Boundary Effects on Exact Solutions of the Lagrangian-Averaged Navier–Stokes-α Equations

Author： Holm Darryl D. Putkaradze Vakhtang Weidman Patrick D. Wingate Beth A.

ISSN： 0022-4715

Source： Journal of Statistical Physics, Vol.113, Iss.5-6, 2003-12, pp. : 841-854

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

Previous Menu Next

Abstract

In order to clarify the behavior of solutions of the Lagrangian-averaged Navier–Stokes-α (LANS-α) equations in the presence of solid walls, we identify a variety of exact solutions of the full equations and their boundary layer approximations. The solutions demonstrate that boundary conditions suggested for the LANS-α equations in the literature⁽¹⁾ for a bounded domain do not apply in a semi-infinite domain. The convergence to solutions of the Navier–Stokes equations as α → 0 is elucidated for infinite-energy solutions in a semi-infinite domain, and non-uniqueness of these solutions is discussed. We also study the boundary layer approximation of LANS-α equations, denoted the Prandtl-α equations, and report solutions for turbulent jets and wakes. Our version of the Prandtl-α equations includes an extra term necessary to conserve linear momentum and corrects an earlier result of Cheskidov.⁽²⁾