Wall shear stress modulation in unsteady turbulent channel flow with high imposed frequencies

Abstract

Results concerning the modulation of the wall shear stress in an unsteady channel flow are presented. The imposed frequency is increased by up to seven times the mean bursting frequency. The imposed amplitude varies from 10% to 60% of the mean centerline velocity. The characteristics of the modulation of the wall shear stress τ̃ and of the turbulent wall shear stress intensity τ′τ′̃ are discussed. The time mean flow is insensitive to the forcing. There is a coexistence of viscous Stokes flow with a fully developed turbulent mean flow for imposed frequencies f such that 0.02uτ2/ν<ω=2πf<0.045uτ2/ν. The flow leaves the Stokes regime at ω≳0.045uτ2/ν. Although the amplitude of the modulation of the turbulent wall shear stress intensity at first decreases from the quasisteady limit, it surprisingly increases when ω≳0.045uτ2/ν. The time lag of τ′τ′̃ with respect to τ̃ remains constant at 130 wall units for ω<0.014uτ2/ν, but it decreases for higher imposed frequencies.

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