Effects of subgrid-scale modeling on time correlations in large eddy simulation

Abstract

The effects of the unresolved subgrid-scale ͑SGS͒ motions on the energy balance of the resolved scales in large eddy simulation ͑LES͒ have been investigated actively because modeling the energy transfer between the resolved and unresolved scales is crucial to constructing accurate SGS models. But the subgrid scales not only modify the energy balance, they also contribute to temporal decorrelation of the resolved scales. The importance of this effect in applications including the predictability problem and the evaluation of sound radiation by turbulent flows motivates the present study of the effect of SGS modeling on turbulent time correlations. This paper compares the two-point, two-time Eulerian velocity correlation in isotropic homogeneous turbulence evaluated by direct numerical simulation ͑DNS͒ with the correlations evaluated by LES using a standard spectral eddy viscosity. It proves convenient to express the two-point correlations in terms of spatial Fourier decomposition of the velocity field. The LES fields are more coherent than the DNS fields: their time correlations decay more slowly at all resolved scales of motion and both their integral scales and microscales are larger than those of the DNS field. Filtering alone is not responsible for this effect: in the Fourier representation, the time correlations of the filtered DNS field are identical to those of the DNS field itself. The possibility of modeling the decorrelating effects of the unresolved scales of motion by including a random force in the model is briefly discussed. The results could have applications to the problem of computing sound sources in isotropic homogeneous turbulence by LES.

LES prediction of space-time correlations in turbulent shear flows

“…This is consistent with the previous observations in isotropic turbulence [6,7,13] and turbulent channel flows [20,21]. Moreover, the discrepancies between DNS and LES are larger in the convection direction than those in other two directions, especially in the viscous wall region.…”

“…Previous work on isotropic turbulence has found that LES with an eddy-viscosity SGS model could over-predict decorrelation time scales of space-time correlations and under-predict their magnitudes [6,7]. These results are supported by the sweeping hypothesis [7,12]: the spacetime correlations in isotropic turbulence are mainly determined by energy spectra.…”

“…One way is to introduce a random force to represent the backscatter effect. He et al [6] has developed a constrain for the random force in LES to recover the decorrelation length scales. Recently, Marstorp et al [27] propose a stochastic Smagorinsky SGS model which allows for backscatter of the energy at unresolved scales.…”

“…Two typical examples are turbulencegenerated noise [3] and turbulent mixing [4]. In the first example, the acoustic intensity radiated by a turbulent flow is dependent on the two-time, two-point correlations of velocity fluctuations in the Eulerian frame [5][6][7]; in the second example, turbulent transport processes are naturally described by particle dispersion [8], or at least two-time velocity correlations of two particles in the Lagrangian frame [9]. The twotime, two-point correlations of velocity fluctuations in either Eulerian or Lagrangian frame are conventionally called as space-time correlations.…”

Stochastic Excitation of Acoustic Modes in Stars

“…The way the small scales are treated in LES can affects our description of turbulence. Indeed, He et al (2002) have shown that LES results in a χ k (ω) that decreases at all resolved scales too rapidly with ω with respect to direct numerical simulations (DNS). Moreover, Jacoutot et al (2008b) found that computed mode excitation rates depend significantly on the adopted sub-grid model.…”