Rotating Taylor–Green flow

Abstract

The steady state of a forced Taylor-Green flow is investigated in a rotating frame of reference. The investigation involves the results of 184 numerical simulations for different Reynolds numbers Re F and Rossby numbers Ro F . The large number of examined runs allows a systematic study that enables the mapping of the different behaviours observed to the parameter space (Re F , Ro F ), and the examination of different limiting procedures for approaching the large Re F small Ro F limit. Four distinctly different states were identified: laminar, intermittent bursts, quasi-twodimensional condensates and weakly rotating turbulence. These four different states are separated by power-law boundaries Ro F ∝ Re −γ F in the small Ro F limit. In this limit, the predictions of asymptotic expansions can be directly compared with the results of the direct numerical simulations. While the first-order expansion is in good agreement with the results of the linear stability theory, it fails to reproduce the dynamical behaviour of the quasi-two-dimensional part of the flow in the nonlinear regime, indicating that higher-order terms in the expansion need to be taken into account. The large number of simulations allows also to investigate the scaling that relates the amplitude of the fluctuations with the energy dissipation rate and the control parameters of the system for the different states of the flow. Different scaling was observed for different states of the flow, that are discussed in detail. The present results clearly demonstrate that the limits of small Rossby and large Reynolds numbers do not commute and it is important to specify the order in which they are taken.

Spectral imbalance in the inertial range dynamics of decaying rotating turbulence

“…Interestingly, it appears that C Π is roughly constant with a numerical value around 0.5 for Ro L 0.3 and decreases for smaller Ro L . Note that C Π is almost independent of the initial Rossby and Reynolds numbers as long as the initial Rossby number is sufficiently large to allow a fully turbulent flow for a given Reynolds number [28]. In turn, the behaviour of C ε for the various initial Rossby numbers is also qualitatively similar to that discussed above, i.e.…”

“…flows where rotation has an important role on turbulence dynamics but it does not fully dominate the flow and lead to a quasi-2D turbulence regime [24][25][26][27][28]. For example, the empirical scaling ε ∝ u ′3 /L is thought to apply to mildly rotating turbulence [28] with different variants to take into account the anisotropy of the flow [29,30].…”

“…For example, the empirical scaling ε ∝ u ′3 /L is thought to apply to mildly rotating turbulence [28] with different variants to take into account the anisotropy of the flow [29,30]. In contrast, strongly rotating flows are weakly turbulent and exhibit marked differences such as laminar-like dissipation scaling [28] and thus the discussions pertaining to turbulence theory are of limited use. Furthermore, this mild rotation regime has, arguably, a closer connection to engineering applications and is also typical of many rotating turbulence laboratory experiments and numerical simulations [24,28,[31][32][33][34][35].…”

Hysteretic transitions between quasi-two-dimensional flow and three-dimensional flow in forced rotating turbulence

“…[10] reported a phase diagram for statistically steady states of forced Taylor-Green flows in a rotating frame. Four different steady states in the parameter space spanned by the Reynolds numbers and the Rossby numbers were numerically obtained by carrying out 184 simulations.…”

“…Because the parameter space analysis was performed with the same random initial condition for every parameter values in Ref. [10], the hysteretic behavior cannot be directly found.…”