Mean effects of turbulence on elliptic instability in fluids

Abstract

Elliptic instability in fluids is discussed in the context of the Lagrangian-averaged Navier-Stokes-alpha (LANS$-\alpha$) turbulence model. This model preserves the Craik-Criminale (CC) family of solutions consisting of a columnar eddy and a Kelvin wave. The LANS$-\alpha$ model is shown to preserve the elliptic instability for the inviscid case. However, the model shifts the critical stability angle. This shift increases (resp. decreases) the maximum growth rate for long (resp. short) waves. It also introduces a band of stable CC solutions for short waves.

4 pages, 2 figures (one in two parts)

References in corpus (5)

• The Camassa-Holm equations as a closure model for turbulent channel flow
• The Navier-Stokes-alpha model of fluid turbulence
• A connection between the Camassa-Holm equations and turbulent flows in channels and pipes
• Direct Numerical Simulations of the Navier-Stokes Alpha Model
• Kármán--Howarth Theorem for the Lagrangian averaged Navier-Stokes alpha model

Cited by in corpus (4)

• Tidal instability in a rotating and differentially heated ellipsoidal shell
• Elliptical instability of compressible flow in ellipsoids
• Euler-Poincare formulation and elliptic instability for nth-gradient fluids
• Elliptic instability in the Lagrangian-averaged Euler-Boussinesq-alpha equations