Velocity gradient statistics in a turbulent channel flow

Abstract

Turbulence is associated with large fluctuations of velocity gradients which appear preferentially at the smallest scales of the flow. The amplitudes of the fluctuations exceed the mean values by orders of magnitude when the Reynolds number of the flow is sufficiently large. This behaviour is known as smallscale intermittency. The small-scale structure and statistics of turbulence has been mostly studied for the case of homogeneous, isotropic and statistically stationary turbulence. Much less work on the subject is reported for wallbounded shear flows. Several reasons for this circumstance can be given. First, it is more challenging to measure all nine derivatives of the velocity gradient tensor with a sufficient resolution in an open shear-flow-setup (see e.g. [1] for a review). Secondly, a wall-bounded shear flow consists of a boundary layer which is dominated by coherent streamwise structures and a central bulk region in which they are basically absent. The statistics in the wall-normal direction is inhomogeneous and requires a height-dependent analysis. Finally, it is frequently believed that shear flow turbulence is in a state of local isotropy at the small-scale end for larger Reynolds numbers. Recent experimental and numerical studies demonstrated however that significant deviations persist, in particular when higher-order moments are discussed [2]. All this suggests to our view a systematic study of the height-dependence of the statistics of the velocity gradient fields in turbulent shear flows.