Related papers: Slender vortex filaments in the Boussinesq Approxi…
We study the Boussinesq approximation for rapidly rotating stably-stratified fluids in a three dimensional infinite layer with either stress-free or periodic boundary conditions in the vertical direction. For initial conditions satisfying a…
The evolution of a vortex line following the binormal flow equation (i.e. with a velocity proportional to the local curvature in the direction of the binormal vector) has been postulated as an approximation for the evolution of vortex…
For the incompressible Navier-Stokes equations in $R^3$ with low viscosity $\nu>0$, we consider the Cauchy problem with initial vorticity $\omega_0$ that represents an infinitely thin vortex filament of arbitrary given strength $\Gamma$…
We consider a family of approximations to the Euler equations obtained by adding $(-\Delta)^{-\alpha/2}$ to the non-locality in the Biot-Savart kernel together with a mollification (with parameter $\varepsilon$). We consider the evolution…
In commonly used formulations of the Boussinesq approximation centrifugal buoyancy effects related to differential rotation, as well as strong vortices in the flow, are neglected. However, these may play an important role in rapidly…
The dynamics of interacting quantized vortex filaments in a rotating trapped Bose-Einstein condensate, which is in the Thomas-Fermi regime at zero temperature and described by the Gross-Pitaevskii equation, is considered in the hydrodynamic…
We consider a viscous fluid with kinematic viscosity $\nu $ and initial data consisting of a smooth closed vortex filament with circulation $\Gamma $. We show that, for short enough time, the solution consists of a deformed Lamb-Oseen…
The Biot-Savart law is relevant in physical contexts including electromagnetism and fluid dynamics. In the latter case, when the rotation of a fluid is confined to a set of very thin vortex filaments, this law describes the velocity field…
We consider a two-dimensional, incompressible, inviscid fluid with variable density, subject to the action of gravity. Assuming a stable equilibrium density profile, we adopt the so-called Boussinesq approximation, which neglects density…
This work investigates intensive vortices, which are characterised by the existence of a converging radial flow that significantly intensifies the flow rotation. Evolution and amplification of the vorticity present in the flow play…
In the nineties, Klein, Majda and Damodaran have formally derived a simplified asymptotic motion law for the evolution of nearly parallel vortex filaments in the context of the three dimensional Euler equation for incompressible fluids. In…
We compute the full set of second-order inertial corrections to the instantaneous force and torque acting on a small spherical rigid particle moving unsteadily in a general steady linear flow. This is achieved by using matched asymptotic…
In this paper, we are interested in the long-time behaviour of stochastic systems of n interacting vortices: the position in R2 of each vortex evolves according to a Brownian motion and a drift summing the influences of the other vortices…
The dynamics of a vortex filament in a trapped Bose-Einstein condensate is considered when the equilibrium density of the condensate, in rotating with angular velocity ${\bf\Omega}$ coordinate system, is Gaussian with a quadratic form ${\bf…
We study the scattering of vortex rings by a superfluid line vortex using the Gross-Pitaevskii equation in a parameter regime where a hydrodynamic description based on a vortex filament approximation is applicable. By using a vortex…
In recognition of the highly non-trivial task of computation of the inverse Hasimoto transformation mapping the intrinsic geometric parameter space onto the extrinsic vortex filament coordinate space a reformulation of the Da Rios-Betchov…
We address the problem in Navier-Stokes isotropic turbulence of why the vorticity accumulates on thin sets such as quasi-one-dimensional tubes and quasi-two-dimensional sheets. Taking our motivation from the work of Ashurst, Kerstein, Kerr…
This paper investigates the global (in time) regularity of solutions to a system of equations that generalize the vorticity formulation of the 2D Boussinesq-Navier-Stokes equations. The velocity $u$ in this system is related to the…
The equation of motion of a quantized vortex filament in a trapped Bose-Einstein condensate [A. A. Svidzinsky and A. L. Fetter, Phys. Rev. A {\bf 62}, 063617 (2000)] has been generalized to the case of an arbitrary anharmonic anisotropic…
If a quantum fluid is driven with enough angular momentum, at equilibrium the ground state of the system is given by a lattice of quantised vortices whose density is prescribed by the quantization of circulation. We report on the first…