Nonlinear evolution of turbulent fluctuations away from a boundary

Abstract

In order to model the evolution of turbulent fluctuations away from a boundary, the one-dimensional Burgers equation is solved on the half-line (0, infinity ), with a prescribed boundary condition f(t) at the origin. Away from the boundary, the amplitude of the fluctuations decreases when the distance increases. However, the fluctuations of the derivative remain large, and become increasingly intermittent. The phenomenon rests on nonlinear interactions between shocks. Similar mechanisms could also be responsible for the very intermittent nature of the turbulent fluctuations already reported in free convection experiments at very high Rayleigh number.