Response of a turbulent boundary layer to steady, square-wave-type transverse wall-forcing

TL;DR

This paper explores how a steady, square-wave spanwise wall-forcing affects the spatial evolution of a turbulent boundary layer, revealing distinct regimes of turbulence attenuation and recovery influenced by the forcing waveform and wavelength.

Contribution

It introduces an experimental setup with extended streamwise forcing and analyzes the boundary layer response to square-wave forcing, highlighting different turbulence regimes and their impact on drag reduction.

Findings

Square-wave forcing causes two distinct turbulence regimes.

Turbulence attenuation occurs near half- and full-phase locations.

Turbulence recovers during near-zero strain rate phases.

Abstract

This study investigates the spatial evolution of a zero pressure gradient turbulent boundary layer (TBL) imposed by a square-wave (SqW) of steady spanwise wall-forcing, which varies along the streamwise direction ($x$). The SqW wall-forcing is imposed experimentally via a series of streamwise periodic belts running in opposite spanwise directions, following the methodology of Knoop et al. (Exp. Fluids, vol 65, 2024), with the streamwise extent increased to beyond $\sim 11$ times the boundary layer thickness (${\delta}_o$) in the present study. This unique setup is leveraged to investigate the influence of viscous-scaled wavelength of SqW wall-forcing on the turbulent drag reduction (DR) efficacy for $\lambda^+_x = $ 471 (sub-optimal), 942 (near-optimal), and 1884 (post-optimal conditions), at fixed viscous-scaled wall-forcing amplitude, $A^+ = 12$, and friction Reynolds number, $Re_\tau = 960$. The TBL's response to this wall-forcing is elucidated by drawing inspiration from established knowledge on traditionally studied sinusoidal forcing (SinW), based on analysis of the streamwise-phase variation of the Stokes strain rate (SSR). The analysis reveals the SqW forcing to be characterized by a combination of two markedly different SSR regimes whose influence on the overlying turbulence is found to depend on the forcing waveform: sub-phase-I of local and strong impulses of SSR downstream of the half- ($\lambda_x$/2) and full-phase ($\lambda_x$) locations, associated with a reversal in spanwise forcing directions, leading to significant turbulence attenuation, and sub-phase-II of near-zero SSR over the remainder of forcing phase that enables turbulence recovery (when wall-forcing magnitudes and direction remain constant).