Numerical 2-D and 3-D models of surface waves allowed to simulate and prove most of the facts studied both experimentally and analytically. In addition, a detailed modelling discovers new regularities beyond the scope of traditional concepts. The results obtained mostly at Saint-Petersburg Branch of Oceanography Institute RAS are listed. The facts, which were never discussed in papers of other authors and never explained are described. These facts are mostly contradict general views. The results are based on accurate numerical models of potential liquid motion with a free surface. Harmonic waves quickly obtain bound modes and, on the average, turn into Stokes waves. The Fourier analysis of exact solutions shows that a real field is rather a superposition of Stokes waves with different amplitudes and phases, than the superposition of linear modes. Wave field is the result of superposition of unstable modes whose amplitudes fluctuate in time under the influence of reversible interactions. Development of extreme waves occurs over the time of the order of one wave period. Such fast evolution cannot be explained by the theory of modulational instability. Calculations of extreme wave probability, using a linear model, provide the results close to the calculations by a non-linear model. This is why the role of the nonlinearity in generation of extreme waves is evidently not very significant. When crest merging occurs, a quick nonlinear wave interaction takes place, which leads to a sharp increase of the resulting wave and further possibility of overturning. A jaggy character of 2-D wave spectrum with high resolution (presence of steady peaks and holes) is a typical result of direct wave modeling. The results of the numerical modeling significantly depend on the minor details of initial conditions. Therefore, the results confirmed statistically should be obtained by ensemble modeling. Such modeling, in particular, does not prove correctness of the Hasselmann’s theory.

Opportunities and restrictions of modeling of nonhydrostatic dynamics of straits of the World Ocean according to the offered classification are discussed. Straits can be subclassified on a standard basis of expediency account of the dynamic pressure in the whole area of the strait or a subdomain, guided both by common ideas, based on morphometric, hydrological and dynamic characteristics of the strait and simple criteria identifying nonhydrostatic. The boundary-value problem for the equations of momentum, continuity, turbulent closure and evolution of water constituents is formulated in an arbitrary 3D domain with two open boundaries. For solution, we use a transfer to the horizontal boundary-fitted coordinates and vertical σ-coordinate mapping the physical domain onto a computational parallelepiped with two opposite open sides. Numerical realization uses geophysical modification of a two-step projective method of the solution of the Navier— Stokes equations. Results contain an assessment of influence of nonhydrostatic on the dynamic and hydrological regimes of three allocated standard straits: Messina, Gibraltar and Bab-el-Mandeb.

In this paper an attempt to numerical research of the single internal wave damping process in a channel have been fulfilled to obtain data about wave evolution and factors which influence at damping speed. The second goal of this work consists of investigation of governing system of the model equations nonlinearity influence at numerical solutions/wave evolution, because nonlinear wave interaction often play the primary role in the processes under investigations. Previously, investigation devoted to generation of internal waves by a single surface had been examined by the authors. In the course of it some evaluations of internal wave damping in dependence of mean flow value and stratification, (two-layer and linear) had been obtained. Now, in the course of numerical experiments with 3-D non-hydrostatic finite element model «air-water» supplemented by VOF block, passing of a single internal wave through a channel with different stratification had been simulated. There are a brief description of the model and its numerical algorithm in the paper. Wavelet analysis of numerical simulations results had been used to describe them in the most compact and full form. It was shown that the main role in the internal wave evolution in our experiments plays non-linear three-wave interaction. In the course of it forcing wave and long wave (originated by forcing peculiarities) produce the third long-live wave which assimilates energy of the first two ones. Its damping begins later.

Mathematical model of fluid mechanics includes the so-called continuity equation, which follows from the mass conservation law. In recent decades this equation repeatedly subjected to revision. However, until now the common viewpoint is not yet developed. This paper examines the expediency of modification of the continuity equation. As an argument in favor of modifications we use a simple example of a problem that has no solution in the framework of the standard approach, i.e. in case of use of the standard continuity equation in the model of the fluid. The matter concerns modeling of evolution of the mass density jump in stationary fluid under the condition of stable stratification. The absence of solution means the presence of a contradiction in the problem posing. Such a contradiction is detected and its causes and ways to overcome it are studied. The latter, as it turns out, can be achieved by proper averaging of the fluid mechanics equations that needs to be done in view of the adopted parametric description of small-scale movements. The analysis of derivation of the system of fluid mechanics equations allows understanding, what requirements should satisfy possible modifications of the continuity equation. We also analyze the averaging procedure and describe the correct averaging of equations of the fluid model, the continuity equation including and without any extra assumptions like incompressibility. Current problem adjoins to the mass density diffusion equation, suggested earlier by P.S. Lineykin. We critically assess the derivation of this equation, and discuss its possible place in the system of fluid mechanics equations.

In view of ongoing industrial development, urbanisation, deterioration of environment and climate change, individuals, organisations and businesses are becoming more and more meteorologically/environmentally vulnerable. Modern life requires knowledge about our personal environment: climate, weather and air/water/soil quality at home or work, outdoors, in a garden or filed, etc. From the scientific standpoint, personal environment is the lower essentially turbulent atmospheric planetary boundary layer (PBL) — immediately affected by interactions with underlying land/water surfaces, separated from the free atmosphere by the low-turbulence interface, and controlled by the properties of underlying soils, buildings, vegetation and surface waters. The time is ripe to employ recent achievements in understanding the nature of atmospheric PBL, turbulence, chemistry and aerosols, so that to radically improve general architecture of meteorological and air quality observations, including those provided from crowdsourcing; very high resolution meteorological and air-quality modelling and forecasting. In the near future traditional top-down meteorological monitoring by national weather services will be ever more supplemented through private bottom-up monitoring by individuals, meteorologically dependent businesses (such as transport, agriculture, energy sector, etc.) and volunteer organisations (e.g., schools). Heavily polluted megacities are disposed for establishing massive private environmental monitoring, and provide an increasing market for inexpensive instruments, e.g., indicators of outdoor and indoor air quality. This process is already on track. It is important to harmonise it with current developments in atmospheric science, industry of observations, and environmental management.

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.

Direct and indirect means of allowing for tidal effects in models of a regional marine system climate are discussed. The first of them is based on inserting a tidal constituent into external forcing. Whereas the second one is based on parameterizing internal tidal wave-induced dissipation of baroclinic tidal energy in terms of diapycnal diffusion. The results of two numerical experiments carried out in the frame of the three-dimensional finite-element hydrostatic model QUODDY-4, which includes or ignores tidal effects, are presented. A purpose of these numerical experiments is to determine how much important these effects are and where precisely they show up most clearly. A comparison of parameters (modulus and direction) of surface permanent currents, seawater temperature and salinity at the depth of pycnocline and mean dynamic topography of the free surface in the marine system considered, predicted in the above cases, is given. It is found that the tidal changes in the climatic characteristics are manifested most clearly in the Pechora Sea and the polar frontal zone. Overall the inclusion of tides does not favour any radical reorganization of the marine system climate, but its local changes can be pronounced. Also, we provide a comparison between differences of the above enumerated climatic characteristics obtained when the tidal effects are described directly and indirectly. It testified that the indirect means is acceptable.

This study is aimed to assess the impact of sea ice on the primary production of phytoplankton in the Barents Sea. To get the estimations, we apply a three-dimensional eco-hydrodynamic model based on the Princeton Ocean Model which includes a module of sea ice with 7 categories and the 11-component module of marine pelagic ecosystem developed in Saint-Petersburg Department of the P.P. Shirshov Institute of Oceanology of RAS. The comparison of the model results for the period 1998—2007 with satellite data showed that the model reproduces the main features of the evolution of the sea surface temperature, seasonal changes in the ice extent, surface chlorophyll-a concentration and the primary production of phytoplankton in the Barents Sea. Model estimates of the annual primary production of phytoplankton for the whole sea turned out to be 1.5—2.3 times higher than similar estimates from satellite data. The main reason for this discrepancy is that the model takes into account the production of the primary production of phytoplankton under the pack ice and the marginal ice zone, and satellite data refer exclusively to the open water. Moreover, the evaluation of the primary production of phytoplankton from satellite data underestimates its importance due to subsurface maximum of chlorophyll. During the period 1998—2007, the modelled maximal (in the seasonal cycle) sea ice area has decreased by 15 %. This reduction was accompanied by an increase in the annual primary production of phytoplankton of the sea at 54 and 63 %, based, respectively, on satellite data and the model for the open water. According to the model calculations for the whole sea area, the increase is only 19 %. We conclude that an adequate assessment of the primary production in ice-covered seas can only be obtained on the basis of eco-hydrodynamic models, including sea ice.

This paper presents the study of intraseasonal, synoptic and mesoscale dynamics of major hydrological fronts in the White Sea based on the high-resolution satellite and shipboard observations performed during 2009—2014. The correlation between the frontal dynamics and the features of the submesoscale structures distribution (short-period internal waves and small eddies) is found. To study the spatiotemporal variability of surface manifestations of fronts, the MODIS images acquired from Terra and Aqua satellites with a spatial resolution of about 1 km were analyzed. Analysis of the sea surface temperature and its gradient data obtained during the 2010 summer season revealed the features of the dynamics of plume, tidal and shelf-break fronts on synoptic timescales, as well as detected the areas of mesoscale frontal activity. Contact measurements of the thermohaline structure taken in the frontal areas in 2009, 2012, 2014 showed the relative importance of vertical and horizontal variations of the thermohaline structure under the influence of tide and wind. Surface manifestations of submesoscale structures were found as a result of the White Sea (the 2010 warm period) satellite radar images processing and analyzing. Among them there were 117 eddies of 1 to 12 km in diameter, as well as 190 packages of short-period internal waves, with the package width of 0.1 to12 km and leading wave`s crest length 2 to 89 km. The areas where the submesoscale structures were observed cover a large space of the sea, but more than half of structures were registered in/near the frontal zones. The factors that determine the features of spatial and seasonal distribution of small eddies and short-period internal waves in the areas of frontal activity are discussed.

A theoretical background for the methods of determination of the total scattering coefficient (b) by measurement of the light field of a wide-angle point source is given. The three versions of the instrument design, each of them including two sensors, are analyzed. The sensors of version 1 measure the total (direct and scattered) and nonscattered irradiances, while the sensors of version 2 measure the total and scattered irradiances, and those of version 3 measure the nonscattered and scattered irradiances. The optimal conceptual versions of the b-meter designing method for coastal and pure seawaters are suggested. It is shown how to find the parameters of light source and receiver to ensure the minimal errors of the b-measurement.