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

Abstract

Two aspects of homogeneous rotating turbulence are quantified through forced Direct Numerical Simulations in an elongated domain, which is in the direction of rotation about 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 , the growth rate of the columnar eddies and its dependency on the Rossby number Ro ε is determined as γ = 4 exp(−17Ro ε ), where γ is the non-dimensional growth rate. Second, a scaling law for the energy dissipation rate ε ν is sought. Comparison with current available scaling laws shows that the relation proposed by Baqui & Davidson (2015), i.e., ε ν ∼ u 3 / , where u is the r.m.s. velocity, approximates well part of our data, more specifically the range 0.39 Ro ε 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 ε 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 (1965). Within this framework, the energy dissipation rate is considered to depend on both the nonlinear time-scale and the relaxation time-scale. Thus, by analyzing our data, expressions for these different time-scales are obtained that results in ε ν ∼ u 4 /( 2 ⊥ Ro 0.62 ε τ iso nl ), where ⊥ is the integral length-scale in the direction normal to the axis of rotation and τ iso nl is the non-liner time-scale of the initial homogeneous isotropic field. † Email address for correspondence: t.pestana@tudelft.nl arXiv:1907.10133v1 [physics.flu-dyn]

Critical transition in fast-rotating turbulence within highly elongated domains

“…In particular, recent experiments were able to investigate the presence of the inverse cascade (Campagne et al 2014, 2015, 2016; Yarom & Sharon 2014). The transition from a forward to an inverse cascade in rotating turbulence was studied systematically using numerical simulations by Smith, Chasnov & Waleffe (1996), Deusebio et al (2014) and Pestana & Hickel (2019, 2020), while the transition to a condensate regime was studied by Alexakis (2015), Yokoyama & Takaoka (2017) and Seshasayanan & Alexakis (2018).…”

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

“…2009). This is observed from visualizing four movies (movie 1, ; movie 2, ; movie 3, ; and movie 4, ), which show the evolution of the flow field in a subset of the computational domain; see our data repository (Pestana & Hickel 2019 a , https://doi.org/10.4121/uuid:324788e3-a64f-4786-9ef9-f97d70a29064) for the animations, and also two movies of the contours of the vorticity vector along the axis of rotation , on a normal (movie 5) and a parallel plane (movie 6). Altogether, the visualizations indicate that rotation destroys the small structures and modulates the flow field such that columns elongated in the direction of rotation emerge.…”