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На примере сейсмического события, обладающего магнитудой и механизмом глубокофокусного землетрясения у берегов Фиджи 19.08.2018, теоретически исследована связь параметров источника цунами с глубиной землетрясения. Показано, что сильные глубокофокусные землетрясения способны создавать обширные области косейсмических деформаций дна, размер которых сопоставим с баротропным радиусом деформации Россби. Волны цунами, формируемые такими источниками, обладают необычайно большой длиной и поэтому подвержены влиянию силы Кориолиса. Это влияние может варьироваться от существенного в высоких широтах до малозначительного в приэкваториальных районах. Методом численного моделирования исследовано влияние силы Кориолиса на слабые волны цунами, вызванные Фиджийским землетрясением 2018 г., Using the example of a seismic event with the same magnitude and mechanism as for the 2018 Fiji deep-focus earthquake the relationship between the parameters of a tsunami source and the depth of an earthquake was theoretically investigated. It is shown that strong deep-focus earthquakes are capable of creating extensive areas of co-seismic deformations for the ocean bottom, the size of which is comparable to the barotropic Rossby deformation radius. Tsunami waves generated by such sources have an unusually large length, and therefore they are subject to the influence of the Coriolis force. The influence of the Coriolis force on the weak tsunami waves caused by the 2018 Fiji earthquake has been studied by numerical simulation. It was found that for a virtual sea-level station located to the south of the source at latitude of 40S, the amplitude of the leading tsunami wave under the influence of the Coriolis force decreased by ≈ 30%. For virtual stations located at the equator or at latitude of 20S, taking into account the Coriolis force changes the amplitude of the waves by no more than 10%. For stations located in the equatorial zone, the effect of delaying of the manifestation of differences in sea-level fluctuations, calculated with and without Coriolis force, as compared with the entry of the leading tsunami wave was discovered. A physical interpretation of the observed delay effect is proposed., №1(24) (2019)

С применением математической модели, включающей осредненные уравнения движения и дифференциальные уравнения переноса нормальных рейнольдсовых напряжений и скорости диссипации, выполнено численное моделирование эволюции безымпульсного закрученного турбулентного следа с ненулевым моментом количества движения за телом вращения. Получено, что начиная с расстояний порядка 1000 диаметров от тела течение становится автомодельным. На основе анализа результатов численных экспериментов построены упрощенные математические модели дальнего следа., Swirling turbulent jet flows are of interest in connection with the design and development of various energy and chemical-technological devices as well as both study of flow around bodies and solving problems of environmental hydrodynamics, etc. An interesting example of such a flow is a swirling turbulent wake behind bodies of revolution. Analysis of the known works on the numerical simulation of swirling turbulent wakes behind bodies of revolution indicates lack of knowledge on the dynamics of the momentumless swirling turbulent wake. A special case of the motion of a body with a propulsor whose thrust compensates the swirl is studied, but there is a nonzero integral swirl in the flow. In previous works with the participation of the authors, a numerical simulation of the initial stage of the evolution of a swirling momentumless turbulent wake based on a hierarchy of second-order mathematical models was performed. It is shown that a satisfactory agreement of the results of calculations with the available experimental data is possible only with the use of a mathematical model that includes the averaged equations of motion and differential equations for the transfer of normal Reynolds stresses along the rate of dissipation. In the present work, based on the above mentioned mathematical model, a numerical simulation of the evolution of a far momentumless swirling turbulent wake with a nonzero angular momentum behind the body of revolution is performed. It is shown that starting from distances of the order of 1000 diameters from the body the flow becomes self-similar. Based on the analysis of the results of numerical experiments, simplified mathematical models of the far wake are constructed. The authors dedicate this work to the blessed memory of Vladimir Alekseevich Kostomakha., №5(23) (2018)

In the paper the results of applying the implicit line-by-line recurrence method for solving of systems of elliptic difference equations, arising, in particular, at numerical simulation of dynamics of incompressible viscous fluid are considered. Research is conducted on the example of the problem about a steady-state two-dimensional lid-driven cavity flow formulated in primitive variables ($u,\, v,\, p$) for large Re (up to 20 000) and grids (up to 2049×2049). High efficiency of the method at calculation of a pressure correction fields is demonstrated. The difficulties of constructing a solution of the problem for large Rе are analyzed.

Pattern formation described by the scalar Fisher-Kolmogorov-Petrovsky-Piscounov equation with nonlocal competition loses and convection linear on coordinates is considered numerically. Initial function localized around a point is shown to transform in a function localized around a ring with symmetrically sited local maxima. The ring radius and number of maxima depend on convection.