Scaling laws of statistics of wall-bounded turbulence at supercritical pressure: Evaluation and mechanism

A growing body of studies support that the real fluid effects related to the abrupt density changes in supercritical fluids significantly affect statistical properties of turbulence, yet developing appropriate scaling laws for wall-bounded turbulence at supercritical state is still difficult. In the present study, we conduct direct numerical simulations on channel flows of supercritical fluids to evaluate the usefulness of classical scaling developed for variable-property flows. We find that the expressions based on semi-local scaling [φ = f (y*, R e τ*) and φ = f (y*, R e τ*, P r*)] fail to collapse the statistical profiles at supercritical pressure. We analyze the mechanism of the failure of semi-local scaling by quantifying the modulations of turbulent structures of supercritical fluids due to changes in fluid properties. The intensified ejection and sweep of low-speed streaks destabilize the stream-wise streaks and reduce the stream-wise coherence, changing the statistics and affecting the usefulness of semi-local scaling. To shed light on the scaling laws of fluctuating velocities, we finally examine the hypotheses in Townsend wall-attached eddy theory in the context of flows at a supercritical state. It is found that the attached eddies are self-similar near-wall structures, which result in the logarithmic profiles of stream-wise and span-wise velocity fluctuations; the population density of the attached eddies can be well approximated by an exponential scaling.