Macroscopic effects of the spectral structure in turbulent flows

Abstract

There is a missing link between the macroscopic properties of turbulent flows, such as the frictional drag of a wall-bounded flow, and the turbulent spectrum. The turbulent spectrum is a power law of exponent α (the spectral exponent) that gives the characteristic velocity of a turbulent fluctuation (or eddy) of size s as a function of s (ref.1). Here we seek the missing link by comparing the frictional drag in soap-film flows, where α=3 (refs9, 10), and in pipe flows, where α=5/3 (refs11, 12). For moderate values of the Reynolds number Re, we find experimentally that in soap-film flows the frictional drag scales as Re-1/2, whereas in pipe flows the frictional drag scales as Re-1/4. Each of these scalings may be predicted from the attendant value of α by using a new theory, in which the frictional drag is explicitly linked to the turbulent spectrum. © 2010 Macmillan Publishers Limited. All rights reserved.