Dynamical and statistical phenomena of circulation and heat transfer in periodically forced rotating turbulent Rayleigh-Bénard convection

Abstract

In this paper, we present results from an experimental study into turbulent Rayleigh-Bénard convection forced externally by periodically modulated unidirectional rotation rates. We find that the azimuthal rotation velocityθ(t) and thermal amplitude δ(t) of the large-scale circulation (LSC) are modulated by the forcing, exhibiting a variety of dynamics including increasing phase delays and a resonant peak in the amplitude ofθ(t). We also focus on the influence of modulated rotation rates on the frequency of occurrence η of stochastic cessation/reorientation events, and on the interplay between such events and the periodically modulated response ofθ(t). Here we identify a mechanism by which η can be amplified by the modulated response and these normally stochastic events can occur with high regularity. We provide a modeling framework that explains the observed amplitude and phase responses, and extend this approach to make predictions for the occurrence of cessation events and the probability distributions ofθ(t) and δ(t) during different phases of a modulation cycle, based on an adiabatic approach that treats each phase separately. Lastly, we show that such periodic forcing has consequences beyond influencing LSC dynamics, by investigating how it can modify the heat transport even under conditions where the Ekman pumping effect is predominant and strong enhancement of heat transport occurs. We identify phase and amplitude responses of the heat transport, and show how increased modulations influence the average Nusselt number.

Periodically driven Taylor–Couette turbulence

“…Periodically driven turbulence also includes studies in a number of different well-known and canonical closed-flow geometries, such as Rayleigh-Bénard convection (Jin & Xia 2008;Sterl et al 2016), and von Kármán flow (Cadot et al 2003). In these systems the forcing was periodically varied over time, with the variations being of O(10%) of either the average forcing or the energy input.…”

Periodically Modulated Thermal Convection

“…In periodically driven turbulence in shear flows, a meanfield theory has been used to analyze the resonance maxima of the Reynolds number [3,4]. Periodic forcing in other turbulent systems, for example, in the homogeneous isotropic turbulence [5][6][7][8], pipe flow [9][10][11][12], channel flow [13,14], Taylor-Couette flow [15,16], and Rayleigh-Bénard (RB) convection [17][18][19], is also shown to have highly nontrivial response properties.…”

“…The RB system, consisting of a fluid layer heated from below and cooled from above, has been extensively studied as the paradigmatic and well-defined system for convective thermal turbulence [20][21][22]. Also, several modulation methods have been studied for that system, such as bottom temperature modulation [17,19,23], rotation modulation [18,24], and gravity modulation [25,26]. Intuitively, one may expect that the modulation effect on time-averaged global quantities is limited because the net force averaged over a cycle vanishes.…”

Thermal Waves and Heat Transfer Efficiency Enhancement in Harmonically Modulated Turbulent Thermal Convection

“…Here the paradigm is the turbulent Rayleigh-Bénard convection (RBC) [1,2], occurring within a layer of Oberbeck-Boussinesq (OB) fluid between two horizontal, ideally conducting and laterally infinite plates separated by the distance L in a gravitational field (acceleration due to gravity g). Confined turbulent RBC, a very useful laboratory tool, belongs to the family of most frequently studied turbulent flows, however, studies of confined RBC driven by steady temperature difference ∆T 0 with a weak superimposed sinusoidal temperature perturbation [3][4][5] up to the case of fully periodic thermal drive [6], periodically forced [7] or kicked thermal turbulence [8] are scarce.…”