The system of the vortex-like structures: the viewpoint on a turbulence modelling

Abstract

In this study we suggest new approach to turbulence modeling. To develop this approach, we construct the set of the vortex-like dynamical systems evolving in the space $E_3$. These systems are constructed using the AKNS hierarchy so that they generalize thin closed vortex filament described in the local induction approximation. We construct and investigate the Hamiltonian dynamics of these systems in terms of the non - standard variables. We formulate the principles of quantization these systems focusing on the quantum description of the filaments with linearized dynamics. To describe the energy of vortex-like structures, we apply a new method based on the use of the central extended Galilei group. In a special case, we calculate the energy levels of a system of quantized vortices. The proposed approach makes it possible to describe both the interaction of such vortex - like filaments and the processes of their creation and annihilation in a natural way. As a result, we have constructed a quantum turbulent flow model that demonstrates the relationship between stochastic and integrable dynamics.

15 pages

References in corpus (5)

• Small Oscillations of a Vortex Ring: Hamiltonian Formalism and Quantization
• Closed Vortex Filament in a Cylindrical Domain: Circulation Quantization
• The turbulence development at its initial stage: a scenario based on the idea of vortices decay
• Towards quantum turbulence theory: A simple model with interaction of the vortex loops
• Higher-order statistics and intermittency of a two-fluid HVBK quantum turbulent flow

Cited by in corpus (2)

• The quantum vortices dynamics: spatio-temporal scale hierarchy and origin of turbulence
• On the group-theoretical approach to energy quantization of a perturbed vortex ring: spectrum calculating in the pipe-type domain