Diffusion of Two Vortices

Flow past a plate with an upstream-moving surface

“…Inside the oval regions the flow must satisfy three conditions: (1) the streamlines are closed; (2) in the leading approximation the vorticity is a function of ψ and t; and (3) the leading approximation is self-similar in t. In [5] the following integral which relates the variation of the circulation Γ and the area σ of the region bounded by the curve ψ = const with the dependence ω = ω(ψ,t) was obtained for a flow satisfying the first two conditions…”

“…The case m = 0 in which the Navier-Stokes equations admit a completely self-similar solution was considered in [7]. In the problem of diffusion of two vortices [5], in the leading approximation the flow with m = −1/2 is realized when Re τ Re 3 . If inside the oval zones the third class of self-similar flows is realized, then from the condition that on the external boundary of the oval zone the velocity must remain constant in time when the boundary varies self-similarly it follows that m = 1/2.…”

A fully meshless method for ‘gas – evaporating droplet’ flow modelling

“…After the injection, a vortex pair is formed. The dynamics of the vortex pair were compared with the prediction of the asymptotic analytical solution [7] for Re = 100 and Re = 1000 ( Fig. 1(i)), the Reynolds number is based on the inlet width and injection velocity, Re = U L/ν.…”

Asymptotic structure of unsteady flow over a semi-infinite plate with a moving surface

“…Similarly to the case of a finite plate [3,4], the pressure difference is produced by the recirculation flow region located inside the D 2 domain. In the recirculation flow zone the ω(ψ) dependence is determined using an additional equation, which for the self-similar flow expanding in accordance with the X ∼ Y ∼ √ νt law takes the form [3,6]: …”