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A conditionally cubic-Gaussian stochastic Lagrangian model for acceleration in isotropic turbulence

Published online by Cambridge University Press:  14 June 2007

A. G. LAMORGESE ,
S. B. POPE ,
P. K. YEUNG  and
B. L. SAWFORD
A. G. LAMORGESE
Affiliation:
Sibley School of Mechanical & Aerospace Engineering, Cornell University, Ithaca, NY 14853-7501, USA
S. B. POPE
Affiliation:
Sibley School of Mechanical & Aerospace Engineering, Cornell University, Ithaca, NY 14853-7501, USA
P. K. YEUNG
Affiliation:
School of Aerospace Engineering, Georgia Institute of Technology, 270 Ferst Drive, Atlanta, GA 30332-0150, USA
B. L. SAWFORD
Affiliation:
Department of Mechanical Engineering, Monash University, Clayton Campus, Wellington Road, Clayton, VIC 3800, Australia
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Abstract

The modelling of fluid-particle acceleration in homogeneous isotropic turbulence in terms of stochastic models for the Lagrangian velocity, acceleration and a dissipation rate variable is considered. The basis for the Reynolds model (A. M. Reynolds, Phys. Rev. Lett. vol. 91, 2003, 084503) is reviewed and examined by reference to direct numerical simulations (DNS) of isotropic turbulence at Taylor-scale Reynolds number (Rλ) up to about 650. In particular, we show DNS data that support stochastic modelling of the logarithm of pseudo-dissipation as an Ornstein–Uhlenbeck process and reveal non-Gaussianity of the acceleration conditioned on fluctuations of the pseudo-dissipation rate. The DNS data are used to construct a new stochastic model that is exactly consistent with Gaussian velocity and conditionally cubic-Gaussian acceleration statistics. This model captures the effects of small-scale intermittency on acceleration and the conditional dependence of acceleration on pseudo-dissipation (which differs from that predicted by the refined Kolmogorov hypotheses). Non-Gaussianity of the conditionally standardized acceleration probability density function (PDF) is accounted for in terms of model nonlinearity. The large-time behaviour of the new model is that of a velocity-dissipation model that can be matched with DNS data for conditional second-order Lagrangian velocity structure functions. As a result, the diffusion coefficient for the new model incorporates two-time information and its Reynolds-number dependence as observed in DNS. The resulting model predictions for conditional and unconditional velocity autocorrelations and time scales are shown to be in very good agreement with DNS.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 582 , 10 July 2007 , pp. 423 - 448
Copyright
Copyright © Cambridge University Press 2007

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