# Resolvent Analysis: Compressibility Effects, Scalar Dynamics, and Analytic Approximations

*Extensions of the resolvent framework for a wider variety of applications in wall-bounded turbulence*

The primary goal of this project is to extend the resolvent framework for modeling structures and statistics in incompressible wall-bounded turbulence to the compressible regime. This in particular requires analysis of thermodynamic variables, the limiting simplest case for which is the behavior of a passive scalar field in an incompressible flow. As well as being an important limiting case for the compressible regime, passive scalar dynamics are relevant for understanding mixing, heat transfer, and experimental techniques for incompressible flows. In addition, resolvent analysis of a scalar operator gives insight into the shape and characteristics of resolvent modes more generally.

**Figure: **Resolvent response mode amplitudes for a nominally incompressible turbulent boundary layer, for a range of spatiotemporal wavenumbers and Prandtl numbers, such that the passive scalar (T) response modes are predicted to collapse to the same shape. An analytic estimate of the scalar response shape is also shown in the lower right subplot.

*Scott Dawson, Theresa Saxton-Fox, Beverley McKeon*

Funding

*AFOSR Grant *FA9550-16-1-0232

References

*Dawson, Saxton-Fox & McKeon, “*Modeling Passive Scalar Dynamics in Wall-Bounded Turbulence using Resolvent Analysis*“, AIAA Conference paper, 2018*