Significance Near a solid wall, the mean velocity of an incompressible fluid is a nearly universal function of the distance from the wall when appropriately transformed (nondimensionalized). For high-speed compressible flows, due to the wall-normal variations of density and viscosity, it has not been established how to transform a dimensional velocity profile into a universal profile. We propose a transformation that is more accurate and more broadly applicable than existing approaches. This improvement results from deploying different physical arguments for the two critical subdomains of a boundary layer. The transformation can be used to extend incompressible turbulence models to compressible turbulent flows, such as those encountered by vehicles for high-speed transportation and planetary reentry.

We revisit the grid-point requirement estimates in Choi and Moin [“Grid-point requirements for large eddy simulation: Chapman’s estimates revisited,” Phys. Fluids 24, 011702 (2012)] and establish more general grid-point requirements for direct numerical simulations (DNS) and large-eddy simulations (LES) of a spatially developing turbulent boundary layer. We show that by allowing the local grid spacing to scale with the local Kolmogorov length scale, the grid-point requirement for DNS of a spatially developing turbulent boundary layer is N∼ReLx2.05 rather than N∼ReLx2.64, as suggested by Choi and Moin, where N is the number of grid points and Lx is the length of the plate. In addition to the grid-point requirement, we estimate the time-step requirement for DNS and LES. We show that for a code that treats the convective term explicitly, the time steps required to get converged statistics are Nt∼ReLx/Rex06/7 for wall-modeled LES and Nt∼ReLx/Rex01/7 for wall-resolved LES and DNS (with different prefactors), where Rex0 is the inlet Reynolds number. The grid-point and time-step requirement estimates allow us to estimate the overall cost of DNS and LES. According to the present estimates, the costs of DNS, wall-resolved LES, and wall-modeled LES scale as ReLx2.91, ReLx2.72, and ReLx1.14, respectively.

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The character of turbulence depends on where it develops. Turbulence near boundaries, for instance, is different than in a free stream. To elucidate the differences between flows, it is instructive to vary the structure of turbulence systematically, but there are few ways of stirring turbulence that make this possible. In other words, an experiment typically examines either a boundary layer or a free stream, say, and the structure of the turbulence is fixed by the geometry of the experiment. We introduce a new active grid with many more degrees of freedom than previous active grids. The additional degrees of freedom make it possible to control various properties of the turbulence. We show how long-range correlations in the turbulent velocity fluctuations can be shaped by changing the way the active grid moves. Specifically, we show how not only the correlation length but also the detailed shape of the correlation function depends on the correlations imposed in the motions of the grid. Until now, large-scale structure had not been adjustable in experiments. This new capability makes possible new systematic investigations into turbulence dissipation and dispersion, for example, and perhaps in flows that * These authors contributed equally: N.

While several velocity transformations for compressible zero-pressure-gradient (ZPG) boundary layers have been proposed in the past decades, their performance for non-canonical compressible wall-bounded turbulent flows has not been systematically investigated. This work assesses several popular transformations for the velocity profile through their application to several types of non-canonical compressible wall-bounded turbulent flows. Specifically, this work explores DNS databases of high-enthalpy boundary layers with dissociation and vibrational excitation, supercritical channel and boundary-layer flows, and adiabatic boundary layers with pressure gradients. The transformations considered include the van Driest [Van