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A phenomenological theory of rotating turbulence

Baqui, YB and Davidson, PA (2015) A phenomenological theory of rotating turbulence. Physics of Fluids, 27. ISSN 1070-6631

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© 2015 AIP Publishing LLC. We present direct numerical simulations of statistically homogeneous, freely decaying, rotating turbulence in which the Rossby number, Ro = u ⊥ /2Ωl ⊥ , is of order unity. This is the regime normally encountered in laboratory experiments. The initial condition consists of fully developed turbulence in which Ro is sufficiently high for rotational effects to be weak. However, as the kinetic energy falls, so also does Ro, and quite quickly, we enter a regime in which the Coriolis force is relatively strong and anisotropy grows rapidly, with l ⊥ ≪ l || . This regime occurs when Ro ~0.4 and is characterised by an almost constant perpendicular integral scale, l ⊥ ~constant, a rapid linear growth in the integral scale parallel to the rotation axis, l || ~ l⊥ Ωt and a slow decline in the value of Ro. We observe that the rate of dissipation of energy scales as ε ~u 3 /⊥ || and that both the perpendicular and parallel energy spectra exhibit a k -5/3 inertial range; E (k ⊥ ) ~ε 2/3 k ⊥ -5/3 and E (k || )2/3 k || 5/3 . We show that these power-law spectra have nothing to do with Kolmogorov's theory, since the equivalent non-rotating turbulence, which has the same initial condition and Reynolds number, does not exhibit a k -5/3 inertial range, the Reynolds number being too low. Nor are the spectra a manifestation of traditional critical balance theory, as this requires ε ~u 3 /l ⊥ . We develop a phenomenological theory of the inertial range that assumes that the observed linear growth in anisotropy, l || /l ⊥ ~Ωt, also occurs on a scale-by-scale basis most of the way down to the Zeman scale, the linear growth in l || being a consequence of inertial wave propagation. Below the Zeman scale, however, inertial waves cannot propagate, and so there is necessarily a transition in spectral behaviour around this scale. The observed spectra are consistent with the predictions of our phenomenological theory.

Item Type: Article
Divisions: Div A > Fluid Mechanics
Depositing User: Cron Job
Date Deposited: 17 Jul 2017 19:41
Last Modified: 03 Aug 2017 03:12