Direct numerical simulation of homogeneous isotropic helical turbulence with the TARANG code

Abstract

The problem of taking into account the influence of flow turbulence appears when solving both fundamental questions of geo- and astrophysics, and applied problems arising in the development of new engineering technologies. Difficulties in applying standard representations of the theory arise when considering special flows - flows with a complex spatial structure. One of such features - helicity of the flow - determines the topology of the vortices. Helicity is conserved in the process of cascade energy transfer in a turbulent flow. In this paper we consider the approach to numerical simulation of the helical homogeneous isotropic turbulence in order to identify characteristics of the inertial range formation and to define distributions of the spectral densities of energy and helicity. To solve this problem it is suggested to use the TARANG software package designed to solve problems of fluid dynamics in developed turbulent flow and to study hydrodynamic instability phenomena of different physical nature (thermal convection, advection of passive and active scalar transport, magnetic hydrodynamics, the influence of the Coriolis force). TARANG is an open source software written in object-oriented C++ language, which implements the technology of parallelizing computations for running on multiprocessor computers. The spectral distributions and fluxes for energy and helicity are calculated for Reynolds numbers 5700 and 14000 on grids 512^3 and 1024^3 , respectively. The validity of the spectral law "-5/3" and the estimation of the universal constants of Kolmogorov and Batchelor in the inertial scale interval are verified. An analysis of the energy and helicity transfer functions between the separated scales (shell-to-shell transfer) reveals a significant contribution of nonlocal interactions to the cascade process.