Enard Convection Research Articles

A generalized curvilinear solver for spherical shell Rayleigh-B\'enard convection

A generalized curvilinear solver for spherical shell Rayleigh-B\'enard convection

Accounting for surface temperature variations in Rayleigh-Bénard convection

Turbulent Rayleigh-B\'enard convection is often modeled with a constant surface temperature. However, the surface temperature of many geophysical systems, such as lakes, is coupled to the atmospheric forcing. In this paper, we account for this dynamic surface temperature and show that many of the classical results from the Rayleigh-B\'enard literature are recovered.

Time-dependent oscillating viscoelastic Rayleigh-Bénard convection: Viscoelastic kinetic energy budget analysis

Numerical simulations of viscoelastic Rayleigh-B\'enard convection (VRBC) are conducted to investigate time-dependent oscillating convection leading to the formation of reverse flowing cells. A viscoelastic kinetic-energy budget method is used to analyze the energy transport and a parametric analysis for the reversal flow dynamics. The emergence of the reversal convection can be explained by potential energy transfer between flow and fluid elasticity. The image shows periodic total kinetic energy (${E}_{t\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}l}$), energy exchange rate (${\mathrm{\ensuremath{\Phi}}}_{G}$), and buoyancy flux (${\mathrm{\ensuremath{\Phi}}}_{F}$) time evolution in VRBC from the local view, during a half-period of a reverse process for Phan-Thien-Tanner (PTT) fluid.

Long-distance migration with minimal energy consumption in a thermal turbulent environment

We adopt the reinforcement learning algorithm to train the self-propelling agent migrating long-distance in a thermal turbulent environment. We choose the Rayleigh-B\'enard turbulent convection cell with an aspect ratio ($\Gamma$, which is defined as the ratio between cell length and cell height) of 2 as the training environment. Our results showed that, compared to a naive agent that moves straight from the origin to the destination, the smart agent can learn to utilize the carrier flow currents to save propelling energy. We then apply the optimal policy obtained from the $\Gamma=2$ cell and test the smart agent migrating in convection cells with $\Gamma$ up to 32. In a larger $\Gamma$ cell, the dominant flow modes of horizontally stacked rolls are less stable, and the energy contained in higher-order flow modes increases. We found that the optimized policy can be successfully extended to convection cells with a larger $\Gamma$. In addition, the ratio of propelling energy consumed by the smart agent to that of the naive agent decreases with the increase of $\Gamma$, indicating more propelling energy can be saved by the smart agent in a larger $\Gamma$ cell. We also evaluate the optimized policy when the agents are being released from the randomly chosen origin, which aims to test the robustness of the learning framework, and possible solutions to improve the success rate are suggested. This work has implications for long-distance migration problems, such as unmanned aerial vehicles patrolling in a turbulent convective environment, where planning energy-efficient trajectories can be beneficial to increase their endurance.

Numerical simulation of tidal synchronization of the large-scale circulation in Rayleigh--Bénard convection with aspect ratio 1

A possible explanation for the apparent phase stability of the 11.07-year Schwabe cycle of the solar dynamo was the subject of a series of recent papers. The synchronization of the helicity of an instability with azimuthal wavenumber m=1 by a tidal m=2 perturbation played a key role here. To analyze this type of interaction in a paradigmatic set-up, we study a thermally driven Rayleigh-B\'enard Convection (RBC) of a liquid metal under the influence of a tide-like electromagnetic forcing. As shown previously, the time-modulation of this forcing emerges as a peak frequency in the m=2 mode of the radial flow velocity component. In this paper we present new numerical results on the interplay between the Large Scale Circulation (LSC) of a RBC flow and the time modulated electromagnetic forcing.

Inverse cascades of kinetic energy and thermal variance in three-dimensional horizontally extended turbulent convection

Inverse cascades of kinetic energy and thermal variance in the subset of vertically homogeneous modes in spectral space are found to cause a slow aggregation to a pair of convective supergranules that eventually fill the whole horizontally extended, three-dimensional, turbulent Rayleigh-B\'{e}nard convection layer when a heat flux is prescribed at the top and bottom. An additional weak rotation of the layer around the vertical axis stops this aggregation at a scale that is smaller than the lateral domain extension and ceases the inverse cascade for the thermal variance. The inverse cascade for the kinetic energy remains intact, even for times at which the root mean square values of temperature and velocity have reached the statistically steady state. This kinetic energy inverse cascade sustains the horizontally extended convection patterns which are best visible in the temperature field. The resulting characteristic length of the aggregated convection patterns depends on the thermal driving and linearly on the strength of rotation. Our study demonstrates the importance of inverse energy cascades beyond the two-dimensional turbulence case in a three-dimensional convection flow that is subject to a multi-scale energy injection by thermal plumes and driven by boundary heat fluxes as typically present in natural geo- and astrophysical systems, such as solar convection.

Viscous dissipation as a mechanism for spatiotemporal chaos in Rayleigh-Bénard convection between poorly conducting boundaries at infinite Prandtl number

Nonlinear Rayleigh-B \ifmmode \acute{}\else \'{}\fi{}enard convection in an infinite Prandtl number fluid layer between poorly conducting boundaries is considered as a model for convection in the Earth's upper mantle. It is shown that accounting for the generally neglected impact of viscous dissipation may lead to the development of large-scale spatiotemporal chaotic dynamics governed by the familiar Kuramoto-Sivashinsky (KS) equation, ${\mathrm{\ensuremath{\Phi}}}_{\ensuremath{\tau}}+{\ensuremath{\nabla}}^{4}\mathrm{\ensuremath{\Phi}}+2{\ensuremath{\nabla}}^{2}\mathrm{\ensuremath{\Phi}}\ensuremath{-}{(\ensuremath{\nabla}\mathrm{\ensuremath{\Phi}})}^{2}+\ensuremath{\alpha}\phantom{\rule{0}{0ex}}\mathrm{\ensuremath{\Phi}}=0,$ known to occur in various physical systems. The figure shows an irregular pattern of chaotically recombining cells developing at $\ensuremath{\alpha}=0.1$.

Bounds for rotating convection at infinite Prandtl number from semidefinite programs

The technique of semidefinite programming is used to replace direct numerical simulations and time integrations of turbulent flows with an optimization problem which is easier to solve but which returns only upper bounds to the time averages the direct numerical simulation would have produced. This idea is applied to rotating Rayleigh-B\'enard convection at infinite Prandtl number. The obtained bounds are not sharp but they reproduce the qualitative behavior of the results known from direct simulations and experiments.

Extreme vorticity events in turbulent Rayleigh-Bénard convection from stereoscopic measurements and reservoir computing

High-amplitude events of the out-of-plane vorticity component ${\ensuremath{\omega}}_{z}$ are analyzed by stereoscopic particle image velocimetry (PIV) in the bulk region of turbulent Rayleigh-B\'enard convection in air. The Rayleigh numbers $\mathrm{Ra}$ vary from $1.7\ifmmode\times\else\texttimes\fi{}{10}^{4}$ to $5.1\ifmmode\times\else\texttimes\fi{}{10}^{5}$. The experimental investigation is connected with a comprehensive statistical analysis of long-term time series of ${\ensuremath{\omega}}_{z}$ and individual velocity derivatives $\ensuremath{\partial}{u}_{i}/\ensuremath{\partial}{x}_{j}$. A statistical convergence for derivative moments up to an order of 6 is demonstrated. Our results are found to agree well with existing high-resolution direct numerical simulation data in the same range of parameters, including the extreme vorticity events that appear in the far exponential tails of the corresponding probability density functions. The transition from Gaussian to non-Gaussian velocity derivative statistics in the bulk of a convection flow is confirmed experimentally. The experimental data are used to train a reservoir computing model, one implementation of a recurrent neural network, to reproduce highly intermittent experimental time series of the vorticity and thus reconstruct extreme out-of-plane vorticity events. After training the model with high-resolution PIV data, the machine learning model is run with sparsely seeded, continually available, and unseen measurement data in the reconstruction phase. The dependence of the reconstruction quality on the sparsity of the partial observations is also documented. Our latter result paves the way to machine-learning-assisted experimental analyses of small-scale turbulence for which time series of missing velocity derivatives can be provided by generative algorithms.

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

We study turbulent Rayleigh-Bénard convection over four decades of Rayleigh numbers 4×10^{8}<Ra<2×10^{12}, while harmonically modulating the temperatures of the plates of our cylindrical cell. We probe the flow by temperature sensors placed in the cell interior and embedded in the highly conducting copper plates and detect thermal waves propagating at modulation frequency in the bulk of the convective flow. We confirm the recent numerical prediction [Yang etal., Phys. Rev. Lett. 125, 154502 (2020)PRLTAO0031-900710.1103/PhysRevLett.125.154502] of the significant enhancement of the Nusselt number and report its dependence on the frequency and amplitude of the temperature modulation of plates.

Pattern selection in Rayleigh-Bénard convection with nonlinear viscoelastic fluids

A numerical investigation is conducted of Rayleigh-B\'enard convection in a rectangular enclosure of aspect ratio 2:1 filled by a class of nonlinear viscoelastic fluids represented by the Phan Thien-Tanner (PTT) constitutive equation. The objective is to provide a detailed interpretation of the physical mechanisms involved in Rayleigh-B\'enard convection for a viscoelastic fluid. An energy analysis highlights the different physical mechanisms involved in oscillatory convection. The results show the contribution of the elastic terms in the evolution of the kinetic energy of the structures. At a second critical Rayleigh number the oscillatory convection with two rollers becomes stationary again.

Dimensionless parameters for cloudy Rayleigh-Bénard convection: Supersaturation, Damköhler, and Nusselt numbers

In this article we bridge between the Rayleigh-B\'enard convection literature and the atmospheric literature by expressing the governing equations for cloudy convection in a dimensionless form. The governing parameters are Rayleigh, Prandtl, Schmidt, Damk\"ohler, and sedimentation numbers for the cloudy case. We further connect to the atmospheric literature by obtaining an expression for the Nusselt number (dimensionless heat flux) for a cloud--convection system, directly from the conservation equations for temperature and water vapor, and illustrate the microphysics independence through large eddy simulation of an idealized cloudy Rayleigh-B\'enard convection flow.

Flow- and temperature-based statistics characterizing the regimes in rapidly rotating turbulent convection in simulations employing no-slip boundary conditions

We present results from direct numerical simulations of rotating Rayleigh--B\'enard convection (RRBC), the quintessential paradigm for investigating buoyancy-driven rotating turbulence, at rather extreme values of the governing parameters and bounded by experimentally realizable no-slip boundary conditions. We provide a statistical characterization of the RRBC flow regimes that can be used as a framework for identification of these flow states in future experiments and simulations at even more extreme parameter values, and for extrapolation to geophysical and astrophysical flow systems.

OnsagerNet: Learning stable and interpretable dynamics using a generalized Onsager principle

Machine learning is becoming an increasingly popular method for building mathematical models from observations of natural processes. Here, the central challenge is to impart structure into the model parameterization to enforce physical relevance, yet retain a degree of generality so that a large variety of dynamics can be learned. We introduce a novel methodology, based on a data-driven extension of the classical Onsager principle, that strikes a balance between these competing aspects. We demonstrate its efficacy by learning quantitatively accurate and qualitatively faithful reduced order models of the Rayleigh-B\'enard convection equations.

Fast Microscale Acoustic Streaming Driven by a Temperature-Gradient-Induced Nondissipative Acoustic Body Force.

We study acoustic streaming in liquids driven by a nondissipative acoustic body force created by light-induced temperature gradients. This thermoacoustic streaming produces a velocity amplitude nearly 100 times higher than the boundary-driven Rayleigh streaming and the Rayleigh-Bénard convection at a temperature gradient of 10 K/mm in the channel. The Rayleigh streaming is altered by the acoustic body force at a temperature gradient of only 0.5 K/mm. The thermoacoustic streaming allows for modular flow control and enhanced heat transfer at the microscale. Our study provides the groundwork for studying microscale acoustic streaming coupled with temperature fields.

Rayleigh-Bénard convection in a dielectric fluid under an external electric field with a melting boundary

Rayleigh-B\'enard convection during a solid-liquid phase change in the presence of an electric field is studied via a lattice Boltzmann method. We investigate both the onset of flow motion and pattern formation in the presence of an electric field and a melting boundary. The critical Rayleigh number decreases monotonically with the timescale separation. We predict the robust locked-in behavior of topography, which is broken when a strong enough electric field is considered.

Universal properties of penetrative turbulent Rayleigh-Bénard convection

Penetrative turbulence, which occurs in a convectively unstable fluid layer and penetrates into an adjacent, originally stably stratified layer, is numerically and theoretically analyzed. We chose the most relevant example, namely thermally driven flow of water with a temperature around $T_m\approx 4^\circ\rm{C}$, where it has its density maximum. We pick the Rayleigh-B\'enard geometry with the bottom plate temperature $T_b > 4^\circ\rm{C}$ and the top plate temperature $T_t \le 4^\circ\rm{C}$. Next to the overall thermal driving strength set by the temperature difference $\Delta = T_b - T_t$ (the Rayleigh number $Ra$ in dimensionless form), the crucial new control parameter as compared to standard Rayleigh-B\'enard convection is the density inversion parameter $\theta_m \equiv (T_m - T_t ) / \Delta$. The crucial response parameters are the relative mean mid-height temperature $\theta_c$ and the overall heat transfer (i.e., the Nusselt number $Nu$). We theoretically derive the universal (i.e., $Ra$-independent) dependence $\theta_c (\theta_m) =(1+\theta_m^2)/2$, which holds for $\theta_m$ below a $Ra$-dependent critical value, beyond which $\theta_c (\theta_m)$ sharply decreases and drops down to $\theta_c=1/2$ at $\theta_m=\theta_{m,c}$. Our direct numerical simulations with $Ra$ up to $10^{10}$ are consistent with these results. The critical density inversion parameter $\theta_{m,c}$ can be precisely predicted by a linear stability analysis. The heat flux $Nu(\theta_m)$ monotonically decreases with increasing $\theta_m$ and we can theoretically derive a universal relation for the relative heat flux $Nu(\theta_m)/Nu(0)$. Finally, we numerically identify and discuss rare transitions between different turbulent flow states for large $\theta_m$.

Bounding temperature dissipation in time-modulated Rayleigh-Bénard convection

We use the background method to find an upper bound on the nondimensional temperature dissipation for Rayleigh-B\'enard convection with the temperature of one boundary modulated in time. The resulting bound depends on characteristics of the temperature modulation profile and its derivative. We investigate the limits of high-frequency modulation and large Rayleigh number, and we also examine two examples of sinusoidal modulation. Asymptotically, the bound for large Rayleigh number has the same leading order behavior as the non-modulated case.

Echo state network for two-dimensional turbulent moist Rayleigh-Bénard convection.

Recurrent neural networks are machine learning algorithms that are well suited to predict time series. Echo state networks are one specific implementation of such neural networks that can describe the evolution of dynamical systems by supervised machine learning without solving the underlying nonlinear mathematical equations. In this work, we apply an echo state network to approximate the evolution of two-dimensional moist Rayleigh-Bénard convection and the resulting low-order turbulence statistics. We conduct long-term direct numerical simulations to obtain training and test data for the algorithm. Both sets are preprocessed by a proper orthogonal decomposition (POD) using the snapshot method to reduce the amount of data. Training data comprise long time series of the first 150 most energetic POD coefficients. The reservoir is subsequently fed by these data and predicts future flow states. The predictions are thoroughly validated by original simulations. Our results show good agreement of the low-order statistics. This incorporates also derived statistical moments such as the cloud cover close to the top of the convection layer and the flux of liquid water across the domain. We conclude that our model is capable of learning complex dynamics which is introduced here by the tight interaction of turbulence with the nonlinear thermodynamics of phase changes between vapor and liquid water. Our work opens new ways for the dynamic parametrization of subgrid-scale transport in larger-scale circulation models.

Scale of plume clustering in large-Prandtl-number convection.

Clustering of plumes in turbulent Rayleigh-Bénard convection has been numerically observed in low-Prandtl-number fluids. In this framework, turbulent plumes undergo a phase-separation process leading to large-scale clusters and circulations, sometimes called plume superstructures and reminiscent of solar granulation and supergranulation. On the other hand, the possible presence of large-scale plume aggregates has not been explored in the case of large values of the Prandtl number, Pr, relevant to geological settings such as convection in planetary interiors. Here we address this problem and numerically explore the behavior of plume ensembles in turbulent convection at very high Prandtl number values, including the case Pr→∞. The results indicate the presence of plume clustering, albeit at smaller scale, also for large Pr number fluids, suggesting interesting consequences for mantle convection processes.