Applied Mathematics Colloquium

The literature contains several distinct approaches to understanding the flow physics underlying wall turbulence, including the characterization of velocity statistics and spectra, identification of dominant coherent structures and analysis of the amplification properties of the Navier-Stokes equations, to name a few. However the detailed connections between these views of the same fluid system have proved elusive. The systems analysis of turbulent pipe flow proposed by McKeon & Sharma (J. Fluid Mech, 2010) provides a simple model by which to understand both qualitative and quantitative aspects of the structure of wall turbulence. This framework utilizes an input-output formulation of the Navier-Stokes equations and a gain analysis to isolate the important regions of parameter space and identify the locally dominant forcing and response mode shapes relevant to experimental observations. In this talk I will expand the approach, describing its mathematical foundations and demonstrating that our model gives important predictive information about both the statistical and structural make-up of both perturbed and unperturbed wall turbulence. Implications for both the classical picture of wall turbulence and control of turbulent flows will be discussed.