Steady-state solutions of the Euler equations in two dimensions. II - Local analysis of limiting V-states
Abstract
Steady-state solutions of the two-dimensional incompressible Euler equations (V-states) are studied analytically. That is, a local expansion is done in the neighborhood of any point on the boundary of a V-state (which consists of piecewise constant regions of vorticity). It is shown that the limiting V-states for the numerically calculated translating and rotating V-states have 90-deg corners and not cusps. It is also proven that, at a point which lies on the boundary of only one region, and at which the tangent angle has a jump discontinuity, the difference in t angent angles can only be 90 deg (a corner) or 180 deg (a cusp). The analytical behavior of doubly and triply connected rotating V-states is also investigated.
- Publication:
-
SIAM Journal of Applied Mathematics
- Pub Date:
- October 1986
- Bibcode:
- 1986SJAM...46..765O
- Keywords:
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- Computerized Simulation;
- Euler Equations Of Motion;
- Incompressible Flow;
- Steady State;
- Two Dimensional Flow;
- Angular Velocity;
- Stream Functions (Fluids);
- Taylor Series;
- Vorticity;
- Fluid Mechanics and Heat Transfer