Turbulence decay rate as a measure of flow dimensionality

The dimensionality of turbulence in fluid layers determines their properties. We study electromagnetically driven flows in finite-depth fluid layers and show that eddy viscosity, which appears as a result of three-dimensional motions, leads to increased bottom damping. The anomaly coefficient, which characterizes the deviation of damping from the one derived using a quasi-two-dimensional model, can be used as a measure of the flow dimensionality. Experiments in turbulent layers show that when the anomaly coefficient becomes high, the turbulent inverse energy cascade is suppressed. In the opposite limit turbulence can self-organize into a coherent flow.