Effect of viscosity gradients on mean velocity profile in temporal mixing layer

Abstract

ABSTRACTWe present a phenomenological and statistical description of the very early stages of a temporal mixing layer (TML), in which the slow fluid is Rν = νhigh/νlow times more viscous than the rapid fluid. Direct numerical simulations (DNS) are performed for two viscosity ratios, Rν = 1 and Rν = 9, whilst the upper and lower streams are density-matched. The space–time evolution of variable-viscosity flow (VVF) is compared with that of a baseline case, which is a constant-viscosity flow (CVF, for which Rν = 1). The initial Reynolds number, based on the initial momentum thickness, δθ, 0, is for CVF, while it varies between 32 and 128 for VVF. It is shown that the mean velocity profile of VVF is affected by the viscosity variations, thus rectifying the myth that viscosity is a small-scale quantity that does not affect the large scales. The transport equation for mean velocity is derived and assessed through DNS data at the initial stages of the TML. The modification of the mean velocity profile is mainly due to the simultaneous occurrence of mean velocity and mean viscosity gradients.