- Email: [email protected]
Internal waves and related initial-value problems
94
ANNUAL LITERATURE SURVEY 1996
calculated jet mixing efficiency displayed higher values than comparable efficiencies for destratification with air-bubble plumes. (from Authors) The structure of the turbulent wake and the random internal wave field generated by a moving sphere in a stratified fluid Bonneton P., Chomaz J.M., Hopfinger E. & Perrier M., Dynamics of Atmospheres & Oceans, 1996, 23/1-4 (299308). In English. Presents experimental results on the structure of the turbulent wake of a sphere and on the frequencies associated with the vortex shedding in a stratified fluid. The strong correlation between the random internal wave field emitted by the wake and the coherent structures of the turbulent wake is demonstrated. (Authors) Internal waves and related initial-value problems Lighthill J., Dynamics of Atmospheres & Oceans, 1996, 23/1-4 (3-17). In English. This paper gives a detailed account of how small disturbances to uniformly stratified fluid develop when the initial disturbances are confined to a limited region. Special stress is laid on properties of vorticity in stratified fluid, with horizontal (yet not vertical) components of vorticity being propagated away, alongside density variations, in any internal wave - an important difference from corresponding properties in homogeneous fluid. The paper includes a comprehensive analysis of the waves which emanate from the initial disturbances, as welt as of those residual motions that are left behind after all waves have been propagated away (those in each horizontal plane being determined from the initial distribution over that plane of the vorticity's vertical component). Some mathematical details are included in an appendix, which outlines too an additional benefit from these studies by showing how the wave motion generated by any transient local forcing effect can always be identified as the solution of a well-defined initial-valueproblem. (Author) A numerical study of wave-breaking in stratified flow over obstacles Paisley M.F. & Castro I.P., Dynamics of Atmospheres & Oceans, 1996, 23/1-4 (309-319). In English. This paper describes results of numerical computations of stratified flow of finite depth D over a variety of obstacles using the time-dependent Navier Stokes equations with stability-dependent eddy viscosity turbulence models. Most computations were performed with the Froude number Fh in the range of 0.5 = or Fh = or 2 and the parameter K = D/(piFb) in the range of 1 = or K = or 10. Here Fh = UfNh, where U is the free stream velocity, N is the buoyancy frequency and h is the height of the body. The domain and boundary conditions correspond to those of a towing tank experiment and the initial conditions were 'impulsive start'. Critical Froude numbers for wave-breaking over two-dimensionalobstacles are compared with theoretical predictions and experimental results. Preliminary results with mixing length and one-equation turbulence models suggest that differences in the representation of flows with breaking waves with such models are small. The occurrence of'merged flow', in which the breaking regionj oins with the secondary separation zone, and which has been seen in experiments, is found in the computations in three dimensions, but not those in two. (Authors) An exact, stratified model of a meddy Maas L.R.M. & Zahariev K., Dynamics of Atmospheres & Oceans, 1996, 24/1-4 (215-225). In English. 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 ofthe'rodon', a special solution of the'lens equations' that govern the evolution of uniform-density, warm-core surface eddies, is obtained. (Authors) Stably stratified flows in meteorology Hunt J.C.R., Shutts G.J. & Derbyshire S.H., Dynamics of Atmospheres & Oceans, 1996, 23/1-4 (63-79). In English. It is generally believed by researchers in the fundamental aspects of geophysical fluid dynamics and meteorology that their results contribute to the improvements to numerical weather prediction and in practical weather forecasting. However, the techniques whereby the appropriate research results are selected and incorporated into the numerical models are not widely known, particularly sub-grid scale phenomena. Atmospheric motions on these scales are not like molecular motions in an ideal gas, but shows considerable structure, approximating to combinations of various idealized states. This paper, focuses on a restricted range of phenomena associated with stably stratified flows, notably mountain waves, convection and clouds, and boundary layer phenomena. This category provides many examples of structures which need to be considered in detail to reconstruct the large-scale picture accurately, as well as in local forecasting. (from Authors) Some similarity states of stably stratified homogeneous turbulence Chasnov J.R., Dynamics of Atmospheres & Oceans, 1996, 23/1-4 (183-192). In English. The decay of statistically homogeneous velocity and density fluctuations in a stably stratified fluid is considered. Over decay times long compared with the turbulence time scale but short compared with the period of internal gravity waves. Three distinct high Reynolds number similarity states may develop. These similarity states are a consequence of the invariance of the low wavenumber coefficients of the three-dimensional kinetic or potential energy spectrum, and their preferential development depends on the relative magnitudes of the initial kinetic and potential energy per unit mass of the fluid. When the turbulence has decayed over a time comparable with the period of the gravity waves, the three similarity states mentioned above are disrupted. Evidence will be presented of a new similarity state which then develops asymptotically. In this similarity state, the time decay exponent of the total energy per unit mass of the turbulence is reduced by a factor of two from its value for decaying isotropic turbulence, and the associated vertical integral scale approaches a constant independent of time. (Author)
ANNUAL LITERATURE SURVEY 1996
calculated jet mixing efficiency displayed higher values than comparable efficiencies for destratification with air-bubble plumes. (from Authors) The structure of the turbulent wake and the random internal wave field generated by a moving sphere in a stratified fluid Bonneton P., Chomaz J.M., Hopfinger E. & Perrier M., Dynamics of Atmospheres & Oceans, 1996, 23/1-4 (299308). In English. Presents experimental results on the structure of the turbulent wake of a sphere and on the frequencies associated with the vortex shedding in a stratified fluid. The strong correlation between the random internal wave field emitted by the wake and the coherent structures of the turbulent wake is demonstrated. (Authors) Internal waves and related initial-value problems Lighthill J., Dynamics of Atmospheres & Oceans, 1996, 23/1-4 (3-17). In English. This paper gives a detailed account of how small disturbances to uniformly stratified fluid develop when the initial disturbances are confined to a limited region. Special stress is laid on properties of vorticity in stratified fluid, with horizontal (yet not vertical) components of vorticity being propagated away, alongside density variations, in any internal wave - an important difference from corresponding properties in homogeneous fluid. The paper includes a comprehensive analysis of the waves which emanate from the initial disturbances, as welt as of those residual motions that are left behind after all waves have been propagated away (those in each horizontal plane being determined from the initial distribution over that plane of the vorticity's vertical component). Some mathematical details are included in an appendix, which outlines too an additional benefit from these studies by showing how the wave motion generated by any transient local forcing effect can always be identified as the solution of a well-defined initial-valueproblem. (Author) A numerical study of wave-breaking in stratified flow over obstacles Paisley M.F. & Castro I.P., Dynamics of Atmospheres & Oceans, 1996, 23/1-4 (309-319). In English. This paper describes results of numerical computations of stratified flow of finite depth D over a variety of obstacles using the time-dependent Navier Stokes equations with stability-dependent eddy viscosity turbulence models. Most computations were performed with the Froude number Fh in the range of 0.5 = or Fh = or 2 and the parameter K = D/(piFb) in the range of 1 = or K = or 10. Here Fh = UfNh, where U is the free stream velocity, N is the buoyancy frequency and h is the height of the body. The domain and boundary conditions correspond to those of a towing tank experiment and the initial conditions were 'impulsive start'. Critical Froude numbers for wave-breaking over two-dimensionalobstacles are compared with theoretical predictions and experimental results. Preliminary results with mixing length and one-equation turbulence models suggest that differences in the representation of flows with breaking waves with such models are small. The occurrence of'merged flow', in which the breaking regionj oins with the secondary separation zone, and which has been seen in experiments, is found in the computations in three dimensions, but not those in two. (Authors) An exact, stratified model of a meddy Maas L.R.M. & Zahariev K., Dynamics of Atmospheres & Oceans, 1996, 24/1-4 (215-225). In English. 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 ofthe'rodon', a special solution of the'lens equations' that govern the evolution of uniform-density, warm-core surface eddies, is obtained. (Authors) Stably stratified flows in meteorology Hunt J.C.R., Shutts G.J. & Derbyshire S.H., Dynamics of Atmospheres & Oceans, 1996, 23/1-4 (63-79). In English. It is generally believed by researchers in the fundamental aspects of geophysical fluid dynamics and meteorology that their results contribute to the improvements to numerical weather prediction and in practical weather forecasting. However, the techniques whereby the appropriate research results are selected and incorporated into the numerical models are not widely known, particularly sub-grid scale phenomena. Atmospheric motions on these scales are not like molecular motions in an ideal gas, but shows considerable structure, approximating to combinations of various idealized states. This paper, focuses on a restricted range of phenomena associated with stably stratified flows, notably mountain waves, convection and clouds, and boundary layer phenomena. This category provides many examples of structures which need to be considered in detail to reconstruct the large-scale picture accurately, as well as in local forecasting. (from Authors) Some similarity states of stably stratified homogeneous turbulence Chasnov J.R., Dynamics of Atmospheres & Oceans, 1996, 23/1-4 (183-192). In English. The decay of statistically homogeneous velocity and density fluctuations in a stably stratified fluid is considered. Over decay times long compared with the turbulence time scale but short compared with the period of internal gravity waves. Three distinct high Reynolds number similarity states may develop. These similarity states are a consequence of the invariance of the low wavenumber coefficients of the three-dimensional kinetic or potential energy spectrum, and their preferential development depends on the relative magnitudes of the initial kinetic and potential energy per unit mass of the fluid. When the turbulence has decayed over a time comparable with the period of the gravity waves, the three similarity states mentioned above are disrupted. Evidence will be presented of a new similarity state which then develops asymptotically. In this similarity state, the time decay exponent of the total energy per unit mass of the turbulence is reduced by a factor of two from its value for decaying isotropic turbulence, and the associated vertical integral scale approaches a constant independent of time. (Author)