Helicity subgrid-scale models and their numerical validation

Abstract

Large-eddy simulations (LES) with an appropriate subgrid-scale (SGS) model provide a powerful tool for investigating real-world turbulence. The Smagorinsky model, one of the simplest and most used SGS models, often shows an over-dissipative behavior even when using dynamic procedures to adjust the model coefficient. By incorporating the structural or geometrical information of turbulence provided by helicity (velocity-vorticity correlations), the helicity SGS model is expected to alleviate these issues in the standard Smagorinsky framework, in which only information of turbulence intensity is considered through the turbulent energy. The validity of helicity SGS models is investigated here with the aid of direct numerical simulations (DNSs). Using configurations with and without net rotation, and with large-scale helicity gradients sustained by a mechanical forcing, we show that to better model SGS turbulence, SGS helicity effects should be incorporated into the model together with the Smagorinsky-like eddy viscosity.

Figures (27)

• Figure 1: Configuration of a turbulent swirling flow in a straight pipe. A dented axial mean velocity profile in the central axis region upstream is slowly relaxed to the usual flat velocity profile far downstream.
• Figure 2: Spatial distributions of the Reynolds stress (a) and the inhomogeneous-helicity effect (b). The Reynolds stress $\langle {u'^y u'^z} \rangle$ is scaled by the turbulent energy. The turbulence timescale $\tau$ is defined by $\tau = 1/(u_{\rm{rms}} k_{\rm{F}})$ with $u_{\rm{rms}}$ being the root mean square velocity, and $k_{\rm{F}}$ the forcing wavenumber. Redrawn from the data of yok2016b
• Figure 3: Spatial distribution of the induced large-scale velocity $U^y$ (a) and the turbulent helicity $\langle {{\bf{u}}' \cdot \hbox{\boldmath$\omega$}'} \rangle$ injected by external forcing (b). The Coriolis number ${\rm{Co}}$ is defined by ${\rm{Co}} = \omega_{\rm{F}} \tau$. Redrawn from the data of yok2016b
• Figure 4: Schematic representation of the simulation domain with the Cartesian coordinates, the mean inhomogeneous helicity profile $H(x)$ indicated by the thick black line, and the direction of rotation $\hbox{\boldmath$\omega$}_{\rm{F}}$ indicated by the thick arrow.
• Figure 5: Time evolutions of (a) the kinetic energy $E$, and (b) the enstrophy $Z$, in the simulation without rotation. After the flow reaches the turbulent steady state, we keep integrating the flow and analyze GS and SGS quantities.