Direct Numerical Simulation of Homogeneous Isotropic Helical Turbulence with the TARANG Code

Abstract

The problem of taking into account the influence of turbulence comes up while solving both fundamental questions of geo- and astrophysics and applied problems arising in the development of new engineering solutions. Difficulties in applying the standard propositions of the theory appear when considering flows with a special spatial structure, for example, helical flows. The flow helicity determines the topology of vortices and is conserved in the process of energy transfer in a turbulent flow. In this paper we suggest an approach for numerical simulation of homogeneous isotropic helical turbulence aimed at detecting characteristic signatures of the inertial range and finding the distributions of the spectral energy and helicity densities. In this approach we use the TARANG code designed to numerically solve various problems of fluid dynamics in the regime of a developed turbulent flow and to study hydrodynamic instability phenomena of a different physical nature (thermal convection, advection of passive and active scalars, magnetohydrodynamics, and the influence of Coriolis forces). TARANG is an open source code written in the object-oriented C++ language with a high efficiency of computation on multiprocessor computers. Particular attention in the paper is given to the application of the tool kit from the package to analyze the solutions obtained. The spectral distributions and fluxes of energy and helicity have been computed for Reynolds numbers of 5700 and 14 000 on 5123 and 10243 grids, respectively. We have checked whether the –5/3 spectral law is realizable and estimated the universal Kolmogorov and Batchelor constants in the inertial range. An analysis of the energy and helicity transfer functions between the selected scales (shell-to-shell transfer) shows a significant contribution of nonlocal interactions to the cascade process.