Abstract
It is known that the cause of the instability of stationary vortex structures are the convective terms of the Navier-Stokes equations. Here, the formation of vortex structures is fundamentally influenced by the vector product of the velocity curl and the velocity vector. Spiral vortices are contingent on the zero value of this product and are one of the causes of the formation of a non-stationary rope in a diffusor. In the paper, equations of spiral vortices are derived and the condition of the vortex stability in a diffusor is determined depending on the existence of spiral vortices. In this sense, new forms of the Navier-Stokes equations are derived. It is possible to analyze the influence of boundary conditions on the stability of vortex structures. The theoretical knowledge is applied to the analysis of the stability of the vortex rope in a diffusor. In addition, a simple method for detecting the onset of the instability of vortex structures is presented.
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