Investigation of transformations of barotropic tides in the coastal zone

Within the framework of the linear theory of long waves, we perform the numerical investigation of transformations of a barotropic diurnal tide in the process of its motion from the deepwater region of the sea into the region of continental slope and shelf zone at any angle to the coast line. For a linear profile of the bottom of the continental slope and shelf, we establish dependences of the amplitudes and velocities of waves on the direction of propagation of the tidal wave and the latitude of the place. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Correlation between the intensity of tsunami in the Black Sea and the magnitude of underwater earthquakes

We perform the analysis of tsunami waves in the shelf zone of the Crimean peninsula generated by underwater earthquakes whose epicentres are located near the lower boundary of the continental slope. For this purpose, we use a one-dimensional nonlinear dissipative numerical model of long waves. The investigated distributions of the depth of the basin correspond to four points of the south coast of the Crimean peninsula. We use the empirical dependences of parameters of the sources of tsunami waves on the magnitude of the earthquake obtained earlier for the Pacific Ocean. It is shown that the height, vertical climb, and duration of tsunami waves increase with the magnitude of the earthquake. For equal magnitudes of the earthquake, the highest tsunamis on the south coast of the Crimea are observed between Alushta and Yalta. We also deduced a generalized regression dependence of the height of tsunami waves near the coast on the magnitude of the earthquake. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Numerical investigation of the influence of various factors on the propagation and transformation of solitary waves in the sea

For various stratifications and different types of bottom patterns we study the transformations of solitary perturbations of density appearing in the depth of the sea. In the two-dimensional case, under the assumption that the average dynamic characteristics weakly vary in time as compared with the wave characteristics, we deduce the equations for mean currents and waves taking into account vertical and horizontal viscosity and the diffusion of density. Numerical examples show that the stratification, bottom topography, nonlinearity, mean currents, and dissipation strongly affect both the process of splitting of a solitary wave into wave trains and their amplitude and length. The wave currents exhibit the oscillatory (train-like) character. It is emphasized that, in the case of propagation of solitary perturbations of density with dissipation, it is also important to take into account the combined influence of nonlinearity, currents, bottom topography, and stratification. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Generation of internal waves by a barotropic tide in the coastal zone

Within the framework of the linear theory of long waves, we study internal waves generated by a barotropic tide in a two-layer ocean of variable depth taking into account the influence of the Coriolis force. Barotropic waves run over an extended unevenness of the bottom at an arbitrary angle. This unevenness is regarded as a model of the continental slope and shelf. We establish the dependences of the amplitudes of generated internal waves on the angle of incidence of the barotropic tide, topography of the bottom, and stratification. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Relatioship between the intensity of tsunami and the location of the epicentre of underwater earthquakes near the continental slope of the South Coast of Crimea

Within the framework of the nonlinear theory of one-dimensional long waves, we performed the numerical analysis of the dependence of the intensity of tsunami on the shelf of the South Coast of Crimea on the location of the epicentre of underwater earthquakes near the continental slope of the basin. The calculations were carried out for the parameters of the model corresponding to the Yalta tsunami of September 12, 1927. It is shown that, for the same magnitude of the earthquake, the smaller the distance from its epicentre to the coastal line, the lower tsunami waves in the coastal zone and the smaller their vertical run-up. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Generation of internal waves in the sea by local perturbations of wind and density flows on the surface

On the basis of a nonlinear model taking into account viscosity, density diffusion, and currents, we perform the numerical analysis of propagation of perturbations formed in the abyssal part of the Black Sea as a result of the action of tangential wind stresses or density flows in the form of a strip on the sea surface. It is shown that, in the course of time, in the region of the bottom slope, these perturbations generate a train of waves in the sea, which causes oscillations of the fields of density and currents. There are some differences between the generation of internal waves by the flows of density and the wind. Unlike the wind action, in the presence of flows of density in the upper layer in the region of the strip, the initial period of generation is characterized by the formation of intense perturbations without train structure. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Generation of internal waves in the region of a bottom ridge with continuously varying height

Internal waves generated by a barotropic wave impinging on a bottom ridge with continuously varying height are studied within the framework of the linear theory of long waves. We consider the case where the diurnal tide travels at an arbitrary angle to the axis of the ridge located in the area of a geostrophic flow caused by tilting of the free sea surface and the interface of a two-layer ocean. We study the dependences of the amplitudes of internal waves on the velocity of the geostrophic flow, the direction of propagation of the barotropic tide, and the geometry of the ridge. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Generation of long waves in a basin of variable depth in the process of formation of a region of perturbations of atmospheric pressure

We perform the numerical analysis of the long-wave response of the free surface of a fluid in a basin of variable depth to the formation of an anomaly of the baric field for a finite period of time. In numerical experiments, we use the distribution of depths typical of the south coast of the Crimea. We also study the dependence of the dynamics of the sea level in the zone of the baric anomaly and in the shelf zone on the space and time scales of local changes in the field of atmospheric pressure in the open part of the basin. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Generation of internal waves in a three-layer ocean

Within the framework of the linear theory of long waves taking into account the action of the Coriolis force, we solve the problem of generation of internal waves by a barotropic tide impinging on a bottom irregularity of the sea-ridge type. The cross section of the ridge is assumed to be rectangular and the stratification of the ocean is regarded as stepwise with two thermoclines (three-layer model). We study the dependences of the characteristics of generated waves on the parameters of stratification and the period of the impinging barotropic tide. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Generation of geostrophic vortices caused by displacements of a part of the bottom of a basin

Within the framework of the general linear statement of the problem, we determine the conditions of generation of a geostrophic current in a layer of uniform rotating fluid for small displacements of the bottom of a basin. We deduce an equation relating the equilibrium shape of the surface of the fluid with residual deformations of the bottom and find its general solution. It is shown that the geostrophic current is generated only in the presence of residual deformations. We present numerical estimates of the intensity of the generated geostrophic formation for a model of motion of the bottom. The investigated mechanism of generation of geostrophic vortex fields is especially efficient in the shelf zone of the ocean. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Run-Up of a Solitary Tsunami Wave on a Sloping Coast

Within the framework of the nonlinear theory of long waves, we perform the numerical analysis of the one-dimensional run-up of solitary tsunami waves upon a plane sloping coast. We study the dependences of the run-up heights on the parameters of waves at the entrance of the shelf zone and on the slope of the coast. The run-up heights of tsunami waves are estimated for the bottom topography typical of the south coast of the Crimean Peninsula. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 4, pp. 11–18, July–August, 2005.     

Evolution of waves induced by periodic variations of pressure in a bounded basin of variable depth

Within the framework of the linear theory of long waves, we study the evolution of a wave process caused by the action of surface pressure periodically varying in time in a bounded basin of variable depth without vertical walls. We assume that the basin is filled with a homogeneous liquid nonperturbed at the initial time and take into account the action of dissipative forces. We obtain the analytic solution of the posed problem. It is used to perform the detailed analysis of the influence of the dissipative forces and the frequency of perturbing pressure on the characteristics of the process of evolution of waves. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Formation of a circulation in the quasiisopycnic model of the Black Sea taking into account the stochastic nature of the wind stress

We discuss the results of numerical experiments carried out within the framework of a new version of the quasiisopycnic model of the Black Sea [1, 2]. We take into account the stochasticity of the wind stress, vertical shift of the flow velocity in the upper quasihomogeneous layer, and diapycnic mixing. We generalize the procedure of “convective adjustment,” which enables us to consider the propagation and transformation of waters of the Sea of Marmara. It is shown that the consideration of these factors enables one to determine the structure and seasonal variability of hydrothermodynamic fields in the sea more correctly. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Turbulent diffusion of impurities in the ocean in the presence of internal waves

We study the influence of baroclinic tidal waves on the diffusion of an impurity spot in a continuously stratified fluid. The equation of turbulent diffusion is solved numerically by taking into account the wave currents. We establish the dependences of the characteristics of the diffusion process on parameters of baroclinic waves and the location of the impurity spot. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Seiches in a circular basin of variable depth

Free waves (seiches) in a circular basin of variable depth are studied numerically within the framework of the linear theory of long waves taking into account the action of the Coriolis force. We determine the frequencies of axisymmetric and circular waves, study the structure of the modes of elevation of the free surface and wave velocities, and establish the dependences of the phase velocities of circular waves on the number of mode and wavelength. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

On the influence of a diurnal baroclinic tide on the diffusion of an impurity

We investigate the influence of baroclinic tidal waves on the diffusion of an impurity spot in a continuously stratified liquid. The equation of turbulent diffusion is solved numerically by taking into account the wave currents. We establish the dependences of the characteristics of the diffusion process on the parameters of the baroclinic wave and the location of the impurity spot. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Distributed thermoprofilometers and their capabilities in oceanographic investigations

We describe the principles of design of distributed thermoprofilometers and analyze their characteristics and the required hardware, algorithms, and software. The capabilities of these instruments in the investigation of temperature fields, vertical displacements, and the parameters of internal waves are evaluated. The results of measurements and numerical calculations are presented. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Manifestations of water dynamics in the coastal zone in the field of breaking of wind waves

In the coastal zone, as a result of mixing of waters, it is difficult to identify turbulent phenomena with a spatial scale of 0.1–1 km accompanied by strong vertical flows according to the data of measuring temperature. On the basis of the data of direct measurements, it is shown that turbulent structures are well pronounced in the field of breaking of wind waves. We deduce empirical estimates of the response of the intensity of wave breaking to the magnitude of divergence of the current and develop a theoretical model of the influence of inhomogeneities of currents on wave breaking capable of describing the experimental data. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Modelling of the ecosystem of the Black-Sea shelf zone near the estuary of the Danube

We analyze the results of numerical calculations performed according to the three-dimensional interdisciplinary model of an ecological system of the Black-Sea shelf zone near the estuary of the Danube. The complete system of equations of hydrothermodynamics is solved together with transport equations of the advection-diffusion-reaction type used to describe the transformation of a substance (nitrogen) between the components of the characteristic vectors of the ecosystem: plankton, detritus, and biogenic elements (nitrates). We describe the distinctive features of the circumcontinental distribution of components obtained as a result of numerical experiments and present arguments for the conclusion that the ecosystem of the Danube estuary water area plays the role of a buffer zone between the press of the Danubian biogenic pollutions and the neighbouring areas of the shelf zone and open sea. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Incidence of flexural gravitational waves on the line of contact of two floating ice plates of different thickness

We analyze the influence of a rift in an ice field on the propagation of flexural gravitational waves in a basin of finite constant depth. The ice cover is simulated by two floating semiinfinite elastic plates of different thickness. We studied the dependence of the amplitude coefficients of reflection and transmission of waves incident on the rift on the frequency of running waves, the thickness of ice on both sides of the rift, and the type of contact boundary conditions at the rift. Translated by Peter V. Malyshev and Dmitry, V. Malyshev