Vaisala-Brunt Frequency Research Articles

The sloshing of stratified liquid in a two-dimensional rectangular tank

The sloshing of inviscid liquid of stratified density in a rectangular tank is analyzed. As the flow is no longer irrotional, the governing equation is found to be quite different from the Laplace equation used for the liquid of constant density. In particular it contains terms of mixed temporal and spatial derivatives. The problem is solved based on the variable separation method and Laplace transform for the constant Vaisala-Brunt frequency. It is found that the stratification of density may have small effects on those natural frequencies associated with the constant density, but many new natural frequencies have appeared as a result of its effect.

MKdV Equation for the Amplitude of Solitary Rossby Waves in Stratified Shear Flows with a Zonal Shear Flow

AbstractIn this paper, modified Korteweg-de Vries (mKdV) equations for the amplitude of solitary Rossby waves in stratified fluids with a zonal shear flow are derived by using a weakly nonlinear method. It is found that the coefficients of mKdV equations depend not only on the β effect and the Vaisala-Brunt frequency, but also on the basic shear flow.

The near field of internal waves after the moving area of atmospheric pressures

The near wave field generated by the travelling atmospheric pressure zone over a stratified fluid is studied within the framework of the linear theory of long waves allowing for the Coriolis force. The exact solution of the problem as a set of single integrals is deduced for the model distribution of pressures. The characteristics of the near wave field have been computed for the Vaisala-Brunt frequency profile takeu from observations. Their dependences on the geographical latitude and the wave generator travelling rate are analysed.

Generation of long internal waves in the ocean by a moving pressure zone

The generation of plane internal waves in a continuously stratified ocean by a steadily moving anomaly of the atmospheric pressure is studied in a linear statement using a quasi-static approximation. Quantitative estimates for the parameters of internal waves in the wake are obtained for the average distribution of the Vaisala-Brunt frequency in the Caribbean Sea.

On the possible generation of low-frequency microseisms by internal waves in the ocean

The conditions under which the interaction between internal waves and the rough bottom topography may be the reason for synchronous fluctuations of pressure at the bottom have been studied. Disturbances of the depth are assumed to be small compared with the mean depth of the ocean, and the Vaisala-Brunt frequency is constant. It is shown that synchronous fluctuations of pressure exist with a frequency equal to that of internal waves. The amplitude of pulsations can be approximately an order lower than the amplitude of fluctuations generated by standing surface waves. However, local maxima can exist in the low-frequency minimum of the spectrum of microseisms (in the range of 20–1000 s).

Resonance excitation of internal waves by fluctuations of the atmospheric pressure and the tangential wind stress

Resonance excitation of internal waves by running waves of the atmospheric pressure and the tangential wind stress in a continuously stratified rotating ocean is studied in a linear statement. A comparative analysis of the rates of the increase in amplitude of resonance-excited waves for these external disturbances is carried out numerically for the case of the average distribution of the Vaisala-Brunt frequency in the Caribbean Sea.

On the small vibrations of a stratified capillary liquid

An initial-boundary value problem is considered for the equation which describes the vibrations of an ideal, stratified liquid occupying the lower half space in the Boussinesq approximation. The Vaisala-Brunt frequency is assumed to be constant. The boundary condition on the planar boundary is a combination of the conditions on the solid cover and the free surface and, moreover, the latter contains a term which takes account of capillarity. A formulation of the problem is given, its solution is constructed and its behaviour at long times is investigated.

Generation of small-scale turbulence in the Antarctic circumpolar current

A functional connection between probability of turbulence generation by shear instability in current velocity and Vaisala-Brunt frequency is obtained. Examples are cited of sections with isoclines of probable turbulence generation in the 30–500-m layer in the Antarctic circumpolar current north of Kergelen island.

Generation of gravity waves by inhomogeneous heating of the atmosphere

Local variation of atmospheric heating which might occur in inhomogeneities of various constituents such as ozone or molecular oxygen may generate gravity waves. These perturbations are induced by the terminator crossing constituent inhomogeneities of short lifetime. The quasi-point heating model developed here shows that the largest amplitude must appear vertically above the source, where the perturbation frequency is close to the Vaisala-Brunt frequency. Numerical calculations not band limited in the frequency suggest several characteristics of the perturbation.

Nonlinear stationary internal and surface waves in shallow seas

It is known that propagation of the two-dimensional stationary internal gravity waves of arbitrary amplitude can be described by a certain nonlinear equation which contains two arbitrary functions. It is shown that for the solitary waves and for infinitesimal periodic internal waves, these two unknown functions are described by the Vaisala-Brunt frequency. For nonlinear periodic waves with weak nonlinearity and dispersion approximation there is an arbitrary function of the transversal coordinate giving rise to a current. By the additional assumption that this current is reduced to zero, the phase velocity of a nonlinear periodic wave has a unique connection with the amplitude. Further, it is shown that additivity of wave motions of different modes takes place in the present approach. Two examples of model stratification are considered. A detailed numerical analysis is performed, illustrating propagation of internal waves, based on experimental data for the Arkona basin in the Baltic Sea. The local Richardson numbers have been calculated. It is shown that Ri < 1/4 can occur for solitary waves which may cause organization of some turbulent regions. DOI: 10.1111/j.2153-3490.1979.tb00892.x

Nonlinear stationary internal and surface waves in shallow seas

It is known that propagation of the two-dimensional stationary internal gravity waves of arbitrary amplitude can be described by a certain nonlinear equation which contains two arbitrary functions. It is shown that for the solitary waves and for infinitesimal periodic internal waves, these two unknown functions are described by the Vaisala-Brunt frequency. For nonlinear periodic waves with weak nonlinearity and dispersion approximation there is an arbitrary function of the transversal coordinate giving rise to a current. By the additional assumption that this current is reduced to zero, the phase velocity of a nonlinear periodic wave has a unique connection with the amplitude. Further, it is shown that additivity of wave motions of different modes takes place in the present approach. Two examples of model stratification are considered. A detailed numerical analysis is performed, illustrating propagation of internal waves, based on experimental data for the Arkona basin in the Baltic Sea. The local Richardson numbers have been calculated. It is shown that Ri < 1/4 can occur for solitary waves which may cause organization of some turbulent regions. DOI: 10.1111/j.2153-3490.1979.tb00892.x

Bounds for initial growth rates on a non-geostrophicf-plane with lateral walls

Bounds for the growth rate in the non-geostrophic non-hydrostatic baroclinic instability problem of Eady, with or without lateral walls is considered. An application of Fourier transforms and Sturm Liouville contraction shows that the growth rate cannot exceed the largest positive root of the equation ? 4 + ( N 2 ? ¼ n 2 ? 2 ? ¼ n 2 f 2 = 0 where n denotes the vertical wind shear. N is the Vaisala-Brunt frequency. A simple physical argument is shown to give the same result. DOI: 10.1111/j.2153-3490.1971.tb00557.x

Bounds for initial growth rates on a non-geostrophic f-plane with lateral walls

Bounds for the growth rate in the non-geostrophic non-hydrostatic baroclinic instability problem of Eady, with or without lateral walls is considered. An application of Fourier transforms and Sturm Liouville contraction shows that the growth rate cannot exceed the largest positive root of the equation ? 4 + ( N 2 ? ¼ n 2 ? 2 ? ¼ n 2 f 2 = 0 where n denotes the vertical wind shear. N is the Vaisala-Brunt frequency. A simple physical argument is shown to give the same result. DOI: 10.1111/j.2153-3490.1971.tb00557.x