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Результаты исследований: Вклад в журнал › Статья › Рецензирование
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TY - JOUR
T1 - Exact Solutions of Navier–Stokes Equations for Quasi-Two-Dimensional Flows with Rayleigh Friction
AU - Burmasheva, Natalya
AU - Ershkov, Sergey
AU - Prosviryakov, Evgeniy
AU - Leshchenko, Dmytro
PY - 2023
Y1 - 2023
N2 - To solve the problems of geophysical hydrodynamics, it is necessary to integrally take into account the unevenness of the bottom and the free boundary for a large-scale flow of a viscous incompressible fluid. The unevenness of the bottom can be taken into account by setting a new force in the Navier–Stokes equations (the Rayleigh friction force). For solving problems of geophysical hydrodynamics, the velocity field is two-dimensional. In fact, a model representation of a thin (bottom) baroclinic layer is used. Analysis of such flows leads to the redefinition of the system of equations. A compatibility condition is constructed, the fulfillment of which guarantees the existence of a nontrivial solution of the overdetermined system under consideration. A non-trivial exact solution of the overdetermined system is found in the class of Lin–Sidorov–Aristov exact solutions. In this case, the flow velocities are described by linear forms from horizontal (longitudinal) coordinates. Several variants of the pressure representation that do not contradict the form of the equation system are considered. The article presents an algebraic condition for the existence of a non-trivial exact solution with functional arbitrariness for the Lin–Sidorov–Aristov class. The isobaric and gradient flows of a viscous incompressible fluid are considered in detail.
AB - To solve the problems of geophysical hydrodynamics, it is necessary to integrally take into account the unevenness of the bottom and the free boundary for a large-scale flow of a viscous incompressible fluid. The unevenness of the bottom can be taken into account by setting a new force in the Navier–Stokes equations (the Rayleigh friction force). For solving problems of geophysical hydrodynamics, the velocity field is two-dimensional. In fact, a model representation of a thin (bottom) baroclinic layer is used. Analysis of such flows leads to the redefinition of the system of equations. A compatibility condition is constructed, the fulfillment of which guarantees the existence of a nontrivial solution of the overdetermined system under consideration. A non-trivial exact solution of the overdetermined system is found in the class of Lin–Sidorov–Aristov exact solutions. In this case, the flow velocities are described by linear forms from horizontal (longitudinal) coordinates. Several variants of the pressure representation that do not contradict the form of the equation system are considered. The article presents an algebraic condition for the existence of a non-trivial exact solution with functional arbitrariness for the Lin–Sidorov–Aristov class. The isobaric and gradient flows of a viscous incompressible fluid are considered in detail.
UR - http://www.scopus.com/inward/record.url?partnerID=8YFLogxK&scp=85153745747
UR - https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=tsmetrics&SrcApp=tsm_test&DestApp=WOS_CPL&DestLinkType=FullRecord&KeyUT=000977490300001
U2 - 10.3390/fluids8040123
DO - 10.3390/fluids8040123
M3 - Article
VL - 8
JO - Fluids
JF - Fluids
SN - 2311-5521
IS - 4
M1 - 123
ER -
ID: 38492248