Quasistationary structures on a class of forced Burgers turbulence between walls

The temporally stationary state of Burgers fluid between walls is discussed in the inviscid limit under a class of external, random forcing. The force and the fixed boundaries are shown to pose determinate restrictions on the fluid motion in the large, and drive the Burgers fluid to construct, and to alternate between, a few characteristic structures for dissipation. A mean-field approximation is presented with its inviscid-limit closed solutions for average profiles in the stationary state. The solutions are not unique and reproduce, though with varying accuracies, the mentioned structures of the fluid motion. Results of numerical runs are also reported, and their statistics is shown to admit reconstructions on this picture, confirming further the existence of these quasistationary structures and the itinerant motion of the fluid among them.