A low-order decomposition of turbulent channel flow via resolvent analysis and convex optimization

Abstract

We combine resolvent-mode decomposition with techniques from convex optimization to optimally approximate velocity spectra in a turbulent channel. The velocity is expressed as a weighted sum of resolvent modes that are dynamically significant, non-empirical, and scalable with Reynolds number. To optimally represent DNS data at friction Reynolds number $2003$, we determine the weights of resolvent modes as the solution of a convex optimization problem. Using only $12$ modes per wall-parallel wavenumber pair and temporal frequency, we obtain close agreement with DNS-spectra, reducing the wall-normal and temporal resolutions used in the simulation by three orders of magnitude.

References in corpus (3)

• A critical layer model for turbulent pipe flow
• On coherent structure in wall turbulence
• Model-based scaling of the streamwise energy density in high-Reynolds number turbulent channels

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