Abstract
The flux of energy from large to small scales in hydrodynamic turbulence controls the dissipation of energy at a given scale in the fluid. An accurate parametrization of this flux is a prerequisite in order to devise reliable methods to simulate turbulent flows without resolving all the scales of motion. This problem is discussed in the context of a particle method based on the Smooth Particles Hydrodynamics algorithm. Motivated by the von Karman–Howarth–Kolmogorov exact relation for the energy flux, and by Lagrangian dynamics considerations we postulate an energy transfer term which is quadratic in the velocity and formally time reversal invariant. The numerical simulation of the model however is observed to spontaneously break the time reversal symmetry, demonstrating that the proposed term acts on average as the desired eddy damping.
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Pumir, A., Shraiman, B.I. Lagrangian Particle Approach to Large Eddy Simulations of Hydrodynamic Turbulence. Journal of Statistical Physics 113, 693–700 (2003). https://doi.org/10.1023/A:1027300400526
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DOI: https://doi.org/10.1023/A:1027300400526