Journal of Fluid Mechanics


Invariants for slightly heated decaying grid turbulence

R. A. Antoniaa1, S. K. Leea1, L. Djenidia1 c1, P. Lavoiea2 and L. Danailaa3

a1 School of Engineering, University of Newcastle, NSW, 2308, Australia

a2 Institute for Aerospace Studies, University of Toronto, ON, Canada M3H 5T6

a3 CORIA CNRS UMR 6614, Université de Rouen, 77801 Saint Etienne du Rouvray, France


The paper examines the validity of velocity and scalar invariants in slightly heated and approximately isotropic turbulence generated by passive conventional grids. By assuming that the variances and ( and represent the longitudinal velocity and temperature fluctuations) decay along the streamwise direction according to power laws and ( is the virtual origin of the flow) and with the further assumption that the one-point energy and scalar variance budgets are represented closely by a balance between the rates of change of and and the corresponding mean energy dissipation rates, the products and must remain constant with respect to . Here and are the Taylor and Corrsin microscales. This is unambiguously supported by previously available data, as well as new measurements of and made at small Reynolds numbers downstream of three different biplane grids. Implications for invariants based on measured integral length scales of and are also tested after confirming that the dimensionless energy and scalar variance dissipation rate parameters are approximately constant with . Since the magnitudes of and vary from grid to grid and may also depend on the Reynolds number, the Saffman and Corrsin invariants which correspond to a value of for and are unlikely to apply in general. The effect of the Reynolds number on is discussed in the context of published data for both passive and active grids.

(Received September 19 2012)

(Revised April 18 2013)

(Accepted April 23 2013)

(Online publication June 26 2013)

Key words

  • homogeneous turbulence;
  • isotropic turbulence;
  • turbulence theory


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