Experimental and numerical investigation of compressibility effects on velocity derivative flatness in turbulence

Compressibility effects on the velocity derivative flatness F ∂ u ′ / ∂ x are investigated by experiments with opposing arrays of piston-driven synthetic jet actuators (PSJAs) and direct numerical simulations (DNS) of statistically steady compressible isotropic turbulence and temporally evolving turbulent planar jets with subsonic or supersonic jet velocities. Experiments using particle image velocimetry show that nearly homogeneous isotropic turbulence is generated at the center of a closed box from interactions between supersonic synthetic jets. The dependencies of F ∂ u ′ / ∂ x on the turbulent Reynolds number R e λ and the turbulent Mach number MT are examined both experimentally and using DNS. Previous studies of incompressible turbulence indicate a universal relationship between F ∂ u ′ / ∂ x and R e λ. However, both experiments and DNS confirm that F ∂ u ′ / ∂ x increases relative to the incompressible turbulence via compressibility effects. Although F ∂ u ′ / ∂ x tends to be larger with MT in each flow, the F ∂ u ′ / ∂ x in the turbulent jets and the turbulence generated from PSJAs deviate from those in incompressible turbulence at lower MT compared with isotropic turbulence sustained by a solenoidal forcing. The PSJAs and supersonic planar jets generate strong pressure waves, and the wave propagation can cause an increased F ∂ u ′ / ∂ x, even at low MT. These results suggest that the compressibility effects on F ∂ u ′ / ∂ x are not solely determined from a local value of MT and depend on the turbulence generation process.