Observation on Liutex similarity in the dissipation subrange of turbulent boundary layer

Abstract

The motion of the small vortices in the dissipation region (large wave number) is not fully understood due to the influence of the kinematic viscosity and energy dissipation rate. Studying the motion law of small vortices is of great significance to understand the physical mechanism of turbulence. It is well known that the motion of small vortices is statistically isotropic in the dissipation region. Liutex is a new physical quantity recently found to define the rigid rotation of fluids in turbulent flow. In this study, the turbulent flow of boundary layer on a flat plate at freestream Mach number of 0.5 was studied based on a high-order direct numerical simulation (DNS). Using our DNS of flat plate and one DNS of plane turbulent channels of Fluid Dynamics Group UPM, the spectrum of Liutex is analyzed, and the similarity law of Liutex in the dissipation region is obtained. The study results show that the wavenumber spectrum of Liutex exactly follows the -5/3 law, i.e. EL(κ)∼Cκ−5/3, where κ=1/l is the wavenumber and EL is the amplitude of the Liutex spectrum. The scaling of Liutex with the frequency shows a same law of -5/3, since turbulent vortices propagate downstream with almost equal speeds. This paper reports the Liutex similarity for the dissipation subrange of different areas in fully developed turbulent boundary layers at low Reynolds number. Meanwhile, the vorticity and Q-criteria are found having no such similarity in boundary layers due to the shear contamination.