Compressed representations and reduced order modeling of the turbulent flow response to roughness*

All surfaces are hydrodynamically rough at sufficiently large Reynolds numbers. While the drag penalty of different engineering-relevant surfaces (sandgrain, biofouled, painted, etc.) can be characterized by various statistical parameters of the surfaces, finding a universal relationship between the flow response and arbitrary surfaces remains an open area of research.

In this work, a resolvent framework for forming compressed representations and reduced order models of the turbulent flow response to generalized roughness, without a-priori knowledge of the rough wall mean flow, is developed and applied in the case of a channel flow over sandgrain roughness. This framework is used to generate reduced representations which reproduce the wakefield fluctuations and dispersive stresses using less than 0.01% of the original degrees of freedom. Furthermore, using trends identified in data, this framework is used to form a predictive model for the dispersive stresses. The theoretical application of compressed representations and dispersive stress modeling to predicting global flow quantities is presented.