In this paper we suppose that the initial datum for the 2D Navier–Stokes equations are of the vortex layer type, in the sense that there is a rapid variation in the tangential component across a curve. The variation occurs through a distance which is of the same order of the square root of the viscosity. Assuming the initial as well the matching (with the outer flow) data analytic, we show that our model equations are well posed. Another necessary assumption is that the radius of curvature of the curve is much larger than the thickness of the layer.
CAFLISCH, R.E., SAMMARTINO, M. (2006). Vortex layers in the small viscosity limit. In WASCOM 2005 (pp.59-70). HACKENSACK : World Scientific Publishing [10.1142/9789812773616_0010].
Vortex layers in the small viscosity limit
SAMMARTINO, Marco Maria Luigi
2006-01-01
Abstract
In this paper we suppose that the initial datum for the 2D Navier–Stokes equations are of the vortex layer type, in the sense that there is a rapid variation in the tangential component across a curve. The variation occurs through a distance which is of the same order of the square root of the viscosity. Assuming the initial as well the matching (with the outer flow) data analytic, we show that our model equations are well posed. Another necessary assumption is that the radius of curvature of the curve is much larger than the thickness of the layer.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.