The mechanism for the generation of vorticity at a viscous free surface is described This is a free surface analogue of Lighthill s strategy for determining the vorticity ux at solid boundaries In this method the zero shear stress and pressure boundary conditions are transformed into a boundary integral formulation suitable for the velocity vorticity description of the ow A vortex sheet along t...

The mechanism for the generation of vorticity at a viscous free surface is described. This is a free-surface analogue of Lighthill’s strategy for determining the vorticity flux at solid boundaries. In this method the zero-shear-stress and pressure boundary conditions are transformed into a boundary integral formulation suitable for the velocity– vorticity description of the flow. A vortex sheet...

We derive the dispersion relation for water waves with surface tension and having a piecewise constant vorticity distribution. More precisely, we consider here two scenarios; the first one is that of a flow with constant non-zero vorticity adjacent to the flat bed while above this layer of vorticity we assume the flow to be irrotational. The second type of flow has a layer of non-vanishing vort...

Viscous depletion of vorticity is an essential and well known property of turbulent flows, balancing, in the mean, the net vorticity production associated with the vortex stretching mechanism. In this letter, we, however, demonstrate that viscous effects are not restricted to a mere destruction process, but play a more complex role in vorticity dynamics that is as important as vortex stretching...

The formation of orographic wakes and vortices is studied within the context of numerically simulated viscous flow with uniform basic-state wind and stability past elongated free-slip ridges. The viscosity and thermal diffusivity are sufficiently large that the onset of small-scale turbulence is suppressed. It is found in Part I of this study that wake formation in the viscous flow is closely t...

The effects of an oscillatory zero-net-mass-flux jet (i.e. synthetic jet) acting on a separated flow over a hump are investigated in terms of two actuation parameters – actuator position and forcing frequency. By considering the vorticity flux balance and introducing a centroid of vorticity production over the hump surface, lift and drag acting on the hump can be expressed as a function of this...

A key feature of three-dimensional fluid turbulence is the stretching and realignment of vorticity by the action of the strain rate. It is shown in this paper, using the cumulant-generating function, that the cumulative vorticity stretching along a Lagrangian path in isotropic turbulence obeys a large deviation principle. As a result, the relevant statistics can be described by the vorticity st...

An ocean general circulation model of the tropical Atlantic Ocean is used to study the vertically integrated vorticity equation for the annual mean flow in the Atlantic North Equatorial Countercurrent (NECC). It is found that the nonlinear terms play an important role in the vorticity budget, in the western part of the basin. Sverdrup balance does not hold in the region of the North Brazil Curr...

By performing estimates on the integral of the absolute value of vorticity along a local vortex line segment, we establish a relatively sharp dynamic growth estimate of maximum vorticity under some assumptions on the local geometric regularity of the vorticity vector. Our analysis applies to both the 3D incompressible Euler equations and the surface quasi-geostrophic model (SQG). As an applicat...