Generation of vorticity near the boundary in planar Navier-Stokes flows
type: Item
instance of: scholarly article
title: Generation of vorticity near the boundary in planar Navier-Stokes flows
zbMATH Open document ID: 0591.76041
DOI: 10.1007/BF01217348
author: Giuseppe Benfatto
author: Mario Pulvirenti
published in: Communications in Mathematical Physics
publication date: 1984-01-01T00:00:00Z
review text: This is an interesting paper, concerned with rigorously constructing two- dimensional solutions to the Navier-Stokes equations with vorticity production on the boundary: it is closely connected to the fundamental work of \textit{A. J. Chorin} on the vortex method [J. Fluid Mech. 57, 785- 796 (1973)]. The writers determine rigorous estimates of the rate of production of vorticity due to the boundary for the case of a half plane, and provide a mathematical justification of the fact that the boundary behaves as a singular source of vorticity. The procedure is to approximate the Navier-Stokes equations by a convergent sequence of linear problems. In each linear problem the correct boundary conditions are satisfied by a vortex sheet on the boundary. The key to the paper is that the sequence of vortex sheets converges to a limit which describes the rate of vorticity production near the boundary. The convergence proof gives rise to explicit estimates of this vorticity production.
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 76F99
Mathematics Subject Classification ID: 35Q30
zbMATH DE Number: 3949983
zbMATH Keywords: two-dimensional solutions
zbMATH Keywords: Navier-Stokes equations with vorticity production on the boundary
zbMATH Keywords: rate of production of vorticity
zbMATH Keywords: half plane
zbMATH Keywords: singular source of vorticity
zbMATH Keywords: convergent sequence of linear problems
zbMATH Keywords: correct boundary conditions
zbMATH Keywords: vortex sheet on the boundary
zbMATH Keywords: sequence of vortex sheets
zbMATH Keywords: convergence
reviewed by: Brian Straughan
MaRDI profile type: Publication
cites work: Q5576913
cites work: Q4163866
cites work: Groups of diffeomorphisms and the motion of an incompressible fluid
cites work: Nonstationary flows of viscous and ideal fluids in \(R^3\)
cites work: Vortex methods in two-dimensional fluid dynamics
cites work: Q5532416
cites work: The Resolvent Problem for the Stokes Equations on Halfspace in $L_p $
description: scientific article; zbMATH DE number 3949983