Effect of generator shape on the structure of internal wave beams in a uniformly stratified fluid

The generation of internal waves by vibrating cylinders with cross sections of various shapes is studied experimentally. It is shown that at large distances from the generator, the profile of the perturbation amplitude of the density gradient can be calculated with satisfactory accuracy using the theory for an equivalent circular cylinder. It is found that at short distances from the generator, its shape has a significant effect on the profile of the generated waves.     

Internal wave generation by a fountain in a stratified fluid

The purpose of the study is the direct numerical and theoretical modeling of fountain dynamics in a fluid with density stratification in the form of a pycnocline. The fountain is formed as a vertical jet penetrates through the pycnocline. In numerical simulation the jet flow is initiated by means of preassigning a boundary condition in the form of an upward-directed laminar flow of a neutral-buoyancy fluid with an axisymmetric Gaussian velocity profile. The calculations show that at a Froude number Fr greater than a certain critical value the flow becomes unstable and the fountain executes self-oscillations accompanied by internal wave generation in the pycnocline. Depending on Fr, two self-oscillation modes can be distinguished. At fairly low Fr the fountain executes circular motion in the horizontal plane, in the vicinity of the center of jet, its shape remaining almost invariant. In this case, internal waves in the form of unwinding spirals are radiated. At fairly high Fr another mode predominates, when the fountain top chaotically “strays” in the vicinity of the center of the jet and, periodically breaking down, generates wave packets propagating toward the periphery of the computation domain. In both cases, the main peak in the frequency spectrum of the internal waves coincides with the fountain top oscillation frequency which monotonically decreases with increase in Fr. In numerical simulation the Fr-dependence of the fountain top oscillation amplitude is in good agreement with that predicted by the theoretical model of the concurrence of the interacting modes in the soft self-excitation regime.     

Internal wave radiation by a turbulent fountain in a stratified fluid

Large eddy simulation is applied to model a fountain in a density-stratified fluid. The fountain is formed, as a vertical turbulent jet penetrates through a pycnocline. The jet flow is initiated by the formulation of a boundary condition in the form of an upward neutral-buoyancy fluid flow with the Gaussian axisymmetric mean-velocity profile and a given fluctuation level. It is shown that at a Froude number Fr higher than a certain critical value the fountain executes self-oscillations accompanied by internal wave generation within the pycnocline. The predominant self-oscillation mode is axisymmetric, when the fountain top periodically breaks down generating internal wave packets traveling toward the periphery of the computation domain. The characteristic frequency of the internal waves coincides with that of the fountain top oscillations and monotonically decreases with increase in Fr. The Fr-dependence of the fountain top oscillation amplitude obtained in the numerical solution is in good agreement with the predictions of the theoretical Landau model for the instability mode in the soft self-excitation regime.     

Internal wave structure in a three-layer fluid with a stratified middle layer

The behavior of internal waves in a vertically bounded channel differs considerably from the wave motion in an infinite stratified fluid. In [1] the phase structure of the internal waves in an exponentially stratified layer of fluid between rigid horizontal planes was experimentally and theoretically investigated. A characteristic feature of such a channel is the boundedness of the phase and group velocities of each mode. Below, the case of an exponentially stratified channel between layers of homogeneous unbounded fluid is considered.In conclusion, the authors wish to thank A. T. Onufriev for his interest in their work.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 128–132, May–June, 1987.     

Internal wave field generated by a source at rest in a moving stratified fluid

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 58–61, July–August, 1989.     

TWO-DIMENSIONAL ALGEBRAIC SOLITARY WAVE AND ITS VERTICAL STRUCTURE IN STRATIFIED FLUID

IntroductionItis known thatthere exists a special kind of solitary waves—the algebraic solitary waveas the disturbance range is close to the scale of vertical variation of density in thecontinuously stratified fluid.The algebraic solitary wave is governe…     

Linear theory of the propagation of internal wave beams in an arbitrarily stratified liquid

Beams of harmonic internal waves in a liquid with smoothly changing stratification are calculated in the Boussinesq approximation taking into account the effects of diffusion and viscosity. A procedure of local reduction of the beam in a medium with an arbitrary smooth stratification to the case of an exponentially stratified liquid is constructed. The coefficient of energy losses in the case of beam reflection on the critical level is calculated. Parameters of internal boundary flows with split scales of velocity and density that are formed by a wave beam on discontinuities of the buoyancy frequency and its higher derivatives are determined. Institute of Problems of Mechanics, Russian Academy of Sciences, Moscow 117526. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 5, pp. 88–98, September–October, 1998.     

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.     

The drag on a vertically moving grid of bars in a linearly stratified fluid

Experiments in Fluids - We present the results of an investigation of the drag force on a horizontal grid of bars moving vertically through a stratified fluid. A novel approach was used to...     

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.     

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.     

Micro-scale instability in a continuously stratified fluid

Experimental observations of small-scale structures caused by flow instabilities at layers of high density gradient in the wake behind a cylinder in a fluid with a continuous salt concentration stratification are reported. In the density wake it is possible to discern a number of structures such as wedge-like structures or cusps; small-scale instabilities (breakers) in the zones of interaction of attached internal waves and the high-gradient wake envelope; small-scale instability of the density boundary layer with a complicated density gradient pattern superimposed on a smooth velocity profile, and small-scale wake structures behind attached vortices in the case of a closed (central) wake envelope.Translated from Izvestiya RossiiskoiAkademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 3–10, May–June, 1995.     

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.     

Effect of rotation on frequency characteristics of a truncated circular conical shell

In the current dynamic model of rotating truncated conical shells, the expressions of centrifugal and coriolis accelerations and initial hoop tension were incomplete and some terms were missing. This might cause the frequency characteristics of rotating conical shells to be overestimated (or underestimated). Therefore, the effects of rotation upon frequency characteristics of rotating truncated conical shell are studied in the paper. Accurate expressions of centrifugal and coriolis accelerations and initial hoop tension are derived, and then a modified dynamic model for the rotating truncated conical shell is presented. The generalized differential quadrature method is utilized to obtain the natural frequencies. The influences of various boundary conditions and rotating speed on the free vibration of the conical shell are discussed in detail. Through comparison analysis, the errors in current model are also pointed out.     

Oscillations of cylinders in a linearly stratified fluid

The paper studies theoretically and experimentally hydrodynamic loads that act on horizontally placed cylinders of rhombic and square cross sections, oscillating harmonically in a linearly stratified fluid. An analytical solution is found with the use of affine similitude. Hydrodynamic force coefficients were evaluated experimentally from Fourier transforms of records of damped oscillations in a time—frequency region. It is shown that for polygonal contours, hydrodynamic loads change abruptly if the slope of the polygon sides coincides with the slope of the internalwave group velocity vector.     

Formation of a tripolar vortex in a stratified fluid

This paper reports on an experimental study of vortices in a stratified fluid. The vortices were generated by two different stirring devices, viz. a rotating sphere and a rotating bent rod. It was found that the vortices created with the rotating sphere are mostly axisymmetric and stable, whereas the vortices produced with the bent rod generally show instabilities, under certain conditions leading to the formation of a tripolar vortex. This report concentrates on this tripolar structure and presents quantitative information about the flow obtained through streak photography of tracer particles.