Physical Mechanism of the Two-Dimensional Inverse Energy Cascade

We study the physical mechanisms of the two-dimensional inverse energy cascade using theory, numerics, and experiment. Kraichnan’s prediction of a -5/3 spectrum with constant, negative energy flux is verified in our simulations of 2D Navier-Stokes equations. We observe a similar but shorter range of inverse cascade in laboratory experiments. Our theory predicts, and the data confirm, that inverse cascade results mainly from turbulent stress proportional to small-scale strain rotated by 45°. This “skew-Newtonian” stress is explained by the elongation and thinning of small-scale vortices by large-scale strain which weakens their velocity and transfers their energy upscale.