A phenomenological theory of rotating turbulence

作者：Bin Baqui Yasir^*; Davidson P A

来源：Physics of Fluids, 2015, 27(2): 025107.

DOI：10.1063/1.4907671

We present direct numerical simulations of statistically homogeneous, freely decaying, rotating turbulence in which the Rossby number, Ro = u(perpendicular to)/2 Omega l(perpendicular to), 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(perpendicular to) << l(parallel to). This regime occurs when Ro similar to 0.4 and is characterised by an almost constant perpendicular integral scale, l(perpendicular to) similar to constant, a rapid linear growth in the integral scale parallel to the rotation axis, l(parallel to) similar to l(perpendicular to)Omega t, and a slow decline in the value of Ro. We observe that the rate of dissipation of energy scales as epsilon similar to u(3)/l(parallel to) and that both the perpendicular and parallel energy spectra exhibit a k(-5/3) inertial range; E (k(perpendicular to)) similar to epsilon(2/3)k(perpendicular to)(-5/3). and E (k(parallel to)) similar to epsilon(2/3)k(parallel to)(-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 epsilon similar to u(3)/l(perpendicular to). We develop a phenomenological theory of the inertial range that assumes that the observed linear growth in anisotropy, l(parallel to)/l(perpendicular to) similar to Omega t, also occurs on a scale-by-scale basis most of the way down to the Zeman scale, the linear growth in l(parallel to) 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.

• 出版日期2015-2