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Ranis N. Ibragimov

Publications and source records attributed to Ranis N. Ibragimov.

4 recordsLinked to original sources
arXiv2011

Group Analysis of Nonlinear Internal Waves in Oceans. I: Self-adjointness, conservation laws, invariant solutions

The paper is devoted to the group analysis of equations of motion of two-dimensional uniformly stratified rotating fluids used as a basic model in geophysical fluid dynamics. It is shown that the nonlinear equations in question have a remarkable property to be self-adjoint. This property is crucial for constructing conservation laws provided in the present paper. Invariant solutions are constructed using certain symmetries. The invariant solutions are used for defining internal wave beams.

math-ph↗
arXiv2011

Group Analysis of Nonlinear Internal Waves in Oceans. II: The symmetries and rotationally invariant solution

74J30The maximal group of Lie point symmetries of a system of nonlinear equations used in geophysical fluid dynamics is presented. The Lie algebra of this group is infinite-dimensional and involves three arbitrary functions of time. The invariant solution under the rotation and dilation is constructed. Qualitative analysis of the invariant solution is provided and the energy of this solution is presented.

math-ph↗
arXiv2006

Incompressible viscous fluid flows in a thin spherical shell

Linearized stability of incompressible viscous fluid flows in a thin spherical shell is studied by using the two-dimensional Navier--Stokes equations on a sphere. The stationary flow on the sphere has two singularities (a sink and a source) at the North and South poles of the sphere. We prove analytically for the linearized Navier--Stokes equations that the stationary flow is asymptotically stable. When the spherical layer is truncated between two symmetrical rings, we study eigenvalues of the linearized equations numerically by using power series solutions and show that the stationary flow remains asymptotically stable for all Reynolds numbers.

math.CA↗