Toward autonomous large eddy simulations of turbulence based on interscale energy transfer among resolved scales

In the present work we show how the subgrid-scale (SGS) energy transfer among resolved scales in large eddy simulations (LESs) and its wave number distribution can be obtained from the evolving LES velocity fields. This information, supplemented by the known asymptotic properties of energy flux in the inertial range, when cast in the form of a spectral eddy viscosity, allows self-contained simulations without use of extraneous SGS models. The method is tested in LESs of isotropic turbulence at high Reynolds number where the inertial range dynamics is expected and for lower-Reynolds-number decaying turbulence under conditions of the classical Comte-Bellot–Corrsin experiments.

Figure 1

Spectral eddy viscosity shape functions. The solid line with circles denotes the analytical expression (29), the dashed line shows a shape function computed from LES data, and the dotted line shows the asymptotic plateau value from the EDQNM theory

Figure 2

Results for forced LES. (a) Lines with circles show the initial conditions for energy spectra. The solid line shows the case eKolmF, the dashed line the case ePulseF, and the dash-dotted line the results of LES performed with the Chollet-Lesieur spectral model. In this and all subsequent figures thin straight lines show, as appropriate, a $-5/3$ slope and a boundary of the forcing band at $k=3$. (b) For compensated spectra horizontal lines mark the expected range of values for the Kolmogorov constant.

Figure 3

Results for the decaying LES case eKolmD for (a) energy spectra and (b) compensated energy spectra. The line with circles denotes the initial condition and solid lines show energy spectra at different times of decay.

Figure 4

Results for the decaying LES case ePulseD for (a) energy spectra and (b) compensated energy spectra. The line with circles denotes the initial condition and solid lines show energy spectra at different times of decay.

Figure 5

Energy and dissipation spectra for forced DNSs. The solid line shows the energy spectrum and the dashed line shows the dissipation spectrum; dashed straight vertical lines denote wave-number band boundaries and the $-5/3$ slope is indicated by a straight solid line.

Figure 6

(a) Experimental energy and viscous dissipation spectra at different times. Lines of the same type show energy spectra $E\left(k\right)$ (with symbols) and dissipation spectra $D\left(k\right)$ (without symbols): solid lines and circles, $U_{0}t/M=42$; dashed lines and squares, $U_{0}t/M=98$; and dotted lines and triangles, $U_{0}t/M=171$. (b) Time evolution of energy spectra in underresolved DNS. Markers correspond to experimental data and lines show progression in time from the initial energy spectrum at $U_{0}t/M=42$ to the final time at $U_{0}t/M=171$ (dotted line).

Figure 7

Time evolution of energy spectra in a LES run (a) for time interval $U_{0}t/M=[42,98]$, continuing in (b) for time interval $U_{0}t/M=[98,171]$.