On the formation of cyclones and anticyclones in a rotating fluid

Abstract

It is commonly observed that the columnar vortices which dominate the large scales in homogeneous, rapidly rotating turbulence are predominantly cyclonic. This has prompted us to ask how this asymmetry arises. To provide a partial answer to this we look at the process of columnar vortex formation in a rotating fluid, and in particular, we examine how a localized region of swirl (an eddy) can convert itself into a columnar structure by inertial wave propagation. We show that, when the Rossby number (Ro) is small, the vortices evolve into columnar eddies through the radiation of linear inertial waves. When the Rossby number is large, on the other hand, no such column is formed. Rather, the eddy bursts radially outward under the action of the centrifugal force. There is no asymmetry between cyclonic and anticyclonic eddies for these two regimes. However, cyclones and anticyclones behave differently in the intermediate 1 Corresponding author; e-mail: binod@earth.leeds.ac.uk 1 regime of Ro ∼ 1. Here we find that the transition from columnar vortex formation to radial bursting occurs at lower values of Ro for anticyclones, with the transition for anticyclones occurring at Ro ∼ 0.5, and that for cyclones at Ro ∼ 2. Thus, in a homogeneous turbulence experiment conducted at, say, Ro = 1, we would expect to see more cyclones than anticyclones. The reason for this asymmetry at Ro ∼ 1 is explained.

Rotating Taylor–Green flow

“…This second structure (best seen in figure 12(b)) is fluctuating strongly having more small scales. The persistence of corotating structures in rotating turbulence has been observed in experiments (Hopfinger et al 1982;Morize et al 2005;Gallet et al 2014) and has been discussed in various works (Hopfinger & van Heijst 1993;Bartello et al 1994;Gence & Frick 2001;Sreenivasan & Davidson 2008;Staplehurst et al 2008;Gallet et al 2014). Perhaps it is not surprising that structures with vorticity anti-aligned to rotation are more responsive to 3D perturbations.…”

Cyclone-anticyclone asymmetry and alignment statistics in homogeneous rotating turbulence

“…7 In the last decades, many studies have also been devoted to the characterization of the cycloneanticyclone asymmetry. This symmetry-breaking was first visualized in inhomogeneous and forced rotating turbulence, 8 then investigated quantitatively in experimental and numerical systems, both in freely decaying 2,7,[9][10][11][12] and in forced 13 turbulence. All these studies characterized the cycloneanticyclone asymmetry through the measurement of the skewness of the vertical vorticity component ω 3 , which vanishes in isotropic turbulence and is positive in rotating flows.…”

Structure and Dynamics of Rotating Turbulence: A Review of Recent Experimental and Numerical Results

“…This predicts a linear growth of hx 3 z i at short time, in qualitative agreement with the observations, but the long-time behavior cannot be inferred from this equation when s ij becomes in turn modified by rotation. It is important to note that this process of emergence of dominant cyclonic motion from an initially isotropic state is different from the selection of cyclonic structures among pre-existing cyclonic and anti-cyclonic vortices [77]. The latter mechanism involves the stability of coherent structures, from various possible mechanisms, such centrifugal or elliptical instability.…”