Testing a Missing Spectral Link in Turbulence

Abstract

Although the cardinal attribute of turbulence is the velocity fluctuations, these fluctuations have been ignored in theories of the frictional drag of turbulent flows. Our goal is to test a new theory that links the frictional drag to the spectral exponent α, a property of the velocity fluctuations in a flow. We use a soap-film channel wherein for the first time the value of α can be switched between 3 and 5/3, the two theoretically possible values in soap-film flows. To induce turbulence with α = 5/3, we make one of the edges of the soap-film channel serrated. Remarkably, the new theory of the frictional drag holds in both soap-film flows (for either value of the spectral exponent α) and ordinary pipe flows (where α = 5/3), even though these types of flow are governed by different equations.