The reciprocity principle in acoustics is known for a long time and has a practical application. The reciprocity relationship is asymptotic one and is true for linear processes in heterogeneous media in the presence reflecting, absorbing or impedance boundaries. Long wave ocean processes (in particular, tsunamis) have features that are not essential in acoustics. These include a significant inhomogeneity (long wave velocities differ by more than 10 times: from 10 m/s on water of 10 m in depth to 200 m/s on water of 4000 m in depth), as well as the possibility of the Coriolis effect manifestation. The reciprocity principle in detail, as well as taking into account the Earth's rotation has not been researched with respect to long waves. The purpose of this paper is to analyze the reciprocity principle for long waves on shallow water propagating on the rotating Earth: the evaluation of limits of the applicability of reciprocity relationship, taking into account the media inhomogeneity and evaluation of the possible influence of the Coriolis effect. The similarity criterion was derived, which links the horizontal sizes of sources and water depths in their epicenters, under which waveforms in reciprocal points coincide. On the basis of numerical experiments using real bathymetry it is found that the reciprocity relationship is valid for distances between sources, comparable to their horizontal sizes (with travel time, comparable with the characteristic wave periods). It is shown that in general case taking into account the Earth's rotation, the reciprocity principle is not satisfied; however, in the special case of symmetric sources it is fair. The reciprocity relationship for long waves in this case coincides with the reciprocity relationship in acoustics. Waveforms from reciprocal sources, located in areas near the Kuril Islands and off the coast of Chile, are in a good agreement with each other. The reciprocity principle (relationship) can be applied to solve problems related to the tsunami problem, and for other applications.

The paper summarizes the results of researches on the study of the Earth's magnetic field made in St.-Petersburg Branch of Pushkov institute of terrestrial magnetism, ionosphere and radio wave propagation of RAS. New problems in building the foundations of a spatial digital model of a component model of the Earth’s magnetic field are discussed. The component model is built based on vector magnetic surveys and estimated component values calculated by dimensions of module of magnetic field induction’s full vector near the Earth's surface. The statistical error estimates of calculated values of the model based on the results of measurements on the World network geomagnetic observatories and magnetic anomalies derived from measurements of the satellite CHAMP are given. On the basis of the component model the solving of the following tasks is proposed: the study of the deep structure of the Earth's crust in the waters of the Arctic and Pacific Oceans; the study of hydrocarbon deposits in the North Sea; the study of allocation of geothermal areas in Western Europe. World magnetic maps of components of Earth's magnetic field are used in sea and air magnetic navigation, including extreme conditions. They are of interest when studying the structure of the crust and mantle, and to allocate promising areas for search of minerals, including hard-to-reach regions of the globe.

Some analytical solutions are found for the problem of three-dimensional instability of a weak geostrophic flow with linear velocity shear taking into account the vertical diffusion of buoyancy. The analysis is based on the potential vorticity equation in a long-wave approximation when the horizontal scale of disturbances is taken much larger than the local baroclinic Rossby radius. It is hypothesized that the solutions found can be applied to describe stable and unstable disturbances of planetary scale with respect, especially, to the Arctic Basin where weak baroclinic fronts with typical temporal variability period of the order of several years or more are observed and the beta-effect is negligible. The unstable (growing with time) solutions are applied to describe the large-scale intrusions typical for the Arctic Basin. Double diffusion being typical and important driver of oceanic intrusions is included to the model by means of a simplest parameterization. Solutions obtained with and without effect of double diffusion are compared with structural features of large-scale intrusive layers observed in the Arctic Basin. Stable (decaying with time) solutions describe disturbances that, in contrast to the Rossby waves, can propagate both to the west and east depending on the sign of linear shear of geostrophic velocity. It is supposed that the analytical solutions found can be useful to validate numerical solutions of the eigen value problems devoted to the analysis of three-dimensional instability of slow baroclinic fronts with the consideration of vertical diffusion of buoyancy. Moreover, the analytical solutions obtained give analytical formulas for the phase velocities and growth/decay rates of disturbances that cannot, as a rule, be found exactly from numerical solutions of the eigen value problems.

The aim of the study is to calculate the impact on aquatic resources dredging in the delta region of the Northern Dvina and the disposal site in the White Sea. The actual assessment of the impact on the food supply of fish is not possible without the use of the most modern and optimized mathematical models to predict the distribution of loops as a suspension in an aqueous medium, and the change of the bottom relief in connection with the loss of suspended soil particles in the sediment The calculation of fish productivity area production work is done. The software model of transport of suspended particles is developed and implemented. The developed numerical algorithms and implementing their complex programs were used to investigate the hydro-biological processes in the maintenance dredging. The amount of polluted water with heaps of soil and dredging equipment operation is calculate to estimate the damage to fish stocks. The values of areas of the regions in which there is destruction of vegetation on the bottom dumps and in the areas of dredging are calculated as well. Based on the developed software package it is found that the decrease of spoil allows to minimize the damage to habitats.

The effect of intense internal waves on towed hydrodynamical depressor is considered on the basis of observations carried out at Mascarene Ridge in the Indian Ocean. Mascarene Ridge belongs to the regions of the World Ocean where internal waves of record (100 m or more) amplitudes are observed. For a few days the research vessel «Academician Nikolay Andreyev» had been carrying out comprehensive studies of internal waves in this area, which were based on towing line temperature sensors. Cross-sections of internal waves for both cases for coinciding with direction of their propagation and for opposite tacks were performed. It was revealed that due to strong orbital currents, accompanying internal waves, a towing depressor made significant vertical dislpacements synchronoused with crossing internal waves. Vertical displacements of the depressor reached as much as 3—11 m during crossing internal waves which amplitudes were in frame of 10—80 m. Examples of manifestations of this effect, as in the case of solitary waves and packets of short-period internal waves are presented. The equations of linear regression, relating the vertical displacement of the depressor with heights of internal waves causing them are obtained. This effect is important for any towed and selfmoving underwater object. At the present time, when the practice of ocean and marine research includes active using underwater unmanned and manned vehicles, it is necessary to take into account the difficulties that may arise during their meeting with the internal waves of large amplitudes.

The present article aims at estimation of creating a mathematical model for urgent predicting the parameters of a bottom hydrodynamic pressure noise in coastal waters in depending on the spectrum of moderate surface waves. The proportions of estimating hydrodynamic pressure spectra, as a result of turbulence in dependence on its spectral composition are given. It is shown that average pressure spectra is close to «−2» power law and at the absence of significant surface waves pressure spectrum noise is corresponding to the turbulence with the dissipation rate ε ≈ 10-⁶–10-⁵ m²⁄s³. For the moderate surface waves conditions regression of turbulent pressure level dependence of the wave spectrum peak magnitude and frequency have been obtained. Regression of low-frequency level of the spectrum wave dependence of the wave spectrum peak magnitude has also been obtained. The data of the low-frequency level of the part of the surface wave spectrum don’t contradict to the Firsov—Rakhmanin model. The mathematical model of hydrodynamic bottom pressure spectra depending on the parameters of the wave spectrum and estimation of model coefficients are proposed. The model takes into account turbulence noise, low-frequency wave noise and «area of the maximum» wave noise. The average difference between predicted and experimental values for the full sample of data is close to 4 dB. Identification of variability of model coefficients under different hydrophysical conditions requires further systematic agreed measurements of surface waves and bottom pressure noise in water areas of practical interest.

This paper presents the consideration of methodological aspects of determination of coefficients of rotary derivatives of hydrodynamic forces and moments of underwater objects. The article shows that mechanism of «sliding computation meshes» implemented in many computing software packages of mechanics of fluids allows setting oscillations of the object in the flow by trim angle and determining hydrodynamic impacts on the object based upon numeric solution of Reynolds-averaged Navier—Stokes equation. The paper contains the main stages of the development of the calculation model for solving similar tasks. The calculation model has been verified using as an example the flow around a wide airfoil profile producing rotary oscillations in the stream. The calculated and experimental data have been compared. Phase difference between the low of airfoil motion and corresponding hydrodynamic impacts has been identified. The non-stationary calculation of the flow of viscous fluid past the underwater object resulted in determination of velocity and pressure fields in the stream. Ratios have been obtained which allows determination of coefficients of rotary derivatives of hydrodynamic forces and moments based on the preset values of hydrodynamic impacts. The presented approach allows the validity of the stationary state hypothesis to be estimated when studying underwater object motion.

The purpose of the study is the modeling of the accuracy of passive ranging using 2 physical methods – the energy method based on the estimate of the absolute value of the signal level at the antenna input and the dynamic method based on the bearing velocity estimate. These methods had been chosen because they did not have special claims to the receiving antenna. The modeling was carried out using the algorithm of combined application of both methods, which was synthesized by the method of maximum likelihood. The independence of errors of measurement of the absolute level of signal and speed of bearing measurement was assumed. The results of the modeling are as follows: 1) the passive ranging accuracy mainly depends on the accuracy of target classification and accuracy of signal level estimate; 2) if the target class was determined correctly the passive ranging mean squared error lies in the bounds of 20—35 %; 3) if the target class was determined incorrectly the passive ranging mean squared error rises greatly.

The model equations of motion of a heterogeneous medium are developed. The model does not use the process of determining the average properties of inhomogeneities. It is assumed that the medium are liquids or gases, which act as the carrier medium. Particles of another state of aggregation can be arbitrary distributed in the carrier medium. For example, it may be near-surface layer of the ocean. Here, the gas bubbles can be considered as particles of inhomogeneities in a homogeneous medium. The model includes the equation of conservation of mass, momentum, angular momentum and energy in relation to the carrier medium. The particles are sources of mass, momentum, angular momentum and energy in relation to the carrier medium. The movement of the particles occurs due to interfacial forces and other internal and external forces. As an application to the problems of the hydrophysics field research, it was derived non-linear system of equations for the wave propagation in liquid with gas bubbles. Verification of wave equations carried out by comparing the numerical solutions with experimental data. The model quantitatively describes the effects observed in the experiments. This suggests that the proposed approach for the description of wave propagation in a liquid with bubbles is applicable in a very wide range of conditions.

The paper considers optimization of receive path for the case of detecting weak local sources in the presence of stronger local sources. The initial classical problem statement based on spectral decomposition with sample estimate of correlation matrix is complemented with matrix correction before its future use using for example Capon algorithm. The estimate of correlation matrix is corrected as follows: based on analysis of numerical values of eigenvalues and analysis of situation using nonadaptive algorithms, the number M1 of interfering signals, which provide the most significant masking action on the weak signals is determined; M1 largest spectral numbers are modified by certain decreasing their values to mitigate the interfering action. Further, the corrected estimate of correlation matrix is used for example in Capon algorithm with corrected matrix used instead of initial one. As a result, a new algorithm is generated, intended for detection of weak signals (hereinafter referred to as CaponW, W meaning weak), with strong signals presents in its bearing plots in suppressed form. Simulation studies have been performed for the tactical situation with 14 signals, with strong signals being multipath and containing a significant dissipated component. Simulation has shown that the modified CaponW algorithm features better resolution and reduced contact loss time as compared with classical Capon algorithm.