A large-scale investigation of wind reversal in a square Rayleigh–Bénard cell

Abstract

We consider the numerical simulation of Rayleigh–Bénard convection in a 2D square cell filled with water ($\mathit{Pr}=4.3$) at a turbulent Rayleigh number of $\mathit{Ra}=5\times 10^{7}$. We focus on the structures and dynamics of the large-scale intermittent flow. Two quasi-stable flow patterns are identified: one consists of a main diagonal roll with two corner rolls; and the other of two horizontally stacked rolls. These stable flow structures are associated with two types of events, which involve corner flow growth and pattern rotation: reversals, when the main roll rapidly switches signs; and cessations, when it disappears for longer periods. Proper orthogonal decomposition (POD) is applied independently to the velocity field and to the temperature field. In both cases, three principal modes were identified: a single-roll, large-scale circulation; a quadrupolar flow; and a double-roll, symmetry-breaking mode. The large-scale circulation is the kinetic mode with the highest energy. The most energetic temperature mode is associated with the mean temperature and corresponds to a velocity field of quadrupolar nature. The vertical heat flux is concentrated in these two modes. The reversal process is characterized by sharp fluctuations in the amplitudes of all modes. Analysis of the interaction coefficients between the spatial modes leads us to propose a three-dimensional model, based on the interaction of the large-scale circulation, the quadrupolar flow and horizontal rolls. The main dynamics and time scales of reversals and cessations are reproduced by the model in the presence of noise.

Koopman analysis of the long-term evolution in a turbulent convection cell

“…This calls for a reduction of the degrees of freedom of the system. Models with different levels of reduction have been developed to understand the long transients of the LSC dynamics, among them a nonlinear oscillator model for a cylindrical cell (Brown & Ahlers 2006) and a three-mode LSC model based on a Proper Orthogonal Decomposition (POD) in a square convection cell (Podvin & Sergent 2015). POD-type extraction of the most energetic degrees of freedom has also been used in the threedimensional case to determine the contribution of the primary and secondary POD modes to the global turbulent heat transfer (Bailon-Cuba et al 2010).…”

On the applicability of low-dimensional models for convective flow reversals at extreme Prandtl numbers

“…The phenomenon of flow reversals is complex, and thus, as motivated earlier, to gain a simplified understanding of their dynamics, researchers have constructed LDMs [13][14][15]. * Present address: Department of Physics, Syracuse University, Syracuse, New York 13244, USA; mmannatt@syr.edu † pambrish@iitk.ac.in ‡ mkv@iitk.ac.in § sagarc@iitk.ac.in Araujo et al [13] derived three nonlinearly-coupled ordinary differential equations representing large-scale temperature Fourier modes.…”

“…This model exhibits reversals similar to that observed in the dynamo field generated during the turbulent flow of liquid sodium. Podvin and Sergent [15] used proper orthogonal decomposition to construct an LDM that captures the reversals in two-dimensional thermal convection.…”

Reversals in infinite-Prandtl-number Rayleigh-Bénard convection

“…Mishra et al [6] and * ambrish.pandey@tu-ilmenau.de † mkv@iitk.ac.in ‡ barma@tifrh.res.in Xi et al [22] investigated the reversals of LSC in a cylindrical geometry, and observed that during a cessation-led reversal, the strength of secondary flow modes increase, whereas that of the primary mode decreases. In 2D RBC, reversals are constrained to occur through a cessation event, and the dominance of secondary modes during a cessation have also been reported [8][9][10][11][12][13][14]. Moreover, it has been observed that the first few most energetic flow modes capture the flow pattern and dynamics of LSC reversals very well [10][11][12][13][14].…”

“…In 2D RBC, reversals are constrained to occur through a cessation event, and the dominance of secondary modes during a cessation have also been reported [8][9][10][11][12][13][14]. Moreover, it has been observed that the first few most energetic flow modes capture the flow pattern and dynamics of LSC reversals very well [10][11][12][13][14]. In this paper, we gathered very long time statistics of the temporal evolution of vertical velocities at various locations in our simulation domain, and observe that their evolution and statistical properties can be described very well by the most energetic Fourier modes of the flow.…”