Experiments on turbulence beneath a free surface in a stationary field generated by a Crump weir: turbulence structure and correlation with the free surface

Abstract

This paper is a companion paper to a study devoted to the analysis of experimental instantaneous fluid levels and three-component fluid velocity measurements in a stationary flow field generated by a Crump weir in a laboratory flume, using an ultrasonic distance sensor and a three-probe arrangement of an ultrasonic Doppler velocity profiler (UVP) (Longo in Exp Fluids, doi: 10.1007/s00348-010-0881-5, 2010). Whereas Longo (Exp Fluids, doi: 10.1007/s00348-010-0881-5, 2010) deals with a general overview of the problem, the description of the experiments and the analysis of the free surface statistics and relevant scales, the present manuscript is devoted to a detailed analysis of the turbulence and the correlation with the free surface. The data are elaborated by obtaining the macroturbulence Reynolds tensor, using conditional averages based on free surface–fluctuation statistics. We also compute the two-point correlations of fluid velocity, the micro-scale and the integral scale, the correlation between free surface and the turbulence beneath. A free surface–boundary layer was detected having a thickness proportional to the root mean square of the free surface–height series and with a velocity scale that correlates well with the free surface–elevation time gradient. Most of the relevant state variables, such as the mean velocity and Reynolds stress components, collapse to a single curve if scaled appropriately. There are many indicators that a specific regime occurs that has an optimal tuning between the free surface and turbulence. In this regime, the length scales are considered as an indicator.