5 papers · 1 filter
Viscous vortex crystals
Michele Dolce, Martin Donati
We study the solution to the two-dimensional incompressible Navier-Stokes equations arising from a sum of Dirac masses in a particular co-rotating configuration. This configuration…
Instability of two-dimensional Taylor-Green Vortices
Gonzalo Cao-Labora, Maria Colombo, Michele Dolce +1
For a wide class of linear Hamiltonian operators we develop a general criterion that characterizes the unstable eigenvalues as the zeros of a holomorphic function given by the dete…
The long way of a viscous vortex dipole
Michele Dolce, Thierry Gallay
We consider the evolution of a viscous vortex dipole in originating from a pair of point vortices with opposite circulations. At high Reynolds number , the dipole ca…
Long-wave instability of periodic shear flows for the 2D Navier-Stokes equations
Maria Colombo, Michele Dolce, Riccardo Montalto +1
In 1959, Kolmogorov proposed to study the instability of the shear flow in the vanishing viscosity regime in tori . This question was…
Large norm inflation of the current in the viscous, non-resistive magnetohydrodynamics equations
Michele Dolce, Niklas Knobel, Christian Zillinger
We consider the ideally conducting, viscous magnetohydrodynamics (MHD) equations in two dimensions. Specifically, we study the nonlinear dynamics near a combination of Couette flow…