Height-dependence of spatio-temporal spectra of wall-bounded turbulence - LES results and model predictions

TL;DR

This study investigates how the height within the logarithmic layer affects the wavenumber-frequency spectra of wall-bounded turbulence, using LES data and analytical models to capture Doppler effects and validate predictions.

Contribution

It extends previous models by focusing on height dependence and benchmarks an analytical spectrum against LES data, including grid resolution effects.

Findings

Main spectral features are captured by the advection model.

Good agreement between analytical model and LES data.

LES grid resolution influences the spectra.

Abstract

Wavenumber-frequency spectra of the streamwise velocity component obtained from large-eddy simulations are presented. Following a recent paper [Wilczek et al., J. Fluid. Mech., 769:R1, 2015] we show that the main features, a Doppler shift and a Doppler broadening of frequencies, are captured by an advection model based on the Tennekes-Kraichnan random-sweeping hypothesis with additional mean flow. In this paper, we focus on the height-dependence of the spectra within the logarithmic layer of the flow. We furthermore benchmark an analytical model spectrum that takes the predictions of the random-sweeping model as a starting point and find good agreement with the LES data. We also quantify the influence of LES grid resolution on the wavenumber-frequency spectra.