New model of the pinning potential barrier in layered HTc superconductors

New model of the pinning potential barrier in multilayered HTc superconductors is presented, based on geometrical approach to the capturing interaction of pancake-type vortices with nano-sized defects. Using the above model the transport current flow phenomena in these materials, especially the current–voltage characteristics and critical current density, have been considered. Details of theoretical analysis are given, including the derivation of basic mathematical equations describing the potential barrier as a function of transport current intensity and the initial position of captured pancake vortex. Computer simulation has been performed of the influence of transport current amplitude on the potential barrier height for various sizes of pinning centers and initial pancake vortex position as well as the influence of fast neutrons irradiation creating nano-sized defects on critical current of HTc layered superconductor.

On the lifetime of a pancake anticyclone in a rotating stratified flow

We present an experimental study of the time evolution of an isolated anticyclonic pancake vortex in a laboratory rotating stratified flow. Motivations come from the variety of compact anticyclones observed to form and persist for a strikingly long lifetime in geophysical and astrophysical settings combining rotation and stratification. We generate anticyclones by injecting a small amount of isodense fluid at the centre of a rotating tank filled with salty water linearly stratified in density. The velocity field is measured by particle image velocimetry in the vortex equatorial plane. Our two control parameters are the Coriolis parameter $f$ and the Brunt–Väisälä frequency $N$. We observe that anticyclones always slowly decay by viscous diffusion, spreading mainly in the horizontal direction irrespective of the initial aspect ratio. This behaviour is correctly explained by a linear analytical model in the limit of small Rossby and Ekman numbers, where density and velocity equations reduce to a single equation for the pressure. In particular for $N/f=1$, this equation ultimately simplifies to a radial diffusion equation, which admits an analytical self-similar solution. Direct numerical simulations further confirm the theoretical predictions that are not accessible to laboratory measurements. Notably, they show that the azimuthal shear stress generates secondary circulations, which advect the density anomaly: this mechanism is responsible for the slow time evolution, rather than the classical viscous dissipation of the azimuthal kinetic energy. The importance of density diffusivity is also analysed, showing that the product of the Schmidt and Burger numbers – rather than the bare Schmidt number – quantifies the importance of salt diffusion. Finally, a brief application to oceanic Meddies is considered.

Stability of an isolated pancake vortex in continuously stratified-rotating fluids

This paper investigates the stability of an axisymmetric pancake vortex with Gaussian angular velocity in radial and vertical directions in a continuously stratified-rotating fluid. The different instabilities are determined as a function of the Rossby number $Ro$, Froude number $F_{h}$, Reynolds number $Re$ and aspect ratio ${\it\alpha}$. Centrifugal instability is not significantly different from the case of a columnar vortex due to its short-wavelength nature: it is dominant when the absolute Rossby number $|Ro|$ is large and is stabilized for small and moderate $|Ro|$ when the generalized Rayleigh discriminant is positive everywhere. The Gent–McWilliams instability, also known as internal instability, is then dominant for the azimuthal wavenumber $m=1$ when the Burger number $Bu={\it\alpha}^{2}Ro^{2}/(4F_{h}^{2})$ is larger than unity. When $Bu\lesssim 0.7Ro+0.1$, the Gent–McWilliams instability changes into a mixed baroclinic–Gent–McWilliams instability. Shear instability for $m=2$ exists when $F_{h}/{\it\alpha}$ is below a threshold depending on $Ro$. This condition is shown to come from confinement effects along the vertical. Shear instability transforms into a mixed baroclinic–shear instability for small $Bu$. The main energy source for both baroclinic–shear and baroclinic–Gent–McWilliams instabilities is the potential energy of the base flow instead of the kinetic energy for shear and Gent–McWilliams instabilities. The growth rates of these four instabilities depend mostly on $F_{h}/{\it\alpha}$ and $Ro$. Baroclinic instability develops when $F_{h}/{\it\alpha}|1+1/Ro|\gtrsim 1.46$ in qualitative agreement with the analytical predictions for a bounded vortex with angular velocity slowly varying along the vertical.

Stability of a Gaussian pancake vortex in a stratified fluid

Vortices in stably stratified fluids generally have a pancake shape with a small vertical thickness compared with their horizontal size. In order to understand what mechanism determines their minimum thickness, the linear stability of an axisymmetric pancake vortex is investigated as a function of its aspect ratio $\alpha $, the horizontal Froude number ${F}_{h} $, the Reynolds number $\mathit{Re}$ and the Schmidt number $\mathit{Sc}$. The vertical vorticity profile of the base state is chosen to be Gaussian in both radial and vertical directions. The vortex is unstable when the aspect ratio is below a critical value, which scales with the Froude number: ${\alpha }_{c} \sim 1. 1{F}_{h} $ for sufficiently large Reynolds numbers. The most unstable perturbation has an azimuthal wavenumber either $m= 0$, $\vert m\vert = 1$ or $\vert m\vert = 2$ depending on the control parameters. We show that the threshold corresponds to the appearance of gravitationally unstable regions in the vortex core due to the thermal wind balance. The Richardson criterion for shear instability based on the vertical shear is never satisfied alone. The dominance of the gravitational instability over the shear instability is shown to hold for a general class of pancake vortices with angular velocity of the form $\tilde {\Omega } (r, z)= \Omega (r)f(z)$ provided that $r\partial \Omega / \partial r\lt 3\Omega $ everywhere. Finally, the growth rate and azimuthal wavenumber selection of the gravitational instability are accounted well by considering an unstably stratified viscous and diffusive layer in solid body rotation with a parabolic density gradient.