Transformation of the Level of Barotropic Ocean under an Elliptic Region of Disturbances of a Baric Field

We study elevations of the level of a homogeneous ocean caused by a large-scale elliptic anomaly of the field of atmospheric pressure and determine the conditions under which Earth's rotation and the asymmetry of the region of disturbances of the baric field lead to significant deviations of the ocean level from its values given by the law of inverted barometer. Our investigation is based on the numerical analysis of the integral solution of the linear problem. It is shown that the deviations from the law of inverted barometer are especially pronounced in shallow-water regions, at high latitudes, and for strongly asymmetric regions of disturbances of atmospheric pressure.     

Spectra of the Black-Sea tsunamis

We perform the analysis of the time spectra of four tsunamis generated in the Black Sea by the earthquakes of 26.07.1927, 11.09.1927, 26.12.1939, and 12.07.1966. For the analysis of the spectra, we used digitized marigrams obtained for 12 points of the Black-Sea coast. The obtained spectra are, as a rule, multimode and have 1–4 spectral maxima. One maximum corresponds to the periods typical of tsunami waves and the other maxima correspond to the oscillations of the sea level with lower frequencies. It seems likely that the events of tsunami are accompanied by low-frequency oscillations of the level caused by the atmospheric forcing, seiches, or other factors. In numerous cases, the oscillations from the predominant energy range lie outside the characteristic range of periods of the tsunami waves. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 5, pp. 21–30, September–October, 2007.     

Some General Properties of Transverse Motions of the Geostrophic Front

Within the framework of the reduced-gravity model of the ocean taking into account the effect of friction in the Rayleigh form, we study the two-dimensional problem of nonlinear motions of a subsurface front of finite width. We consider the conservation laws and the character of motion of the center-of-mass of the cross section of the front and their variations caused by the losses of energy. For fields with special structure, the problem is reduced to the solution of a system of nonlinear ordinary differential equations. It is shown that the initially geostrophic frontal current decays with time according to a power law. The deviations of the initial state of the front from the state of geostrophic balance result in the generation of superinertial oscillations of the hydrodynamic fields.     

Numerical modelling of tsunami propagation in the open Black Sea

This paper focuses on the numerical modelling of tsunami propagation in the open Black Sea. Two types of numerical models are discussed: a model for the radial propagation of long waves and an evolutionary finite-difference prognostic model. Experimentally derived numerical data on the model source of tsunamis are reported. Translated by Vladimir A. Puchkin.     

The directional radiation of long waves from bottom deformations of finite duration

The process of generation of two-dimensional (2D) wave motions during small elliptical displacements of the bottom which occur for a finite time interval is considered within the framework of the linear theory of long waves in a basin of constant depth. The spatial structure and the amplitudinal and energy characteristics of the emerging directional surface wave are analysed for bottom deformations of a special form.Translated by Mikhail M. Trufanov.     

Nonlinear inertial oscillations of a multilayer eddy: An analytical solution

Nonlinear axisymmetric oscillations of a warm baroclinic eddy are considered within the framework of an reduced-gravity model of the dynamics of a multilayer ocean. A class of exact analytical solutions describing pure inertial oscillations of an eddy formation is found. The thicknesses of layers in the eddy vary according to a quadratic law, and the horizontal projections of the velocity in the layers depend linearly on the radial coordinate. Owing to a complicated structure of the eddy, weak limitations on the vertical distribution of density, and an explicit form of the solution, the latter can be treated as a generalization of the exact analytical solutions of this form that were previously obtained for homogeneous and baroclinic eddies in the ocean.     

Baroclinic seiches in rotating basins of variable depth in the case of two-layer density stratification

We solve a plane problem of linear baroclinic seiches in closed rotating basins of variable depth with two-layer density stratification. In the long-wave approximation, we get a boundary-value problem for a system of ordinary differential equations and propose a numerical procedure for finding internal seiches. The analytic solutions of the problem are obtained for a basin of constant depth. The numerical analysis of seiches is performed for the distributions of depth corresponding to the zonal and meridional sections of the Black Sea and model basins including the cases of a shelf zone and an underwater ridge. It is shown that the baroclinic seiches become more intense in shallow-water regions and that the intense longshore currents caused by Earth’s rotation are formed in the shelf zones and over the underwater ridges.     

Stationary waves in the flow of a homogeneous fluid with vertical shear of the velocity

A plane problem of free stationary gravitational waves in a horizontal current with vertical shear of the velocity is studied in the linear statement. The determination of the parameters of waves is reduced to the solution of the Sturm–Liouville boundary-value problem. For some vertical distributions of current velocity, we obtain analytic solutions. We propose a numerical algorithm for finding the parameters of waves. On the basis of the performed analysis, we establish the possibility of existence of stationary surface waves in currents for certain ranges of the Froude number. As the Froude number decreases, the waves become shorter, which leads to a faster attenuation of waves disturbances with depth. Under the actual conditions, the waves are short and suffer the influence of shear currents only in the subsurface layer of the ocean.