Intermittency Effects in Rotating Decaying Turbulence

Rotation modulates turbulence causing columnar structuring of a turbulent flow in case of sufficiently strong rotation. This yields significant changes in the flow characteristics and dispersion properties, which makes rotational turbulence modulation particularly relevant in the context of atmospheric and oceanic flows. Here we investigate the canonical flow of turbulence in a periodic box, subjected to rotation about a fixed vertical axis. As point of reference we consider direct numerical simulations of homogeneous isotropic turbulence. Modulation due to rotation at various rotation rates (i.e., different Rossby numbers) is investigated. Special attention is paid to the alteration of intermittency, which is measured in terms of changes in the scaling of the structure functions. A reduction of intermittency quantified with the longitudinal structure functions in the direction perpendicular to the rotation axes will be presented. These numerical findings correspond well to recent results obtained in experiments by Seiwert et al. (2008) [1]. TURBULENCE AND ROTATION Turbulence exhibits intense bursts of vorticity and strain that can be important for example in production of forceful vortices in atmospheric flows. An important interest in atmospheric fluid dynamics is concentrated around the impact of the Coriolis force on turbulence that tends to the twodimensionalization of the flow. In this paper we consider direct numerical simulations of decaying turbulence in a rotating frame of reference studying the effect of the Coriolis force on turbulence. For high rotation rates the Coriolis force is dominant in a wide range of scales and plays an important role balancing the convective nonlinearity and viscous forces [2]. We will show that the Coriolis force not only suppresses the forward energy transfer to small scales, but also modifies the dynamics of turbulence measured in terms of the structure functions. These are explored in this paper via direct numerical simulations at various rotation rates. The Kolmogorov K41 description of turbulence [3, 4] results in scaling laws for structure functions of the velocity increments. The second order structure function is the best-known, characterized by the famous Kolmogorov energy spectrum with a −5/3 slope. The Kolmogorov approach predicts a linear dependence of the scaling exponents on the order of the structure function [3]. However, in three-dimensional isotropic turbulence a so-called anomalous scaling of the structure functions is observed [4, 5, 6]. This is visible in a nonlinear dependence of the scaling exponents on the order of the structure function. This anomaly is associated with the effect of ‘intermittency’. One may expect that rotation, which induces a ‘trend’ toward partial twodimensionalization of the flow, will reduce intermittency and thereby also the anomalous scaling. Recent experiments in a freely decaying rotating turbulence using PIV show a strong increase of the exponents of the structure functions [1]. This is particularly pronounced for the second-order structure function. Correspondingly, a reduced scaling anomaly was reported. The main aim of this work is to complement these experimental findings with numerical simulations, allowing a direct correlation between reduced scaling anomaly and rotational flow structures. The organization of this paper is as follows. First, we introduce the computational setting for simulations of turbulence in a rotating frame of reference. Then, we present results of direct numerical simulations, quantifying the suppression of the energy decay for growing rotation rates. Afterwards, we quantify the intermittency via computation of the structure functions. The tendency to two-dimensionalize due to rotation is clearly expressed in a reduced presence of smaller scales in the flow and correspondingly increases scaling exponents. Finally, concluding remarks are collected in the last section. COMPUTATIONAL SETTING The decay of turbulence with an additional Coriolis force is investigated in a simple temporal setting using a parallelized, fully de-aliased pseudo-spectral method to simulate the flow in a computational box endowed with periodic boundary conditions. The incompressible Navier-Stokes equations for velocity v(x, t), pressure p(x, t), and external force f :