Conservation of Turbulence in Rapidly Rotating Flow

Abstract

The behavior of an incompressible homogeneous turbulence in a rapidly rotating system is investigated. Linearized equations based on Rapid Distortion Theory (RDT) are used to analyze the rotating turbulence. In the rotating system without mean velocity-gradients, it is shown that the trace, which is defined by the phase space of the Fourier spectrum of the velocity fluctuation and the time-derivative of the Fourier spectrum of the velocity fluctuation, has an elliptic trajectory-the system has periodicity. Such a rotating system involves the conservation of the sum of the Reynolds stress tensor and the tensor composed of the vector streamfunction gradient correlation. The latter tensor describes the large-scale structure of vorticity field [for example, Reynolds et al., Phys. Fluids, 14 (2002), 2485-2492]. The tensors were calculated numerically with various initial anisotropic conditions using the solutions derived from the linearized equations. The results were found to substantiate the conservation relation under various conditions.