The lecture is motivated by the regularity criteria, showing that some particular quantities (one or two components of velocity, two components of vorticity, some chosen components of the gradient of velocity, etc) control the regularity of a weak solution to the Navier–Stokes equations. We show that a certain spectral projection of vorticity, or even one its component, also belong to such quan...

The fundamental equations that model turbulent flow do not provide much insight into the size and shape of observed turbulent structures. We investigate the efficient and accurate representation of structures in two-dimensional turbulence by applying statistical models directly to the simulated vorticity field. Rather than extract the coherent portion of the image from the background variation,...

Interaction between synoptic eddy and lowfrequency flow (SELF) has been the subject of many studies. In this study, we further examine the interaction by introducing a transformed eddy-potential-vorticity (TEPV) flux that is obtained from eddy-potential-vorticity flux through a quasi-geostrophic potential-vorticity inversion. The main advantage of using the TEPV flux is that it combines the eff...

Motivated by the success of potential vorticity (PV) thinking for Rossby waves and related shear flow phenomena, this work develops a buoyancy–vorticity formulation of gravity waves in stratified shear flow, for which the nonlocality enters in the same way as it does for barotropic/baroclinic shear flows. This formulation provides a time integration scheme that is analogous to the time integrat...

In this study, the relation between the interior and the surface dynamics for nonlinear baroclinically unstable flows is examined using the concepts of potential vorticity. First, it is demonstrated that baroclinic unstable flows present the property that the potential vorticity mesoscale and submesoscale anomalies in the ocean interior are strongly correlated to the surface density anomalies. ...

The main objective of the present study is to examine the characteristics of the vortical structures in a turbulent far wake using the wavelet multiresolution technique by decomposing the vorticity into a number of orthogonal wavelet components based on different central frequencies. The three vorticity components were measured simultaneously using an eight-wire probe at three Reynolds numbers,...

The formation of vortices in protoplanetary disks is explored via pseudospectral numerical simulations of an anelastic-gas model. This model is a coupled set of equations for vorticity and temperature in two dimensions which includes baroclinic vorticity production and radiative cooling. Vortex formation is unambiguously shown to be caused by baroclinicity because (1) these simulations have zer...