Objectivity in Turbulence under Change of Reference Frame and Superposed Rigid Body Motion

Abstract

The validity of objectivity or frame-indifference in turbulence is examined simultaneously from the dual perspective of change of reference frame and superposed rigid-body motion. Similarities and differences arising from the two approaches and their effect on modeling in turbulence are discussed in detail. The use of the absolute spin for noninertial frames and of the net spin for superposed rigid-body motions in closure representations for the pressure-strain-rate correlations tensor are critically discussed. The enigmatic statement made by Speziale that the frame-indifference or objectivity of Reynolds stress does not establish the validity of material frame-indifference in turbulence and the subsequent case-study test of objectivity under superposed rigid-body mean motion within a rotating frame presented to prove it are investigated and fully explained. It is shown analytically that such apparently contrasting conclusions on the validity of objectivity result from the application of the objectivity test to the mean rather than the instantaneous motion, a case not encountered in classical continuum mechanics, which considers only one motion, the instantaneous.