Experimental test of a missing spectral link in turbulence

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 $\alpha$, a property of the velocity fluctuations in a flow. We use a soap-film channel wherein for the first time the value of $\alpha$ can be switched between 3 and 5/3, the two theoretically possible values in soap-film flows. Remarkably, the new theory holds in both soap-film flows and ordinary pipe flows, even though these types of flow are governed by different equations. We conclude that even where the governing equations are unknown and $\alpha$ can take anomalous values (as in sediment-laden rivers and polymer-doped oil pipelines), the frictional drag might be estimated from simple measurements of $\alpha$.