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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. E L (κ) ∼ C κ − 5 / 3 , where κ = 1 / l is the wavenumber and E L 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. [ABSTRACT FROM AUTHOR]

• Vorticity is not vortex • Correlation between vorticity and vortex is very small or even negative. • Previous vortex identification methods are contaminated by shear/stretching • ρ (λ c i , R) ≈ ρ (λ 2 , R) ≈ ρ (Q , R) > ρ (V o r t i c i t y , R). • Q, λ 2 , Δ have different dimension from vortex • As these methods are scalar and contaminated, they are not appropriate to represent vortex • Liutex can represent fluid rotation or vortex correctly and accurately For a long time, people hold an idea that vorticity is equivalent to vortex for fluid flow since vorticity represents rotation for rigid body. Nevertheless, many experimental results do not support this opinion. So, several improved methods have been proposed, including Q, λ c i , λ 2 , Δ methods and etc, which are all based on the eigenvalues of the velocity gradient tensor. These methods share a common drawback that they are all scalars and, as a result, are unable to locate the swirling axis which is an important information of rotation. To overcome this shortage, Liutex was proposed as a vector indicator of vortex. The direction of Liutex represents the swirling axis and the magnitude of Liutex is defined as twice the angular speed of rotation. After the introduction of Liutex, many experiments and numerical simulations have shown that Liutex can accurately and correctly capture both big and small vortex, which is better than the existing methods. In this paper, the explicit formulae of vorticity, Q, λ c i and Δ in terms of Liutex are derived, followed by correlation analysis based on a direct numerical simulation (DNS) result of boundary layer transition and a large eddy simulation (LES) result of supersonic ramp flow with a fully developed turbulent boundary layer. The results show that correlation between vorticity and Liutex is very small and even negative in strong shear regions. Although the correlations of Q, λ c i , λ 2 and Δ are better than vorticity, they are still small in strong shear regions. The expression of relation between vorticity, Q, λ c i , Δ and Liutex reveals how these methods are contaminated by shear or stretching or both. [ABSTRACT FROM AUTHOR]