Turbulence in the ocean: Development of investigations, evolution of ideas, and prospects

We present an analytic survey of a series of works devoted to the direct methods for the investigation of turbulence in natural basins originated under the guidance of A. G. Kolesnikov in the 50s. We describe the principal results of the early stage which formed the basis for future investigations. The main scientific directions of the latest period are also considered from the viewpoint of the development of Kolesnikov's ideas: investigation of the processes of generation and energy supply of small-scale turbulence, relationship between turbulence and the fine vertical structure and internal waves, and the mechanisms of vertical turbulent exchange in the ocean. A model of vertical exchange under the conditions of intermittent “source” turbulence is distinguished. We also discuss the directions of development and prospects of the investigation of turbulence. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Distinctive features of data processing for the side-looking radar of theSich-1 satellite

We show that the parameters of primary radar images obtained from theSich-1 satellite depend on the mode of survey and that the time dependence of the coefficient of correction of amplification in the channel of formation of radar signals is nonlinear. We propose to process radar images of the sea surface by using the so-called Bragg normalization of signals, which enables one to get a physically correct dependence of specific effective scattering surface on the elevation angle. We also consider a procedure of determination of the dependence of specific effective scattering surface of the sea on the wind velocity on the basis of the data accumulated by the side-looking radar of theSich-1 satellite. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Analysis of primary production in the Seto Inland Sea, Japan, using a simple ecosystem model

A simple model of lower trophic level ecosystem has been created to analyze possible environmental control of primary production in eight sub-areas of the Seto Inland Sea. The primary production rates observed by Hashimotoet al. (1997a) in these sub-areas are well reproduced by the model, including horizontal processes such as horizontal transport of nutrients and vertical processes such as vertical mixing, light intensity and sinking of particulate matter. Without taking account of horizontal processes the model also successfully reproduces the observed primary production rates in some areas, but if fails to reproduce those in the others. This shows that the relative importance of the horizontal transport on the primary production differs are by area. Two time scales,T _z andT _H, are introduced to explain this difference.T _z is a vertical cycling time of material, which is defined as the time during which the stock of the material in the water column is utilized for primary production;T _H is the horizontal transit time of the material. The relative importance of the horizontal process is well explained by theT _H/T _z ratio; that is, the horizontal transport process is important in the areas where this ratio is small. Further the possible mechanisms of nutrient supply for the primary production in each sub-area are investigated using this model.     

Vertical structure of geostrophic currents in the fields of density of water and hydrostatic pressure

We analyze geostrophic currents with nonmonotonic vertical profiles, of velocity and present the distributions of the density of water and hydrostatic pressure corresponding to possible types of the vertical kinematic structure. To prove the existence of the indicated complex layered structures, we use, the data of instrumentalin situ measurements of currents in the Black Sea and in the west part of the Tropical Atlantic. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Trapped bottom topographic waves over the inclined bottom

In the Boussinesq approximation, we study baroclinic topographic waves trapped by the flat meridional slope. The existence of these waves is explained by stratification, inclined bottom, and Earth's rotation. We deduce the evolutionary equation for the square of the envelope of a narrow-band wave packet of trapped waves. In the second order of smallness relative to the wave amplitude, we find the mean fields of velocity and density induced by the packet. It is shown that, in the limiting case of weakly nonlinear plane waves, the induced current is zonal. In the Northern hemisphere, depending on the slope of the bottom γ₁, the sign of the phase velocity σ/k (k is the zonal wave number) is either always positive (for γ₁>γ_1cr) or always negative (for γ₁<γ_1cr). If we neglect the vertical component of the Coriolis acceleration, then γ_1cr=0. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

North Brazil Current: Variability, stability and transport of waters

On the basis of the data of thein situ measurements of current velocities and other basic hydrophysical parameters (temperature and salinity) performed in the course of Cruise 41 of the R/VAkademik Vernadsky, we analyze the variability and stability of the North Brazil Current in winter. We also study the possibility of the influence of the baroclinic component of the horizontal drop of hydrostatic pressure on the vertical profile of the current velocity and estimate the intensity of the transport of waters. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Convection of salt fingers in theC-SALT region

We study possible mechanisms of mixing in the northwest part of the Tropical Atlantic (C-SALT) and show that homogeneous layers in the staircase structure can be observed across the entire frontal zone of the North Equatorial Countercurrent. In the central region of the frontal zone, one may observe horizontal motions of the upper parts of quasihomogeneous layers with respect to their lower parts and an essential role in the exchange processes is played by turbulence. The peripheral regions of the frontal zone are characterized by the presence of horizontal advection and isopycnic mixing. Far from the frontal interface, the principal contribution to the exchange processes is made by double diffusion. We demonstrate that, for the analysis of the vertical buoyancy fluxes caused by salt fingers, one can use both the Stern relation and the “law of 4/3”. Translated by Peter V. Malyshev and Dmitry V. Malyshev.     

Diffusion in the ocean with diffusion coefficient depending on the scale and concentration of impurities

We solve a nonlinear problem of diffusion from a concentrated source in a moving medium with diffusion coefficient depending on the scale of the phenomenon, time, and the concentration of impurities. We obtain a family of exact solutions of this problem, which can be regarded as a generalization of the class of linear problems of diffusion considered earlier for the conditions of the ocean and atmosphere by Roberts, Ozmidov, Obukhov,et al. Translated by Peter V. Malyshev and Dmitry V. Malyshev.     

Seasonal and spatial variability of the content of suspended organic substances in the active layer of the Black Sea

On the basis of the generalized data of multiannual observations (1985–1994), we analyze the seasonal variability of the vertical and spatial distributions and composition (C_sos, N_sos, C_sos/cha, and C/N) of suspended organic substances (SOS) in the shelf zone and in the upper active layer of the abyssal part of the Black Sea. The results of our analysis enable us to conclude that only a narrow coastal band of the shelf in the northwest and west parts of the sea suffers to an extremely pronounced anthropogenic impact, which manifests itself in a significant increase in the mass of suspended organic substances. The formation of new organic substances and, hence, the mass of suspended organic substances in these regions attain the level of eutrophic waters in the late-spring and summer periods. In the open-sea region, the anthropogenic impact is less pronounced and the spatial distribution of suspended organic substances is determined by the general dynamics of waters and the intensity of phytoplankton production. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Vertical transport in the Black Sea

Investigations of the vertical exchange coefficientK _z , considering turbulent and advective transport, are summarized. The values ofK _z are determined from the climaticT, S characteristics, heat and salinity fluxes, and the rate of the low-Bosporus water transformation over the entire Black Sea water column; namely, in the upper mixed layer, the active layer, the cold intermediate layer, the halocline, and in the deep and near-bottom waters. A characteristic for annual fluctuations ofK _z in the active layer is given; it is noted that the coefficient tends to grow in transit from the centre of the cyclonic gyre toward its periphery.Translated by V. Puchkin.     

A model of the evolution of vertical thermohaline inhomogeneities of an oceanic thermocline taking into account the effects of double diffusion

We construct a numerical model of the evolution of the structure of an oceanic thermocline in the presence of “salt-finger” convection. The model explains the formation of a piecewise homogeneous vertical structure of the temperature and salinity fields in the ocean. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Method for the evaluation of the spectral values of underwater quantum irradiance within the band of photosynthetically active radiation according to the depth of visibility of a Secchi disk

On the basis of the data of optical investigations performed in the Black Sea, we develop a method for the evaluation of the spectral values of underwater quantum irradiance within the band of photosynthetically active radiation according to the depth of visibility of a Secchi disk and the intensity of illumination of the sea in luxes. The method is based on the use of the correlations between the following optical parameters: of the vertical daylight attenuation factor α with the depth of visibility of a Secchi disk and of the spectral values of α(λ) within the band of photosynthetically active radiation with α(λ_min) for sea waters. This method is applicable in the winter-spring period when the seasonal thermocline is absent, the upper layers of the sea are mixed, and the vertical distribution of α is uniform. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Evaluation of the submarine discharge of karst waters in the region of Cape Aiya

For the submarine springs of underground water located in the karst cavities of Cape Aiya, we suggest a solution based on the modification of the model of flow rate of water and application of the formulas of mixing. We also give methodical recommendations helpful for the reliable determination of empirical parameters under thein situ conditions. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Analysis of the surface circulation in the Black Sea performed by using drifting buoys with satellite communications

We present the results of drift experiments with 14LOBAN-TM buoys carried out for the first time in the Black Sea in 1987–1997. We analyze the specific features of application of buoys in summer and winter. We present the main results of investigation of the Main Black Sea Current by drift methods and joint processing of drift contact and remote infrared observations. We demonstrate the possibility of enhancement of the quality of observations due to the application of SVPB drifters of new generation equipped with underwater sails and meters of atmospheric pressure in the near-surface atmospheric layer. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Essential properties of Boussinesq equations for internal and surface waves in a two-fluid system

Boussinesq equations describing motions of internal waves in a two-fluid system with the presence of free surface are theoretically derived, and the associated essential properties are examined in this study. Eliminating the dependence on the vertical coordinate from all variables, four equations constitute the Boussinesq model with two flexible parameters, z_u and z_l, which indicate the specific elevations, respectively, in the upper and lower fluids. Similar to the Boussinesq model for a single-layer fluid, z_u and z_l are determined by matching the linear dispersion relation with Lamb's solution. This determines the optimal model. In the analysis stage, this problem is classified into two cases, the thicker-upper-layer case and the thicker-lower-case case, to avoid the possible divergence of wave properties as the thickness ratio grows. Since there exist two modes of motions that may be excited, cases of both modes are separately analyzed. Linear characteristics including the amplitude ratios and normalized particle velocities are analyzed. Second-order harmonic waves are examined to validate nonlinear behaviors of present model. Results of linear and nonlinear investigations show that the present model indeed extends the applicable range of traditional Boussinesq equations.     

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     

A numerical model for the evaluation of the depth of penetration of two-dimensional turbulent convection

For a one type of temperature turbulent convection observed in the ocean, i.e., for the two-dimensional roller-type convection, we propose a model intended for the evaluation of the intensity and depth of penetration of convective motions as functions of a given heat flow from the sea surface and the temperature gradient in the thermocline. This model is based on the methods of the theory of turbulent jets and experimental data on the vertical distribution of temperature in the course of convection. The comparison of the calculated dimensionless values of the depth of penetration of the thermocline in autumn and winter shows a good qualitative agreement with the data ofin situ measurements. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Optimal statistical estimates of the vertical current velocity in the north-western Black Sea

The paper discusses a method for the statistical evaluation of the vertical current velocity componentV _z(z) using data provided by profilers. The calculation of theV _z(z) profiles involves the determination of the root-mean-square deviation of the error of determination of the vetical current velocity component at each level and the RMS deviation of the sample statistical variability of this quantity's estimates. ProfilesV _z(z) have been computed for the north-western Black Sea using three surveys, with the involvement of an OLT profiler. The computations have shownV _z(z) to have a two-layer structure, with zero being crossed in the main pycnocline. Such structure of the current velocity vertical component is consistent with the hydrodynamic model of the field of currents induced by buoyancy fluxes through the lateral boundaries of the basin. The availability of the zero values of the vertical current velocity in the pycnocline yields a tool for gaining insight into the mechanism controlling the emergence of the oxic/anoxic interface and areas with sharp vertical gradients of chemical and hydro-optical characteristics. Translated by Vladimir A. Puchkin.     

Hydrological structure of waters of the persian gulf according to the data of observations in 1992

We describe the hydrological structure of waters of the Persian Gulf and its seasonal variability according to the data of CTD surveys carried out in February–June 1992 in the course of the cruises of the NOAA R/VMt. Mitchell aimed at the analysis of the consequences of the ecological catastrophe caused by the spread of oil spots formed as a result of war operations in the Persian Gulf in 1991. Translated by Peter V. Malyshev and Dmitry V. Malyshev