OFF-WALL BOUNDARY CONDITIONS FOR TURBULENT SIMULATIONS FROM MINIMAL FLOW UNITS IN TRANSITIONAL BOUNDARY LAYERS

Abstract

A reduced order model for off-wall boundary conditions for turbulent flows is proposed. The model circumvents the need to resolve the buffer layer near the wall by providing conditions directly above it for the overlying flow. The effect of the buffer layer is modeled as a pattern of periodic blocks similar to the minimal unit of Jimenez & Moin (1991). The model is reduced to the imprint of such blocks on a plane at y+ ≈ 100, at which Dirichlet boundary conditions are imposed for the rest of the flow. Blocks are constructed from a variety of canonical flows, from low-Reynolds-number turbulent channels to the transitional-boundary-layer direct simulation of Sayadi et al. (2012). The block sizes are selected so that they are statistically representative of fully turbulent flow, and so that they contain the dominant structures at y+ ≈ 100, as educed from direct mode decomposition. The model has the form of a collection of Fourier modes in space and time, and comprises ∼1% of the parameters necessary to describe the full flow field at the plane considered, while it reproduces ∼90% of the amplitudes of the flow statistics. The simulations conducted with these modeled off-wall boundary conditions correctly reproduce the turbulent statistics of the overlying flow.