Abstract
The influence of a traveling sound wave on the stability of an advective flow with respect to spiral perturbations is studied. A weak nonlinear stability analysis and direct numerical simulation were performed. From the condition of solvability of a third-order problem, a differential equation is obtained, which describes the evolution of amplitude functions. At the same time, to calculate the constants in this equation, it is necessary to determine the eigenfunctions of the linear problem of stability and the solution of some inhomogeneous linear problems. The shooting method was used using the orthogonalization procedure. It is shown that supercritical regimes appear soft and stable near the threshold with respect to modulation. Direct numerical simulation of the problem was carried out using the finite difference method. A study of convective flow with a significant distance from the stability threshold was carried out. It has been established that for a certain value of parameters in the layer, oscillations of a complex structure occur.
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