We consider a model equation for 3D vorticity dynamics of incompressible viscous fluid proposed by K. Ohkitani and the second author of the present paper. We prove that a solution blows up in finite time if the L1-norm of the initial vorticity is greater than the viscosity.

The paper presents computations of decaying two{dimensional turbulence in an adaptive wavelet basis. At each time step the vorticity is represented by an adaptively selected set of wavelet functions which adjusts to the instantaneous distribution of vorticity. The results of this new algorithm are compared to a classical Fourier method and a Fourier method supplemented with wavelet compression ...

Model equations are derived from what we call the strain-vorticity dynamics of the incompressible viscous uid motion. The global existence and blow-up are examined for them and we see that the L 1 norm of the vorticity plays an important role. Blow-up solutions are obtained as self-similar solutions.

Circularly polarized electric fields incident on subwavelength apertures produce near-field phase singularities with phase vorticity +/-1 depending on the polarization handedness. These near-field phase singularities combine with those associated with orbital angular momentum and result in polarization-dependent transmission. We produce arbitrary phase vorticity in the longitudinal component of...

We prove uniqueness and existence of the weak solutions of Euler equations with helical symmetry, with initial vorticity in L∞ under ”no vorticity stretching” geometric constraint. Our article follows the argument of the seminal work of Yudovich. We adjust the argument to resolve the difficulties which are specific to the helical symmetry.

When anticommuting Grassmann variables are introduced into a fluid dynamical model with irrotational velocity and no vorticity, the velocity acquires a nonvanishing curl and the resultant vorticity is described by Gaussian potentials formed from the Grassmann variables. Upon adding a further specific interaction with the Grassmann degrees of freedom, the model becomes supersymmetric.

1 Abstract The role of vorticity dynamics in vortex breakdown is examined in a theoretical and computational study. Under the assumptions of steady, incompressible, axisymmetric, invis-cid ow, a theory is developed concerning the interaction of vortex tilting and stretching in the breakdown process. This analytic theory is then connrmed using an unsteady, incompressible, axisymmetric viscous ow...

1 low-vorticity waves in deep water 2 3 Anatoly Abrashkin 1 and Efim Pelinovsky 2,3 4 1 National Research University Higher School of Economics (HSE), 5 25/12 Bol'shaya Pecherskaya str., Nizhny Novgorod, 603155, Russia 6 2 Institute of Applied Physics RAS, 46 Ulyanov str., Nizhny Novgorod, 603950, Russia 7 3 Nizhny Novgorod State Technical University n.a. R. Alekseev, 24 Minin str., Nizhny 8 No...

This paper reports the results of lattice Boltzmann simulations of the rotation behaviour of neutrally buoyant spheroidal particles in a three-dimensional Couette flow. We find several distinctive states depending on the Reynolds number range and particle shape. As the Reynolds number increases, rotation may change from one state to another. For a prolate spheroid, two rotation transitions are ...