Two Fundamental Relations for Turbulent Flows

Two fundamental effects of turbulence are (i) an increased rate at which kinetic energy is dissipated into heat and (ii) an enhanced momentum (and heat) flux across boundary layers leading to much higher skin friction drag forces (and surface heat transfer). This presentation will introduce and apply two exact relations related to these fundamental effects, respectively. First, the concept of Stokes Flow Regularization (SFR) provides an exact expression for the scale-wise energy cascade rate in terms of vortex stretching and strain-rate self-amplification. Applied to data from fully-resolved simulations, this precisely quantifies the mechanisms responsible for generating large dissipation rates at small scales. SFR also serves as an intriguing alternative to spatial filtering as the basis of large-eddy simulation modeling. Specific potential modeling advantages will be discussed. Second, the Angular Momentum Integral (AMI) equation for turbulent boundary layers will be introduced. The AMI equation quantifies the impact of various flow phenomena throughout a boundary layer flow on the skin friction relative to a baseline laminar flow. An analogous integral equation for the surface heat transfer will also be introduced. Together, these provide a powerful method for probing flow data in terms of key engineering quantities of interest. Example applications for AMI-based analysis will be shown for boundary layer transition and supersonic turbulent boundary layers.