Stochastic analysis of Rayleigh-Taylor mixing

Rayleigh-Taylor (RT) mixing occurs at the interface of fluids with different densities and is encountered in many disciplines of science and engineering ranging from those in accelerating systems with heat transfer, laser fusion targets, ocean flows and the unstable atmospheric boundary layer. RT mixing is described here from a viewpoint of nonlinear stochastic partial differential equations with correlated noise. Such an equation is developed and solved numerically to calculate the changing structure of the interface between the two liquids, which are saltwater and decane. The results from the calculations compare well to the experimental results.; An algorithm for Gaussian white noise with a very large period of 10 171 will be developed as the basis to generate correlated noise with a new type of an evolution equation. A new set of boundary conditions in connection with stochastic simulations will be introduced and applied to a linear (Edwards-Wilkinson equation) and a nonlinear (Kardar-Parisi-Zhang equation) stochastic partial differential equation. Simulations of both equations by two methods of integration are performed with the new type of boundary conditions.; The new type of boundary conditions when applied to the Kardar-Parisi-Zhang equation produce a growth process which is influenced by the boundary noise and cause phase transition in the system. This phase transition is the result of the nonlinearity in the Kardar-Parisi-Zhang equation and the boundary noise. The new evolution equation for modeling RT mixing with additional necessary nonlinearities captures the transition to turbulence.