Direct and inverse energy cascades in a forced rotating turbulence experiment

TL;DR

This paper experimentally investigates energy transfer in rotating turbulence, revealing a double cascade in horizontal energy and a consistent forward cascade in vertical energy, with flow behavior approaching two-dimensionality at high rotation rates.

Contribution

It provides the first experimental evidence of a double cascade in rotating turbulence and extends the Kármán-Howarth-Monin equation to inhomogeneous flows.

Findings

Horizontal energy exhibits both inverse and direct cascades depending on scale.

Vertical energy consistently cascades from large to small scales.

Flow becomes nearly two-dimensional at high rotation rates.

Abstract

We present experimental evidence for a double cascade of kinetic energy in a statistically stationary rotating turbulence experiment. Turbulence is generated by a set of vertical flaps which continuously injects velocity fluctuations towards the center of a rotating water tank. The energy transfers are evaluated from two-point third-order three-component velocity structure functions, which we measure using stereoscopic particle image velocimetry in the rotating frame. Without global rotation, the energy is transferred from large to small scales, as in classical three-dimensional turbulence. For nonzero rotation rates, the horizontal kinetic energy presents a double cascade: a direct cascade at small horizontal scales and an inverse cascade at large horizontal scales. By contrast, the vertical kinetic energy is always transferred from large to small horizontal scales, a behavior reminiscent of the dynamics of a passive scalar in two-dimensional turbulence. At the largest rotation rate the flow is nearly two-dimensional, and a pure inverse energy cascade is found for the horizontal energy. To describe the scale-by-scale energy budget, we consider a generalization of the K\'arm\'an-Howarth-Monin equation to inhomogeneous turbulent flows, in which the energy input is explicitly described as the advection of turbulent energy from the flaps through the surface of the control volume where the measurements are performed.