Timewise recycling-rescaling to simulate statistically stationary Rayleigh-Taylor mixing layers

A Rayleigh-Taylor (RT) mixing layer grows in time with thickness, h~t², and Reynolds number, Re~t³. DNS grid requirements grow accordingly, which result in large computational costs. The streamwise recycling-rescaling method for simulating boundary layers (Lund et al., 1998) is applied timewise to an otherwise temporally growing RT mixing layer. The procedure recycles and rescales a turbulent RT mixing layer at a target layer thickness, h*, to generate a new initial condition at a smaller thickness, h_i. It is then allowed to grow by △h = h*-h_i back to the target thickness, h*. Repeated application of this procedure drives the flow towards self-similarity and allows statistics to converge over a finite h (and Re) range. In the limit, Δh→0, the recycling-rescaling procedure is mathematically equivalent to implementing additional terms to the Navier-Stokes equations, resulting in a statistically stationary flow with thickness, h = h*. First, we demonstrate the rescaling requirements necessary to maintain the self-similar characteristics of the RT layer using the finite △h case. Second, we describe the mathematical formulation for the statistically stationary case and validate the method against existing DNS results.