Scaling law of mixing layer in cylindrical Rayleigh-Taylor turbulence.

The nonlinear evolution of mixing layer in cylindrical Rayleigh-Taylor (RT) turbulence is studied theoretically and numerically. The scaling laws including the hyperbolic cosine growth for outward mixing layer and the cosine growth for inward mixing layer of the cylindrical RT turbulence are proposed for the first time and verified reliably by direct numerical simulation of the Navier-Stokes equations. It is identified that the scaling laws for the cylindrical RT turbulence transcend the classical power law for the planar RT turbulence and can be recovered to the quadratic growth as cylindrical geometry effect vanishes.

Route to a chaotic state in fluid flow past an inclined flat plate.

We present the results of a numerical study of flow past an inclined flat plate and reveal a route of the transition from steady to chaotic flow. We find that the chaotic flow regime can be reached through the sequential occurrence of successive period-doubling bifurcations and various incommensurate bifurcations. The results provide physical insight into the understanding of fundamental flow behaviors underlying in this flow system and complement the transition phenomenon from steady to chaotic flow.