Energy Transfer by Inertial Waves during the Buildup of Turbulence in a Rotating System

Abstract

We study the transition from fluid at rest to turbulence in a rotating tank. The energy is transported by inertial wave packets through the fluid volume. These high amplitude waves propagate at velocities consistent with those calculated from linearized theory [H. P. Greenspan, (Cambridge University Press, Cambridge, England, 1968)]. A "front" in the temporal evolution of the energy power spectrum indicates a time scale for energy transport at the linear wave speed. Nonlinear energy transfer between modes is governed by a different, longer, time scale. The observed mechanisms can lead to significant differences between rotating and two-dimensional turbulent flows.

An experimental investigation of forced steady rotating turbulence

“…Since the rotation of the reference frame occurs along a single direction, the symmetry between the stabilisation characteristics of eddies with cyclonic and anti-cyclonic vorticity starts to break apart [9,19], resulting in the cyclonic dominance mentioned earlier. Mathematically, this condition of small Ro and high Re, permits the reduction of (1) to a wave-like equation where the Coriolis term gives rise to inertial waves -the linear propagation of which is crucial 30 in explaining the formation of columnar structures [3,2,10]. This theory is supported by findings in physical [17, for example] and numerical [16, among others] experiments.…”

“…Detailed analysis of the experimental observations showed that, among the columnar eddies, the cyclonic ones, which spin in the same direction as the bulk rotation, dominate the oppositely spinning anti-cyclones [7]. The presence of these columnar eddies were also found to reduce the turbulence 10 dissipation rate compared to an equivalent non-rotating case. However, very few studies, if any, address the case where the rotation is not of a solid-body type.…”

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

“…[41] and [42] for more recent realizations, using fractal grids). Other forcings have been used with similar results, like arrays of tubes acting as sinks and sources [43][44][45] and electromagnetic forcing (see Fig. 3(d)) [37,46,47].…”

“…[4] and [33]). In recent years, a series of rotating platforms of smaller diameters have been set up in different laboratories, with comparable values of Re/Ro, in Austin (Texas) [38], Orsay (France) [31,50], Cambridge (United Kingdom) [34], Turin (Italy) [51], Eindhoven (Netherlands) [37], Zurich (Switzerland) [41], Tel Aviv (Israel) [44], etc. (see Table 1).…”

The twists and turns of rotating turbulence

“…Cambon, Mansour &Godeferd 1997 andSmith &Waleffe 1999) and the possible role of linear wave propagation (e.g. Staplehurst, Davidson &Dalziel 2008 andKolvin et al 2009), yet their results will feed into the discussion.…”