We study a finite element method for the 3D Navier-Stokes equations in velocityvorticity-helicity formulation, which solves directly for velocity, vorticity, Bernoulli pressure and helical density. Moreover, the algorithm strongly enforces solenoidal constraints on both the velocity (to enforce the physical law for conservation of mass) and vorticity (to enforce the mathematical law that div(cu...

Physics of Fluids 11(1999), 875-879. In this paper, we discuss zonally periodic steady quasigeostrophic waves in a β−plane channel, by using variational methods. A class of steady quasigeostrophic waves are determined by the potential vorticity field profile, g(·), which is a function of the stream function. We show that zonally periodic steady quasigeostrophic waves exist when the bottom topog...

Effects of landfall location and approach angle on track deflection associated with a tropical cyclone (TC) passing over an idealized and Central Appalachian Mountain is investigated by a series of idealized numerical experiments. When the TC landfalls on the central portion of the mountain range, it is deflected to the south upstream, passes over the mountain anticyclonically, and then moves w...

This work studies the three-dimensional Stokes problem expressed in terms of vorticity and velocity variables. We make general assumptions on the regularity and the topological structure of the flow domain: the boundary is Lipschitz and possibly non-connected and the flow domain may be multiply connected. Upon introducing a new variational space for the vorticity, five weak formulations of the ...

We adapt the formalism of the statistical theory of 2D turbulence in the case where the Casimir constraints are replaced by the specification of a prior vorticity distribution. A new relaxation equation is obtained for the evolution of the coarse-grained vorticity. It can be used as a thermodynamical parametrization of forced 2D turbulence (determined by the prior), or as a numerical algorithm ...

The persistence of the southern annular mode (SAM) is studied during austral winter (June–September) and summer (December–March) using observations of the three-dimensional vorticity budget. Analysis of the relative vorticity tendency equation shows that convergence of eddy vorticity flux in the upper troposphere, coupled with a secondary circulation, constitutes a positive eddy feedback that a...

We prove unconditional long-time stability for a particular velocity-vorticity discretization of the 2D Navier-Stokes equations. The scheme begins with a formulation that uses the Lamb vector to couple the usual velocity-pressure system to the vorticity dynamics equation, and then discretizes with the finite element method in space and implicit-explicit BDF2 in time, with the vorticity equation...

The single-mode equations of Boussinesq thermal convection have been modified to include the vertical component of vorticity, which has led, in certain parameter ranges, to a new family of solutions for stationary convection in the absence of external constraints. The features of these solutions are discussed and a comparison with the family of solutions possessing zero vertical vorticity, whic...

We prove unconditional long-time stability for a particular velocity-vorticity discretization of the 2D Navier-Stokes equations. The scheme begins with a formulation that uses the Lamb vector to couple the usual velocity-pressure system to the vorticity dynamics equation, and then discretizes with the finite element method in space and implicit-explicit BDF2 in time, with the vorticity equation...

Abstract We present here an original approach to reconstruct the vorticity distribution inside an axisymmetric vortex ring from some incomplete and possibly noisy measurements of the corresponding velocity field. The idea is to formulate an inverse problem for identifying the structure of the vorticity distribution and solve this problem by a suitable numerical optimization algorithm. The novel...