Turbulent flow Question

Sirvonny · April 13, 2020, 23:31

Before i dwell into CFD, I am trying to analytically prove this statement to be true for incompressible turbulent flow.

Im struggling to prove that in homogeneous, isotropic turbulent ﬂows the average rate of kinetic energy dissipation per unit mass of ﬂuid is: (attached image).

LuckyTran · April 14, 2020, 04:33

It looks like your image is cropped because your formula is incomplete and missing some terms if Rii is the auto-correlation function.

Nonetheless if you start with the definition of the turbulent dissipation rate, recognize that there is the trace of the Reynolds stress tensor hiding in there. Not that many tricks except abusing relations.

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April 14, 2020, 04:33		#2
LuckyTran Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,762 Rep Power: 66	It looks like your image is cropped because your formula is incomplete and missing some terms if Rii is the auto-correlation function. Nonetheless if you start with the definition of the turbulent dissipation rate, recognize that there is the trace of the Reynolds stress tensor hiding in there. Not that many tricks except abusing relations.