Slow motions of a solid in a continuously stratified fluid

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 55–60, March–April, 1991.     

Breaking and cascade of internal gravity waves in a continuously stratified fluid

The evolution of a few large scale high frequency standing internal waves confined to a vertical plane is studied numerically. The growth of nonlinear interactions leads to a transfer of energy toward small vertical scales and lower frequencies: the result is a steep energy decrease due to wave breaking. Induced mixing is evaluated. A parametric forcing is also introduced in order to compare with laboratory experiments. Wave breaking also occurs but as opposed to the unforced case different phases are next observed: internal wave growth due to constructive forcing alternate with energy decrease.     

Vortex ring instability and collapse in a stably stratified fluid

Exploratory measurements of the effect of a stable continuous vertical stratification on horizontally propagating vortex rings show that the rings are subject to a stratification induced instability and subsequent collapse, which forms a well mixed intrusion. For initial ring Froude numbersF ₀=U ₀/Nd ₀=1.0–2.0, instability and collapse occurs when the ring Froude number has decreased to a value in the range 0.6–1.0.     

Evolution of the diffusion-induced flow over a sphere submerged in a continuously stratified fluid

The problem of the stabilization of the diffusion-induced flow over a sphere submerged in a continuously stratified fluid is solved using both asymptotic and numerical methods. The analytical solution describes the structure of the main convective cells, including thin meridional jets flowing along the surface and plumes spreading from the flow convergence regions above the upper and lower poles of the sphere which gradually return the fluid particles to the neutral buoyancy horizon. The total width of the flows adjacent to the surface exceeds the thickness of the salinity deficit layer or the density boundary layer. The numerical solution of the complete problem in the nonlinear formulation describes the main convective cells and two systems of unsteady integral waves formed in the vicinity of the sphere poles. At large times, out of the entire system of internal waves only those nearest to the neighborhood of their horizon of formation remain clearly defined. The calculated flow patterns are in agreement with each other and the data of shadow visualization of the stratified fluid structure near a submerged obstacle at rest.     

Nonstationary waves in the continuously stratified flow of a fluid of finite depth

A theoretical investigation is made of the development of linear two-dimensional waves in a continuously stratified flow of an ideal incompressible fluid. The waves are generated by pressures that are independent of time and that are applied at time t=0 to a bounded region on the free surface of an initially undisturbed flow. The stationary internal waves generated by such a disturbance have been investigated in [1–3]. The nonstationary waves in a continuously stratified fluid that are generated by initial disturbances or periodic surface pressures applied to the entire free surface have been studied in [4–7] in the absence of a slow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 87–93, November–December, 1976.     

Hydrodynamics of natural oscillations of neutrally buoyant bodies in a layer of continuously stratified fluid

The flow patterns induced by floats of different shapes (sphere, short and long cylinders) freely sinking to the neutral-buoyancy horizon in a continuously stratified fluid are investigated using optical methods. General flow elements, both large-scale (waves, vortices, hydrodynamic wake) and fine-scale (boundary layers, extended autocumulative jets), are distinguished. For large times, the float oscillation frequencies are of the order of or greater than the buoyancy frequency of the medium. This indicates the significant effect of the induced flows on the motion of the float.     

Shear instability of flows of a stratified ideal fluid of finite depth

A linear analysis is made of the stability of flows, stratified with respect to depth, of an ideal liquid of finite depth with a Helmholtz velocity profile. Apart from a Kelvin-Helmholtz wave, additional unstable modes are also discovered. Analytical expressions are obtained for the neutral curve of these modes. Their nature is discussed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 176–179, November–December, 1988.The author is grateful to V. I. Klyatskin and L. Ya. Lyubavin for their interest in the study and for fruitful discussions.     

Internal waves arising in the presence of the unsteady motion of a source in a continuously stratified fluid

A general approach to the investigation of linear internal and surface waves in a stably stratified fluid, arising from different types of perturbations, is presented in [1]. The methods of calculation of the internal waves generated by the motion of a mass source are developed for particular cases of steady horizontal motion in a continuously stratified fluid in [2] and arbitrary motion in an unbounded exponentially stratified fluid in [3]. Internal waves generated by other types of perturbations have also been investigated but only for particular cases of motion (see, for example, [4]). This paper presents a method for the calculation of unsteady, linear, internal gravity waves arising in an inviscid incompressible fluid with continuous stable stratification.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 122–130, July–August, 1985.     

Plane problem of wave motions occurring in a continuously stratified fluid during the flow around a submerged body

The plane stationary problem of wave motions occuring in the flow of a uniform inviscid incompressible gravity fluid with an arbitrary continuous (stable) change in density with depth around submerged sources and sinks of equal intensity is investigated in a linear formulation. An analysis of the structure of the wave motion in a flow with an arbitrary density change is performed in [1].Paper presented at the First Soviet-American Symposium on Internal Waves in the Ocean, Novosibirsk, December 3–8, 1976.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 148–152, July–August, 1978.     

The development of three-dimensional waves generated by perturbations of varying intensity in a flow of continuously stratified fluid

An analysis is made in the linear formulation of the three-dimensional structure of unsteady waves created in a flow of continuously stratified fluid by a region of pressures which are harmonic with respect to time.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 71–77, November–December, 1984.     

Parametric excitation of internal waves in a continuously stratified liquid

A study is made of the parametric excitation of internal waves in a continuously stratified liquid in a vessel executing oscillations in the vertical direction. It is shown that vertical oscillations of the vessel will excite oscillatory modes with eigenfrequencies equal to half of the oscillation frequency of the vessel.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 167–169, September–October, 1982.I thank S. V. Nesterov for interest in the work.     

Horizontal submerged jet in a stratified fluid

The problem of jet flow excited in a viscous density-stratified fluid by a point source of momentum acting horizontally is considered. Simplified asymptotic equations are obtained in the boundary layer approximation. It is shown that the vertical velocity component is small and the motion in the jet has a layered structure. The longitudinal velocity distributions in the jet are measured experimentally. It is shown that these distributions are affine and can be satisfactorily approximated by Schlichting's well-known boundary layer solution for a round submerged jet in a fluid uniform with respect to density.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.6, pp. 10–16, November–December, 1993.We are grateful to I. A. Filippov for assisting with the experiments.     

Hydrodynamics of a sphere in a stratified fluid

The flow pattern around a sphere moving at constant velocity in a fluid with an exponential density distribution is investigated by optical methods. The thin density boundary layer forming the high-gradient envelope of the wake is distinguished as one of the elements of the structure. The symmetry properties of the flow are investigated. The limits of applicability of the traditional approximation of weak stratification in the problem of excitation of attached internal waves are noted.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 3–9, January–February, 1989.     

Three-dimensional wake in a stratified incompressible fluid

On the basis of the boundary layer equations in the linear approximation and the equations for the single-point second-order moments of the velocity and temperature fields closed by means of the semiempirical Kolmogorov-Rotta hypotheses, the problem of the development of a wake behind an axisymmetric body in a temperature-stratified incompressible fluid flow is solved using the integral relation method. The anisotropic nature of the expansion of the wake behind the body is established.Almaty. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 71–77, July–August, 1996.