Rossby-number effects on columnar eddy formation and the energy dissipation law in homogeneous rotating turbulence

Two aspects of homogeneous rotating turbulence are quantified through forced direct numerical simulations in an elongated domain, which, in the direction of rotation, is approximately 340 times larger than the typical initial eddy size. First, by following the time evolution of the integral length scale along the axis of rotation l(parallel to), the growth rate of the columnar eddies and its dependence on the Rossby number Ro(epsilon) is determined as gamma = 3.90 exp (-16.72 Ro(epsilon)) for 0.06 <= Ro(epsilon) <= 0.31, where gamma is the non-dimensional growth rate. Second, a scaling law for the energy dissipation rate epsilon(nu) is sought. Comparison with current available scaling laws shows that the relation proposed by Baqui & Davidson (Phys. Fluids, vol. 27(2), 2015, 025107), i.e. epsilon(nu) similar to u'(3)/l(parallel to), where u' is the root-mean-square velocity, approximates well part of our data, more specifically the range 0.39 <= Ro(epsilon) <= 1.54. However, relations proposed in the literature fail to model the data for the second and most interesting range, i.e. 0.06 <= Ro(epsilon) <= 0.31, which is marked by the formation of columnar eddies. To find a similarity relation for the latter, we exploit the concept of a spectral transfer time introduced by Kraichnan (Phys. Fluids, vol. 8(7), 1965, p. 1385). Within this framework, the energy dissipation rate is considered to depend on both the nonlinear time scale and the relaxation time scale. Thus, by analysing our data, expressions for these different time scales are obtained that result in epsilon(nu) similar to (u'(4)Ro(epsilon)(0.62)tau(iso)(nl))/l(perpendicular to)(2), where l(perpendicular to) is the integral length scale in the direction normal to the axis of rotation and tau(iso)(nl) is the nonlinear time scale of the initial homogeneous isotropic field.