Direct numerical simulations of non-helical and helical stratified turbulent flows

ABSTRACT

Direct numerical simulations of weakly and strongly stratified decaying homogenous turbulence are conducted for two transition-to-turbulence cases with different initial conditions: the non-helical Taylor–Green vortex (TGV) and the helical Arnold–Beltrami–Childress (ABC) configurations. These simulations are carried out using a pseudo-spectral formulation with a 512³ grid resolution at varying Froude numbers, . First, an effort is made to classify the various regimes represented by and 0.08, or alternatively, buoyancy Reynolds number () values from to for non-helical and helical stably stratified turbulence. Second, various quantities including enstrophy, dissipation, vertical shearing, coherent vortical structures, density fields, energy spectra and fluxes in the different directions, and helicity are analysed to understand the effects of stratification on the development of turbulence and the turbulent structure in these different regimes. Consistent with previous studies by Riley and deBruynKops (Phys. Fluids, 2003) and Rorai et al. (Phys. Rev. E, 2013), both the TGV and ABC simulation results showed that stratification slowed down the development of turbulence. At the lowest (0.16 and 0.08) tested here, for which , the fluid motions in TGV were inhibited significantly by the strong stratification so as to eliminate the energy cascade regime and in turn, the inertial subrange. This led to an increased dissipation at the large scales in these cases as also observed in Brethouwer et al. (J. Fluid Mech., 2007). Spectral fluxes also showed an inverse energy cascade for very high stratification. Due to the nature of the ABC's initial configuration, it was observed that for the same values, its energy cascade was less inhibited in comparison to TGV and always forward as opposed to inverse for the very low- TGV cases, a behaviour that was also reflected in the different evolutions between the two flows. So compared to TGV, the large scales were more energetic in ABC for the same . In addition, horizontal velocity and density fluctuation fields of ABC simulation results, both showed the density layering effect from increased stratification.

Keywords:

• anisotropic turbulence
• direct numerical simulation
• stratification
• helicity