On reversals in 2D turbulent Rayleigh-Bénard convection: Insights from embedding theory and comparison with proper orthogonal decomposition analysis

Faranda, Davide; Podvin, Bérengère; Sergent, Anne

doi:10.1063/1.5081031

Cited by 2 publications

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References 50 publications

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“…Decomposing the turbulent flow into coherent flow structures and incoherent turbulence, allows us to focus on dynamically significant events (Hussain 1986). Such decomposition is usually performed either in terms of predetermined basis functions, like spatial Fourier decomposition (see, for instance, Das, Ghosal & Kumar 2000, Chandra & Verma 2011), or in terms of basis functions extracted from the data, like proper orthogonal decomposition (POD) (see, for instance Bailon-Cuba, Emran & Schumacher 2010, Podvin & Sergent 2015, 2017, Faranda, Podvin & Sergent 2019), dynamic mode decomposition (DMD) (Schmid 2010; Horn & Schmid 2017) or Koopman eigenfunction analysis (Giannakis et al. 2018).…”

Section: Introductionmentioning

confidence: 99%

Cessation and reversals of large-scale structures in square Rayleigh–Bénard cells

et al. 2019

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We consider direct numerical simulations of turbulent Rayleigh–Bénard convection inside two-dimensional square cells. For Rayleigh numbers $Ra=10^{6}$ to $Ra=5\times 10^{8}$ and Prandtl numbers $Pr=3$ and $Pr=4.3$, two types of flow regimes are observed intermittently: consecutive flow reversals (CR), and extended cessations (EC). For each regime, we combine proper orthogonal decomposition (POD) and statistical tools on long-term data to characterise the dynamics of large-scale structures. For the CR regime, centrosymmetric modes are dominant and display a coherent dynamics, while non-centrosymmetric modes fluctuate randomly. For the EC regime, all POD modes follow Poissonian statistics and a non-centrosymmetric mode is dominant. To explore further the differences between the CR and EC regimes, an analysis based on a cluster partition of the POD phase space is proposed. This data-driven approach confirms the successive mechanisms of the generic reversal cycle in CR as proposed in Castillo-Castellanos et al. (J. Fluid Mech., vol. 808, 2016, pp. 614–640). However, these mechanisms may take one of multiple paths in the POD phase space. Inside the EC regime, this approach reveals the presence of two types of coherent time sequences (weak reversals and actual cessations) and more rarely intense plume crossings. Finally, we analyse within a range of Rayleigh numbers up to turbulent flow, the relation between dynamical regimes and the POD energetic contents as well as the residence time in each cluster.

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Section: Introductionmentioning

confidence: 99%

Cessation and reversals of large-scale structures in square Rayleigh–Bénard cells

et al. 2019

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Dynamics of large-scale circulation and energy transfer mechanism in turbulent Rayleigh–Bénard convection in a cubic cell

Vishnu

Mishra

2020

Physics of Fluids

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We present the characteristics and dynamics of large-scale circulation (LSC) in turbulent Rayleigh–Bénard convection (RBC) inside a cubic cell. The simulations are carried out for a Rayleigh number range of 2 × 106 ≤ Ra ≤ 109 and using air (at Prandtl number Pr = 0.7) as the working fluid. Using the Fourier mode analysis, the strength, orientation, and associated dynamics of LSC are characterized. Following previous two-dimensional studies in RBC, we propose a mechanism of flow reversals based on the dynamics of corner vortices, which is less attempted in three-dimensional counterparts. We observe that the plane containing LSC is generally aligned along one of the diagonals of the box accompanied by a four-roll structure in the other. In addition to the primary roll, two secondary corner-roll structures are also observed in the LSC plane, which grow in size and destabilize the LSC, resulting in partial (ΔΦ1 ≈ π/2) and complete (ΔΦ1 ≈ π) reversals. In addition to previously reported rotation-led reorientations, we also observe cessation events that are rare in cubic cells. We observe that as the Rayleigh number is increased from Ra = 2 × 106 to 107, the number of reorientations reduces by one third. With an increase in Ra, the strength of LSC (SLSC) increases and the corner rolls reduce in size, which leads to the reduction in the occurrence of reorientations. At higher Rayleigh numbers (Ra > 108), the strength saturates around SLSC ≈ 0.75. To connect the dynamics between different coherent structures, we evaluate the turbulent kinetic energy (TKE) budget. Notably, our novel approach to study the variation of TKE along the azimuthal direction helps in identifying the dynamical coupling between the LSC and non-LSC planes. The analysis suggests that TKE is generally produced in localized regions in both the planes, while its dissipation mainly happens in the vicinity of the plane that contains LSC. The transport mechanism redistributes the energy between these planes and thus sustains the LSC and other coherent structures.

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On reversals in 2D turbulent Rayleigh-Bénard convection: Insights from embedding theory and comparison with proper orthogonal decomposition analysis

Cited by 2 publications

References 50 publications

Cessation and reversals of large-scale structures in square Rayleigh–Bénard cells

Cessation and reversals of large-scale structures in square Rayleigh–Bénard cells

Dynamics of large-scale circulation and energy transfer mechanism in turbulent Rayleigh–Bénard convection in a cubic cell

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