Vortex-stretching and, consequently, the evolution of the vorticity is localized on an arbitrarily small space-time cylinder. This yields a complete localization of the geometric condition(s) for the regularity involving coherence of the vorticity direction. In particular, it implies the regularity of any geometrically constrained Leray solution independently of the type of the spatial domain o...

This letter reports the first experimental observation, to our knowledge, of optical vector solitons composed of two incoherently coupled vortex components. We employ nematic liquid crystal to generate stable vector solitons with counterrotating vortices and hidden vorticity. In contrast, the solitons with explicit vorticity and corotating vortex components show azimuthal splitting.

In this paper we consider the application of least-squares principles to the approximate solution of the Stokes equations cast into a first-order velocity-vorticity-pressure system. Among the most attractive features of the resulting methods are that the choice of approximating spaces is not subject to the LBB condition and a single continuous piecewise polynomial space can be used for the appr...

Abstract. The asymptotic structure of laminar modulated travelling waves in two-dimensional high-Reynolds-number plane Poiseuille flow is investigated on the upper-energy branch. A finite set of independent slowly varying parameters are identified which parameterize the solution of the Navier–Stokes equations in this subset of the phase space. Our parameterization of the weakly stable modes des...

A commonplace view of pressure-driven turbulence in pipes and channels is as “cascades” of streamwise momentum toward the viscous layer at the wall. We present in this paper an alternative picture of these flows as “inverse cascades” of spanwise vorticity, in the cross-stream direction but away from the viscous sublayer. We show that there is a constant spatial flux of spanwise vorticity, due t...

While it has been recognized for some time that isentropic coordinates provide a convenient framework for theories of the global circulation of the atmosphere, the role of boundary effects in the zonal momentum balance and in potential vorticity dynamics on isentropes that intersect the surface has remained unclear. Here, a balance equation is derived that describes the temporal and zonal mean ...

The drift of ions in a magnetized plasma or the height fluctuations of a rotating fluid layer are described by the conservation equation of a potential vorticity. This potential vorticity contains an intrinsic length scale, the hybrid Larmor radius in plasma, and the Rossby length in the quasigeostrophic flow. The influence of this scale in the evolution of a random initial vorticity field is i...

Bruce Morton’s early research career was centred on the dynamics of plumes, which is the focus of most of this article. As described below, the process of entrainment plays an important role in plume dynamics, at least in the mathematical models he studied. And in his teachings he made a point of emphasising the importance of vorticity in understanding fluid flow. ‘Vorticity is the flow field’,...

The interaction of a shock wave with quasivortical isotropic turbulence (IT) represents a basic problem for studying some of the phenomena associated with high speed flows, such as hypersonic flight, supersonic combustion and Inertial Confinement Fusion (ICF). In general, in practical applications, the shock width is much smaller than the turbulence scales and the upstream turbulent Mach number...

The three-dimensionality of the velocity field in the wake of a circular cylinder has excited considerable interest and debate over the past decade. Presented here are experimental results that characterize the underlying vorticity field of such wakes. Using particle image velocimetry (PIV), instantaneous velocity fields were measured and from these the vorticity of the longitudinal vortices ly...