With II Figures  相似文献   

17.
Turbulent fluctuations in active mixed layers can excite internal waves in stably stratified fluid regions adjoining them. Expressions are derived for the energy and momentum fluxes radiated away by internal waves from an oceanic mixed layer, in terms of the spectrum of the static pressure fluctuations imposed at the base of the mixed layer by the turbulent eddies. The role of these internal wave fluxes in questions such as the determination of the rate of deepening of the layer due to an applied surface stress and the origin of internal waves in the deep ocean is discussed.  相似文献   

18.
The influence of an accelerating shear flow on the propagation of an internal gravity wave in a continuously stratified fluid is studied by means of two-dimensional numerical simulations. These are motivated by earlier laboratory experiments [Thorpe, S.A. 1978b. On internal gravity waves in an accelerating shear flow, Vol. 88. J. Fluid Mech. pp. 623–639]. In these experiments the mean flow is an accelerated Couette flow and the mean density profile is linear. The laboratory experiments revealed the striking effect of the unsteady shear flow in the evolution of an internal gravity wave leading to the wave focusing in a region where the flow is extremum. This phenomenon is associated with the growth of small scale density fluctuations. As a result density overturns are sometimes observed. This behaviour is well reproduced by the numerical simulations. We provide insights on the flow dynamics in particular on the possible occurrence of wavebreaking. We show that the dynamics is characterized by two competitive mechanisms that is a damping of the wave and a local enhancement of its steepness leading sometimes to density overturns. The budget for the energy of the wave reveals that the initial damping of the wave results from wave-mean flow interactions. These interactions lead to the development of a fine scale vertical density structure which is associated with high vertical shear. We find that in some cases wavebreaking occurs as a result of shear instability. The value of the acceleration of the mean flow is very likely to influence the onset of the instability. The scaling laws of the wave evolution, in particular the rate of decrease of its energy, are determined. From these laws the lifetime of the wave is found as a function of the acceleration of the shear. It may be expected that, in the ocean, this development will result in the largest fluctuations derived from wave-flow interactions occurring where the mean flow in the wave direction is greatest. Waves travelling normal to a two-dimensional shear flow will be unchanged. Waves travelling parallel will be damped. This may have particular application at the continental shelf where flow, mainly parallel to the isobaths, will damp waves travelling along-slope, but allows waves travelling normal to the isobaths (e.g., directly across the shelf-break) to be transmitted without attenuation. Similar effects are expected for the evolution of a high frequency wave interacting with a lower frequency (e.g., near inertial) motion.  相似文献   

19.
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, Ecrit, 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 AM, 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/(4AM2), above which waves are stationary in the flow. Longer waves, k2 h/(4AM2), 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 AH 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.  相似文献   

20.
Issues pertaining to a mechanism whereby long internal waves in shallow seas may give rise to enhanced rates of resuspension of sedimentary material are addressed. The proposed mechanism is intimately related to the creation of conditions in the bottom boundary layer which are favorable for flow separation and spontaneous onset of global instability. It is shown that long waves generated by topographic resonance and propagating upstream against the oncoming current, especially a sheared current, have a strong tendency to release a coherent, pulsating dynamics in their footprint. The passage-through-resonance problem for a sheared, stratified flow is considered, conditions for topographic resonance in the flow model are defined, and preliminary results for the unsteady dynamics in the boundary layer under the footprint of a long wave packet are presented.  相似文献   

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