Stretching in continuum mechanics is naturally described using the Cauchy–Green strain tensors. These tensors quantify the Lagrangian stretching experienced by a material element, and provide a powerful way to study processes in turbulent fluid flows that involve stretching such as vortex stretching and alignment of anisotropic particles. Analysing data from a simulation of isotropic turbulence...

An effect of a mean velocity shear on a turbulence and on the effective force which is determined by the gradient of the Reynolds stresses is studied. Generation of a mean vorticity in a homogeneous incompressible nonhelical turbulent flow with an imposed mean velocity shear due to an excitation of a large-scale instability is found. The instability is caused by a combined effect of the large-s...

3 Anatoly Abrashkin and Efim Pelinovsky 4 5 a National Research University Higher School of Economics (HSE), Nizhny Novgorod 6 603155, Russia 7 b Institute of Applied Physics, 603950, 46 Ulyanov str., Nizhny Novgorod, Russia 8 c Nizhny Novgorod State Technical University, Nizhny Novgorod, Russia 9 10 11 Abstract: 12 The nonlinear Schrödinger equation (NLS equation) describing weakly 13 rotation...

We discuss here the evolution of vorticity and potential vorticity (PV) for a bottom current crossing a marine channel in shallow-water approximation, focusing on the effect of friction and mixing. The purpose of this research is indeed to investigate the role of friction and vertical entrainment on vorticity and PV spatial evolution in channels or straits when along-channel morphology variatio...

We derive boundary conditions for the vorticity equation with solid wall boundaries. The formulation uses a Dirichlet condition for the normal component of vorticity, and Neumann type conditions for the tangential components. In a Galerkin (integral) formulation the tangential condition is natural, i.e. it is enforced by a right-hand side functional and does not impose a boundary constraint on ...

In this paper we prove two results regarding the large-time behavior of vortex dynamics in the full plane. In the first result we show that the total integral of vorticity is confined in a region of diameter growing at most like the square-root of time. In the second result we show that if a dynamic rescaling of the absolute value of vorticity with spatial scale growing linearly with time conve...

We study numerically a recently introduced formulation of incompressible Newtonian fluid equations in vorticity – helical density and velocity – Bernoulli pressure variables. Unlike most numerical methods based on vorticity equations, the current approach provides discrete solutions with mass conservation, divergencefree vorticity, and accurate kinetic energy balance in a simple and natural way...

Remarks are made about the status of research on the role of vorticity in fluid dynamics and some unsolved problems of current int,erest are described.

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