Burgers flow past arbitrary ellipse

Connection between corner vortices and shear layer instability in flow past an ellipse

We investigate, by numerical simulation, the shear layer instability associated with the outer layer of a spiral vortex formed behind an impulsively started thin ellipse. The unstable free shear layer undergoes a secondary instability. We connect this instability with the dynamics of corner vortices adjacent to the tip of the ellipse by observing that the typical turnover time of the corner vor...

Universal Statistics of Inviscid Burgers Turbulence in Arbitrary Dimensions

We investigate the non-perturbative results of multi-dimensional forced Burgers equation coupled to the continuity equation. In the inviscid limit, we derive the exact exponents of two-point density correlation functions in the universal region in arbitrary dimensions. We then find the universal generating function and the tails of the probability density function (PDF) for the longitudinal vel...

The Flow Completion of the Burgers Equation

For a manifold equipped with vector field there exists the universal completion consisting of a (possibly non-Hausdorff) manifold with a complete vector field on it. We describe the universal completion of the partial differential equations ut + F (u)ux = 0 viewed as vector fields on infinite dimensional manifolds.

Taylor's frozen-flow hypothesis in Burgers turbulence.

By detailed analytical treatment of the shock dynamics in the Burgers turbulence with large scale forcing we calculate the velocity structure functions between pairs of points displaced both in time and space. Our analytical treatment verifies the so-called Taylor's frozen-flow hypothesis without relying on any closure and under very general assumptions. We discuss the limitation of the hypothe...

THE FLOW COMPLETION OF THE BURGERS EQUATIONBoris