INTERMITTENCY EFFECTS IN ROTATING DECAYING TURBULENCE

Abstract

ABSTRACTRotation modulates turbulence causing columnar struc-turing of a turbulent flow in case of sufficiently strongrotation. This yields significant changes in the flow charac-teristics and dispersion properties, which makes rotationalturbulence modulation particularly relevant in the contextof atmospheric and oceanic flows. Here we investigate thecanonical flow of turbulence in a periodic box, subjectedto rotation about a fixed vertical axis. As point of refer-ence we consider direct numerical simulations of homoge-neous isotropic turbulence. Modulation due to rotation atvarious rotation rates (i.e., different Rossby numbers) is in-vestigated. Special attention is paid to the alteration ofintermittency, which is measured in terms of changes in thescaling of the structure functions. A reduction of intermit-tency quantified with the longitudinal structure functions inthe direction perpendicular to the rotation axes will be pre-sented. These numerical findings correspond well to recentresults obtained in experiments by Seiwert et al. (2008) [1].TURBULENCE AND ROTATIONTurbulence exhibits intense bursts of vorticity and strainthat can be important for example in production of forcefulvortices in atmospheric flows. An important interest in at-mospheric fluid dynamics is concentrated around the impactof the Coriolis force on turbulence that tends to the two-dimensionalization of the flow. In this paper we considerdirect numerical simulations of decaying turbulence in a ro-tating frame of reference studying the effect of the Coriolisforce on turbulence. For high rotation rates the Coriolis forceis dominant in a wide range of scales and plays an impor-tant role balancing the convective nonlinearity and viscousforces [2]. We will show that the Coriolis force not only sup-presses the forward energy transfer to small scales, but alsomodifies the dynamics of turbulence measured in terms ofthe structure functions. These are explored in this paper viadirect numerical simulations at various rotation rates.The Kolmogorov K41 description of turbulence [3, 4]results in scaling laws for structure functions of the ve-locity increments. The second order structure function isthe best-known, characterized by the famous Kolmogorovenergy spectrum with a −5/3 slope. The Kolmogorov ap-proach predicts a linear dependence of the scaling exponentson the order of the structure function [3]. However, inthree-dimensional isotropic turbulence a so-called anoma-lous scaling of the structure functions is observed [4, 5, 6].This is visible in a nonlinear dependence of the scaling expo-nents on the order of the structure function. This anomaly isassociated with the effect of ‘intermittency’. One may expectthat rotation, which induces a ‘trend’ toward partial two-dimensionalization of the flow, will reduce intermittency andthereby also the anomalous scaling. Recent experiments in afreely decaying rotating turbulence using PIV show a strongincrease of the exponents of the structure functions [1]. Thisis particularly pronounced for the second-order structurefunction. Correspondingly, a reduced scaling anomaly wasreported. The main aim of this work is to complement theseexperimental findings with numerical simulations, allowinga direct correlation between reduced scaling anomaly androtational flow structures.The organization of this paper is as follows. First, weintroduce the computational setting for simulations of tur-bulence in a rotating frame of reference. Then, we presentresults of direct numerical simulations, quantifying the sup-pression of the energy decay for growing rotation rates. Af-terwards, we quantify the intermittency via computation ofthe structure functions. The tendency to two-dimensionalizedue to rotation is clearly expressed in a reduced presence ofsmaller scales in the flow and correspondingly increases scal-ing exponents. Finally, concluding remarks are collected inthe last section.COMPUTATIONAL SETTINGThe decay of turbulence with an additional Coriolis forceis investigated in a simple temporal setting using a paral-lelized, fully de-aliased pseudo-spectral method to simulatethe flow in a computational box endowed with periodicboundary conditions. The incompressible Navier-Stokes