Equations of Multimoment Hydrodynamics in the Problem of Flowing Around a Sphere. 2. The Basic Asymmetric Solution

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Abstract

The equations of multimoment hydrodynamics are used to interpret flows behind the sphere that do not have axial symmetry. In accordance with the general approach to solving the equations of multimoment hydrodynamics, a set of nonlinear first-order differential equations for unknown coefficients is derived. Numerical integration of the derived equations shows that a high value of the turbulence coefficient provides a transition from the basic axisymmetric solution to the basic weakly asymmetric solution. It was found that the asymmetric solution is not stable. The instability of the asymmetric solution creates prospects for interpreting the observed evolution of weakly asymmetric flow. It becomes possible to reproduce the vortex shedding observed at moderately high values of the Reynolds number. There are prospects for interpreting the turbulence that develops with a further increase in the Reynolds number.

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About the authors

I. V. Lebed

Institute of Applied Mechanics of the Russian Academy of Sciences

Author for correspondence.
Email: lebed-ivl@yandex.ru
Russian Federation, Moscow

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Supplementary files

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2. Fig. 1. Behaviour of coefficients in time; Re = 150. a - curve 1 sets the time dependence of the coefficient, curve 2 sets the time dependence of the coefficient; b - curve 1 sets the time dependence of the coefficient, curve 2 sets the time dependence of the coefficient.

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3. Fig. 2. Flow pattern in the trace of the sphere, Re = 150, φ = 0.

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