Low dimensional models, the minimal flow unit and control

Abstract

Near-wall turbulence is dominated energetically by a few large-scale, coherent flow structures which are responsible for the production of much of the turbulence in the boundary layer. We have studied the dynamics of these structures through direct numerical simulations of turbulent channel flow in the minimal flow unit(Jiménez & Moin 1991), the smallest computational box in which turbulence may be sustained. The minimal flow unit contains exactly one set of these coherent structures in each wall region and, as a result, provides an ideal setting for the study of their dynamics and control. We have constructed a low dimensional model for the dynamics of these coherent structures in the minimal flow unit, identifying the structures with the Proper Orthogonal (or Karhunen-Loève) Decomposition. Low dimensional models have been shown in the past to reproduce many of the qualitative features of boundary layer dynamics. Here we will explore the evidence for stronger, quantitative connections between the model and (a simulation of) the real flow, justifying the assumptions which have gone into the construction of the model and identifying intermittency in the model with the intermittent bursting events in the real flow. In addition, we will use the model to motivate control strategies for the turbulent boundary layer where the model may be applied both as an interpreter of the limited and noisy sensor information available at the wall and as a predictor of the dynamical behavior of the flow. Some simple control strategies based on preventing the instability of these coherent structures have been tested computationally, yielding reductions in skin friction (drag) as large as 20%.