Scaling of statistics in wall-bounded turbulent flows

Abstract

High-resolution laser Doppler anemometry ( Lda ) and hot-wire anemometry ( Hwa ) measurements are utilized to study a zero-pressure-gradient turbulent boundary layer over the range of momentum thickness Reynolds number of 1170–3720. The primary objective is to investigate the near-wall behavior of this type of flow. We are particularly interested in possible Reynolds- and Kármán-number dependencies. The experimental results are in excellent agreement with most recent direct numerical simulations ( Dns ), which allow direct comparison of detailed results such as peak value and position of streamwise Reynolds stress, wall values of skewness and flatness factors, and turbulence dissipation rate. Systematic changes of some of these parameters with Kármán number are found when scaled with the inner parameters. A remedy seems to be the alternative mixed scaling that is based on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>u</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>τ</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> <mml:mo stretchy="false">/</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msubsup> <mml:msubsup> <mml:mrow> <mml:mi>U</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo stretchy="false">/</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> , instead of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>u</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>τ</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> , which admits direct influence of the outer velocity scale on the wall parameters.