Spatio-temporal Proper Orthogonal Decomposition of turbulent channel flow

Abstract

An extension of Proper Orthogonal Decomposition is applied to the wall layer of a turbulent channel flow (Re τ = 590), so that empirical eigenfunctions are defined in both space and time. Due to the statistical symmetries of the flow, the igenfunctions are associated with individual wavenumbers and frequencies. Self-similarity of the dominant eigenfunctions, consistent with wall-attached structures transferring energy into the core region, is established. The most energetic modes are characterized by a fundamental time scale in the range 200-300 viscous wall units. The full spatio-temporal decomposition provides a natural measure of the convection velocity of structures, with a characteristic value of 12 u τ in the wall layer. Finally, we show that the energy budget can be split into specific contributions for each mode, which provides a closed-form expression for nonlinear effects.

References in corpus (2)

• Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis
• Space-time correlations in turbulent flow: A review

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