Eddying flow in the ocean develops as a result of baroclinic instability, and the environment in which the flow develops is vertically and horizontally inhomogeneous. A theory that takes into account the vertical inhomogeneities and predicts the magnitude and structure of the eddy potential vorticity flux for strongly baroclinically unstable mean shears is reviewed and extended to include the f...

The effects of a higher vorticity moment on a variational problem for barotropic vorticity on a rotating sphere are examined rigorously in the framework of the Direct Method. This variational model differs from previous work on the Barotropic Vorticity Equation (BVE) in relaxing the angular momentum constraint, which then allows us to state and prove theorems that give necessary and sufficient ...

A method is presented to compute the spanwise vorticity in polar coordinates from 2D vertical cross sections of high-resolution line-of-sight Doppler wind lidar observations. The method uses the continuity equation to derive the velocity component perpendicular to the observed line-of-sight velocity, which then yields the spanwise vorticity component. The results of the method are tested using ...

We generalize the mean field magnetic dynamo to include local evolution of the mean vorticity in addition to the mean magnetic field. The coupled equations exhibit a general mean field dynamo instability that enables the transfer of turbulent energy to the magnetic field and vorticity on larger scales. The growth of the vorticity and magnetic field both require helical turbulence which can be s...

In this work, the authors develop new methods for the accurate and efficient solution of the two-dimensional, incompressible Euler equations in the vorticity form. Here, the velocity is recovered directly from the Biot-Savart relation with vorticity, and the vorticity is evolved through its transport equation. Using a generalized Poisson summation formula, the full asymptotic error expansion is...

We show that the vorticity appearing in stationary vacuum spacetimes is always related to the existence of a flow of super–energy on the plane orthogonal to the vorticity vector. This result, toghether with the previously established link between vorticity and super–energy in radiative (Bondi–Sachs) spacetimes strength further the case for this latter quantity as the cause of frame dragging.

We prove that there are solutions to the Euler equation on the torus with C vorticity and smooth except at one point such that the vorticity gradient grows in L∞ at least exponentially as t → ∞. The same result is shown to hold for the vorticity Hessian and smooth solutions. Our proofs use a version of a recent result by Kiselev and Šverák [5].

Classes of vortex formation from a horizontal cylinder adjacent to an undulating free-surface wave are characterized using high-image-density particle image velocimetry. Instantaneous representations of the velocity "eld, streamline topology and vorticity patterns yield insight into the origin of unsteady loading of the cylinder. For su$ciently deep submergence of the cylinder, the orbital natu...

We present results on the connection between the vorticity equation and the shape and evolution of the single-point vorticity probability density function. The statistical framework for these observations is based on the classical hierarchy of evolution equations for the probability density functions by Lundgren, Novikov, and Monin combined with conditional averaging of the unclosed terms. The ...