Twisted Contact Structures in Turbulent Flows

Abstract

The “hairpin” vortical structure initiated from a conceptual model of Theodorsen refers to a Ω-shaped vortex with two streamwise-oriented legs connected via a raised spanwise-oriented arch. Both computational and experimental studies in flow visualization revealed considerable disagreement as to the underlying hairpin vortex generation mechanism as well as its interpretation. The goal of this paper is to give a deeper insight of this key issue closely related to the turbulence as a dynamic stochastic phenomenon involving the origin and its generation mechanism. The topological concept of twisted contact structures associated with vorticity concentrations in wall-bounded flows strongly contorted at the starting-time is used to explain the genuine structured turbulence of Lagrangian nature at sufficiently large Reynolds numbers. The dynamical stochastic models of starting impact permit to identify two intrinsic scales for describing the starting impact-wall twist relationship generating a local turbulence mechanism. The inertia scale (rate of inertia, e) and circulation scale (azimuthal wave length, π) are measures for impact and twist, respectively, the turbulence lying in their dynamics like a torsion pendulum mechanism. The intrinsic scales of molecular nature have an interesting correspondence in macro-flow field through two relativistic well-known parameters: Mach number and Reynolds number playing the role of some reduced amplitudes and frequencies of the compressibility waves generated by the starting impact/shock. The maximum amplitude 2/3M∞= defines a critical Reynolds number 25200Re1/22/310/scraNm≡=⋅ρ (a0 –sound velocity of air at rest), numerically equal to the maximum impact pressure where the frictional shearing stress is near annulled, and its inverse value is the equilibrium kinematic viscosity 2201.510/ms−=⋅ν or the stable minimum circulation at a contact surface. These reference dimensional quantities are used to a more comprehensive definition of the current Reynolds numbers as the ratio of 20(/)V∞ν contact to (/)Vl∞ outer flow frequencies. Then, it is shown that the wave behavior of wall-bounded flows have a universal character (regardless of much diversity of flow cases) where the wall torsion pressure and the frictional wave drag are more realistic models than Lighthill’s boundary vorticity flux (BVF) mechanism and semi-empirical Prandtl’s wall law.

Keywords

• Laminar-turbulent transition
• shear turbulence
• coherent hydrodynamic structures
• vortex dynamics