Some Investigation Results for Vortex-Potential Inviscid Fluid Flows

Abstract

1. Some investigation results are presented for a one-parameter class of the simplest vortex-potential inviscid fluid flows i. e. two-dimensional pair vortices in a potential flow in absence a body. One of the families of this class is used in constructing a global pattern of a limiting (Re−>∞) separated flow behind bluff bodies in models of Taganov (1969–70), Smith (1985–86), Chernyshenko (1988). Each element of the investigated class is a pair of vortex regions that are symmetric with respect to the direction of the free-stream flow with a unit velocity of vortex regions where the vortex value is constant and equal to ±ω. On the streamline, dividing the vortex and potential flows, a Bernoulli constant jump of Δ/2 is allowed where $\Delta = V_e^2 - V_i^2$ (V_e and V_i are the velocity values on the dividing streamline (DSL) from the potential and vortex flows respectively, 0≤Δ<1). The vortex regions can have a common portion of the boundary but they can also be at a distance, from each other. Shabat (Δ=0; 1963), Wheatley (Δ−>1; 1975), Pierrehumbert (Δ=0; 1980), Smith F. T. (Δ−>1; 1986) along whith the author of this paper investigated various vorticities related to this class.