Vortex solitary waves in a rotating, turbulent flow

Abstract

Turbulent flow in a rotating container has been widely studied^1–5, but here we consider an experiment in which the axis of rotation is vertical, the tank deep and a vigorous turbulence is produced near the bottom by a horizontal grid oscillating in the vertical direction. The flow within the rotating container can be envisioned to result from: (1) the disorganized, turbulent motion produced by the grid which, in the absence of rotation, would yield a random field with turbulent intensity decreasing upwards (away from the grid) and turbulent length scale increasing upwards⁶; (2) the organizing influence of rotation which, in the absence of turbulence, would generate a (trivial) flow having a single vertical component of vorticity, 2Ω (Ω is the tank rotation rate), uniform throughout the tank. These two competing effects combined produce a flow field which is surprisingly complex. The major feature of the flow consists of a collection of regions of highly concentrated vorticity, or vortices. These vortices extend coherently throughout the depth of the container. Waves having the form of compact, helical distortions propagate along the vortex cores. We show that the waves are well described by the vortex soliton theory of Hasimoto⁷.