Energy Dissipation in a Weakly Non-Axisymmetric Burgers Vortex Tube.

Abstract

Reynolds number dependence of the structure of energy dissipation is investigated analytically in a weakly non-axisymmetric Burgers vortex tube. An asymptotic solution representing the viscous dissipation rate as well as the axial vorticity is obtained in the weak non-axisymmetry limit λ=(α-β)/(α+β)«1, α and β being strain rates of background flow normal to the tube, at finite Reynolds number Γ/(2πν) ranging from 0 to 100, where Γ is the circulation of the vortex and ν the kinematic viscosity. The asymptotic solution demonstrates that a Burgers vortex tube is deformed into an elliptical shape by the non-axisymmetry of the ambient strain and that the major axis of the ellipse. turns from the principal axis of the strain at a 45° angle, as the Reynolds number is increased. The variation of the rotation angle against the Reynolds number is in excellent agreement with that in the numerical solution obtained by Robinson and Saffman (1984). In contrast to the axial vorticity, i.e. the vortex itself, the high dissipation region stays almost independent of the Reynolds number. At relatively low Reynolds number Γ/(2πν)=O(1), the high dissipation region deviates from the high vorticity (and so the high enstrophy) region. The reason for this deviation is discussed.