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1.
The interaction of an internal wave beam (IWB) with an idealized oceanic pycnocline is examined using two-dimensional fully nonlinear direct numerical simulations based on a spectral multidomain penalty method in the vertical direction. The phenomenon of focus is the nonlinear generation of harmonics. A total of 24 simulations have been performed, varying the normalized pycnocline thickness and the ratio of peak pycnocline Brunt-Väisälä frequency to that of the stratified lower layer. Harmonics at the point of IWB entry into the pycnocline increase in amplitude and number with a measure of the maximum gradient of the Brunt-Väisälä frequency, suggesting refraction as an important factor in harmonic generation. Among the simulations performed, two distinct limits of pycnocline thickness are identified. For thin pynoclines, whose thickness is 10% of the incident IWB's horizontal wavelength, harmonics trapped within the pycnocline have maximum amplitude when their frequency and wavenumber match those of the natural pycnocline interfacial wave mode. Results in this case are compared with weakly nonlinear theory for harmonic generation by plane wave refraction. For thicker pycnoclines, whose thickness is equal the incident IWB's horizontal wavelength, IWB refraction results in harmonic generation at multiple locations in addition to pycnocline entry, giving rise to complex flow structure inside the pycnocline. 相似文献
2.
Lakshmi H. Kantha 《Dynamics of Atmospheres and Oceans》1979,3(1):47-54
When the fluid below a buoyancy interface such as the seasonal thermocline in the ocean is stably stratified as it is often, energy radiation by internal waves into regions deep below is possible. In this paper, the dispersion relation for a sharp thermocline separating a well-mixed layer from a weakly but stably stratified fluid below is derived and examined for such energy leakage into the fluid below. It is found that the interfacial waves running along such a buoyancy interface leak their energy to radiating internal waves and are rapidly attenuated, if their frequency is less than the buoyancy frequency of the fluid below. The implications the leaky nature of the modes have on resonant excitation of internal waves in the ocean by atmospheric pressure fluctuations and turbulence in the mixed layer are also examined. It is found that efficient resonant build up of interfacial waves is possible only for nonleaky modes and even then their growth rate is modified slightly by the presence of stratified fluid below the interface. 相似文献
3.
On the breakdown into turbulence of propagating internal waves 总被引：1，自引：0，他引：1
The breakdown of propagating internal waves is studied using linear stability analysis and direct numerical simulations. Sinusoidal wave trains in a uniformly stratified, non-rotating environment are considered. Cases are addressed with differing wave amplitudes and directions of propagation. For large-amplitude waves it is found that the primary instabilities are both two- and three-dimensional. It is also found that there is no qualitative difference in the breakdown process for waves with amplitude slightly below or slightly above the amplitude of incipient overturning. For the parameter regimes considered, the breakdown process could not be attributed to convective or shear instability alone, but a combination of the two. Owing to the growth of instabilities, local patches of statically unstable fluid and also of intense shear form, leading ultimately to local patches of turbulence. 相似文献
4.
The three-dimensional stability problem is investigated for a family of velocity and density profiles similar in form to those expected for large-amplitude internal gravity waves near a critical level. These profiles exhibit regions of high shear and stable stratification alternating with regions of weak shear and unstable stratification. Analytical solutions are given for inviscid, neutral modes that are similar to those found under neutral conditions with stable stratification. Neutral modes form closed streamline patterns centered at locations of maximal shear, and are not strongly influenced by nearby regions of unstable stratification. Unstable modes are computed numerically. It is shown that the instability mechanism for these wave-like flows fundamentally three-dimensional in character and exhibits both shear and convective dynamics. For flows with parameter values below the neutral curves, unstable modes oriented in the streamwise direction undergo shear instability, while modes oriented orthogonally are convectively unstable. In addition to their intrinsic physical relevance, the results of this study have important implications for the physics and the numerical modeling of breaking internal gravity waves. Two-dimensional models will bias the breaking dynamics by eliminating the possibility for convection oriented in the transverse plane. 相似文献
5.
Results are presented from numerical simulations of the incidence of a spatially-compact beam of internal waves on a shear layer containing a critical level. It is found that a significant fraction of the energy of the incident beam is transmitted across the critical level when the packet is narrow in physical space and when the energy density of the packet is not too high so that nonlinear effects are weak. As either the packet width or its energy density increases, the presence of a critical level renders the shear layer increasingly opaque to the transmission of energy. The familiar exponentially small value of the transmission coefficient is recovered as the spatial width of the packet exceeds (roughly) eight to ten wave lengths. 相似文献
6.
A sequence of numerical experiments is conducted using a linear, semi-spectral equatorial ocean model and an advanced data assimilation scheme. The numerical model is based on decomposition of the oceanic fields into Kelvin and Rossby waves belonging to the baroclinic modes of a stratified equatorial ocean. The assimilation procedure finds that solution to the model equations that best fits, in the generalized least-squares sense, all observations made within some specified space-time interval. All experiments are of the ‘identical twin’ type; synthetic data are generated by sampling the observable fields produced by a control run of the model, then the data are assimilated using the same model. The sequence of numerical experiments serves two purposes; to demonstrate the performance of the assimilation procedure in the context of a fully three-dimensional, time-varying equatorial ocean model; and to examine the utility of specified data sets, in particular, observations of sea level, in estimating the state of the equatorial ocean. The results indicate that the assimilation procedure works very well when sufficient data are provided. However, sea-level data alone are not sufficient and must be supplemented with subsurface observations if more than a few baroclinic modes are allowed in the model ocean. The required amount of supplementary subsurface data (in the form of density profiles in these experiments) can be reduced by imposing smoothness contraints on the recovered model solution. 相似文献
7.
A class of non-linear instabilities of a vertically sheared zonal flow is discussed. This is a type of baroclinic instability that lies outside the purview of a linear eigenmode analysis of baroclinic instability problems. The form taken by the instability is that of an ensemble of three neutral Rossby waves whose amplitudes are slowly modified by their mutual non-linear interactions. For a triad of small amplitude, these interactions introduce a weak, vertical variation of phase to the structure of the individual waves. This allows the generation of rectified heat fluxes and an exchange of energy with the mean flow.This instability exhibits explosive growth and spans a range of horizontal wavenumbers that exceeds the range that is unstable in the corresponding linear model. It is shown that the type of instability discussed can only occur when the model used admits unstable eigenmodes as well as neutral Rossby waves.The mechanism for the non-linear instability discussed here is believed to be fairly general and should exist also in the context of a horizontally sheared flow where it would take the form of a barotropic instability. 相似文献
8.
《Dynamics of Atmospheres and Oceans》1999,29(1):41-63
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
9.
C. J. C. Reason 《Meteorology and Atmospheric Physics》1996,61(1-2):1-18
Summary Parameterisations of mixing induced through shear instability, internal wave breaking, and double diffusion are investigated in simulations of ocean climate using a global ocean general circulation model (OGCM). Focus is placed on the sensitivity of the large scale circulation, water mass formation and transport of heat as measures of the model's ability to represent current climate. The model resolution is typical of OGCMs being coupled to atmospheric. GCMs in climate models and the parameterisations investigated are all computationally inexpensive enough to allow for integrations on long time scales. Under the assumption of constant vertical eddy coefficients (the control case), the model climatology displays acceptable values of North Atlantic Deep Water formation, Antarctic Circumpolar Current (ACC) transport, and Indonesian through-flow but an excessively deep and diffuse pycnocline structure with weak stratification in the deep ocean. It is found that various circulation and water mass properties are sensitive to the choice of parameterisation of vertical mixing and that determining a scheme which works satisfactorily over all regions (tropical, mid-latitude, and polar) of the domain is not straightforward. Parameterisations of internal wave breaking or upper ocean shear instability lead to some improvements in the model water mass formation. ACC and poleward heat transport when compared to the control case whereas parameterisations of double diffusive processes did not. Based on these and other results, various recommendations are made for mixing parameterisations in ocean climate models.With 8 Figures 相似文献
10.
A.V. Ivanov L.A. Ostrovsky I.A. Soustova L.Sh. Tsimring 《Dynamics of Atmospheres and Oceans》1983,7(4):221-232
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
11.
《Dynamics of Atmospheres and Oceans》2006,41(4):254-282
Coastal ocean numerical modeling is basically the representation of the dynamics of the coastal ocean in a chosen range of length scales and over an associated frequency band, including the modeling of both coherent processes and associated transient processes. The ocean dynamical features can be individually identified by combining wavelet analysis for time and frequency localization and principal component analysis to “decorrelate” physically consistent structures. In the present paper, the so-called WEof analysis is applied for the extraction of external gravity waves and internal gravity wave lower modes in a simple case of a flat bottom, constant Brunt-Väisälä ocean. It is shown that, with some well known restrictive assumptions, WEof analysis is an efficient candidate for the recognition of frequency localized dynamical processes. 相似文献
12.
《Dynamics of Atmospheres and Oceans》2005,40(3):209-236
Recent advances in observational technology have led to a more detailed knowledge of the low-level flow in hurricanes. In particular, quasi-streamwise rolls on a variety of scales have been observed. Some of these rolls have radial wavelengths of 4–10 km, which is comparable to rolls associated with instabilities inherent to Ekman-type boundary layers.The evolution and stability of the swirling boundary layer underneath a hurricane-like vortex is studied using both a nonlinear model and linearized stability analysis. The nonlinear model is an axisymmetric model of incompressible fluid flow, which is used to simulate the development of boundary layers underneath vortices with hurricane-like wind profiles. Axisymmetric rolls appear in these boundary layers, which have some similarities to the observed rolls in hurricanes. The axisymmetric flow is also used as the basic-state for a linearized stability analysis. The analysis technique allows for arbitrary variation in the radial and vertical directions for both the basic-state flow and the perturbations. Thus, the strong radial variations and curvature effects common to strong vortices are part of the analysis. The analysis finds both symmetric and asymmetric instabilities that are similar to those in the nonlinear simulations and in observations. The instabilities acquire some of their energy from the vertical shear associated with a reversal of the radial inflow at the top of the boundary layer, and some of their energy from vertical shear of the azimuthal flow. The radial flow energy conversion tends to increase for flows with less inertial stability and for modes oriented across the low-level shear; the azimuthal flow conversion increases for larger inertial stability and for modes aligned with the low-level shear. 相似文献
13.
The generation mechanisms of convective gravity waves in the stratosphere are investigated in a three-dimensional framework by conducting numerical simulations of four ideal storms under different environmental conditions: one un-sheared and three constant low-level sheared basic-state winds with the depth of the shear layer of 6 km and the surface wind speeds (Us) of 8, 18, and 28 m s?1, using the Advanced Regional Prediction System (ARPS) model. The storms simulated under the un-sheared (Us = 0 m s?1), weakly sheared (Us = 8 and 18ms?1), and strongly sheared (Us = 28ms?1) basicstate winds are classified into single-cell, multicell, and supercell storms, respectively. For each storm, the wave perturbations in a control simulation, including nonlinearity and microphysical processes, are compared with those in quasi-linear dry simulations forced by diabatic forcing and nonlinear forcing that are obtained from the control simulation. The gravity waves generated by the two forcing terms in the quasi-linear dry simulations are out of phase with each other for all of the storms. The gravity waves in the control simulation are represented by a linear sum of the wave perturbations generated by the nonlinear forcing and diabatic forcing. This result is consistent with the results of previous studies in a two-dimensional framework. This implies that both forcing mechanisms are important for generating the convective gravity waves in the three-dimensional framework as well. The characteristics of the three-dimensional gravity waves in the stratosphere were determined by the spectral combination of the forcing terms and the wave-filtering and resonance factor that is determined from the basic-state wind and stability as well as the vertical structure of the forcing. 相似文献
14.
We investigate numerically and theoretically the nonlinear evolution of a parallel shear flow at moderate Reynolds number which has embedded within it a mixed layer of intermediate fluid. The two relatively thin strongly stratified density interfaces are centered on the edges of the shear layer. We are particularly interested in the development of primary and secondary instabilities. We present the results of a stability analysis which predicts that such flows may be unstable to stationary vortical disturbances which are a generalization of an inviscid instability first considered by G.I. Taylor. We investigate the behavior of these “Taylor billows” at finite amplitude through two-dimensional numerical simulations. We observe that the braid regions connecting adjacent primary Taylor billows are susceptible to secondary, inherently two-dimensional instabilities. We verify that these secondary instabilities, which take the form of small elliptical vortices, arise due to a local intensification of the spanwise vorticity in the braid region. 相似文献
15.
This paper reports on experimental observation of internal waves that are focused due to a sloping topography. A remarkable mixing of the density field was observed. This result is of importance for the deep ocean, where internal waves are believed to play a role in mixing. The experiments were performed on the rotating platform at the Coriolis Laboratory, Grenoble. The rotation, its modulation and density stratification were set to be in the internal wave regime. After applying various data processing techniques we observe internal wave rays, which converge to a limiting state: the wave attractor. At longer time scales we observe a remarkably efficient mixing of the density field, possibly responsible for driving observed sheared mean flows and topographic Rossby waves. We offer the hypothesis that focusing of internal waves to the wave attractor leads to the mixing. 相似文献
16.
Coastal ocean numerical modeling is basically the representation of the dynamics of the coastal ocean in a chosen range of length scales and over an associated frequency band, including the modeling of both coherent processes and associated transient processes. The ocean dynamical features can be individually identified by combining wavelet analysis for time and frequency localization and principal component analysis to “decorrelate” physically consistent structures. In the present paper, the so-called WEof analysis is applied for the extraction of external gravity waves and internal gravity wave lower modes in a simple case of a flat bottom, constant Brunt-Väisälä ocean. It is shown that, with some well known restrictive assumptions, WEof analysis is an efficient candidate for the recognition of frequency localized dynamical processes. 相似文献
17.
Lakshmi H. Kantha 《Dynamics of Atmospheres and Oceans》1979,3(1):39-46
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.
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
19.
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. 相似文献
20.
By using a linear oceanic mixed layer model, the long period waves in the tropical ocean are investi-gated numerically. Due to the inhomogeneity of the large-scale average sea temperature field of the ocean in tropical regions, besides the westward propagating equatorial Rossby wave to be modified, there will be a kind of long period thermal wave which propagates eastward under certain oceanic background conditions. Under the influences of these two kinds of waves, the propagating and evolving processes of the sea surface temperature anomalies (SSTA) are dearly shown by numerical experiments. The results of numerical ex-periments are consistent with the ones obtained by the theoretical analysis in Part I. The possible relation-ship between these two kinds of waves and El Nino events is also discussed indirectly. 相似文献