Turbulent motions due to flux-driven thermal convection is investigated by numerical simulations and stochastic modelling. Tilting of convection cells leads to the formation of sheared flows and quasi-periodic relaxation oscillations for the energy integrals far from the threshold for linear instability. The probability density function for the temperature and radial velocity fluctuations in the fluid layer changes from a normal distribution at the onset of turbulence to a distribution with an exponential tail for large fluctuation amplitudes for strongly driven systems. The frequency power spectral density has an exponential shape, which is a signature of deterministic chaos. By use of a novel deconvolution method, this is shown to result from the presence of Lorentzian pulses in the underlying time series, demonstrating that exponential frequency spectra can persist in also in turbulent flow regimes.
We consider a low-dimensional model of convection in a horizontally magnetized layer of a viscous fluid heated from below. We analyze in detail the stability of hydromagnetic convection for a wide range of two control parameters. Namely, when changing the initially applied temperature difference or magnetic field strength, one can see transitions from regular to irregular long-term behavior of the system, switching between chaotic, periodic, and equilibrium asymptotic solutions. It is worth noting that owing to the induced magnetic field a transition to hyperchaotic dynamics is possible for so…
Magnetic field generation in three-dimensional Rayleigh-Bénard convection of an electrically conducting fluid is studied numerically by fixing the Prandtl number at $P=0.3$ and varying the Rayleigh number (Ra) as a control parameter. A recently reported route to hyperchaos involving quasiperiodic regimes, crises and chaotic intermittent attractors is followed, and the critical magnetic Prandtl number ($P_m^c$) for dynamo action is determined as a function of Ra. A mechanism for the onset of intermittency in the magnetic energy is described, the most beneficial convective regimes for dynamo act…
We investigate the utility of the convex hull of many Lagrangian tracers to analyze transport properties of turbulent flows with different anisotropy. In direct numerical simulations of statistically homogeneous and stationary Navier-Stokes turbulence, neutral fluid Boussinesq convection, and MHD Boussinesq convection a comparison with Lagrangian pair dispersion shows that convex hull statistics capture the asymptotic dispersive behavior of a large group of passive tracer particles. Moreover, convex hull analysis provides additional information on the sub-ensemble of tracers that on average di…
We compute fully local boundary layer scales in three-dimensional turbulent Rayleigh-Benard convection. These scales are directly connected to the highly intermittent fluctuations of the fluxes of momentum and heat at the isothermal top and bottom walls and are statistically distributed around the corresponding mean thickness scales. The local boundary layer scales also reflect the strong spatial inhomogeneities of both boundary layers due to the large-scale, but complex and intermittent, circulation that builds up in closed convection cells. Similar to turbulent boundary layers, we define inn…
We report measurements of the instantaneous viscous boundary layer (BL) thickness $δ_v(t)$ in turbulent Rayleigh-Bénard convection. It is found that $δ_v(t)$ obtained from the measured instantaneous two-dimensional velocity field exhibits intermittent fluctuations. For small values, $δ_v(t)$ obeys a lognormal distribution, whereas for large values the distribution of $δ_v(t)$ exhibits an exponential tail. The variation of $δ_v(t)$ with time is found to be driven by the fluctuations of the large-scale mean flow velocity and the local horizontal velocities close to the plate can be used as an in…
We investigate experimentally the statistical properties of active and passive scalar fields in turbulent Rayleigh-Bénard convection in water, at $Ra\sim10^{10}$. Both the local concentration of fluorescence dye and the local temperature are measured near the sidewall of a rectangular cell. It is found that, although they are advected by the same turbulent flow, the two scalars distribute differently. This difference is twofold, i.e. both the quantities themselves and their small-scale increments have different distributions. Our results show that there is a certain buoyant scale based on time…
We discuss two aspects of turbulent Rayleigh-Bénard convection (RBC) on the basis of high-resolution direct numerical simulations in a unique setting; a closed cylindrical cell of aspect ratio of one. First, we present a comprehensive comparison of statistical quantities such as energy dissipation rates and boundary layer thickness scales. Data are used from three simulation run series at Prandtl numbers $Pr$ that cover two orders of magnitude. In contrast to most previous studies in RBC the focus of the present work is on convective turbulence at very low Prandtl numbers including $Pr=0.021$ …
Statistical properties of turbulent Rayleigh-Benard convection at low Prandtl numbers (Pr), which are typical for liquid metals such as mercury, gallium or liquid sodium, are investigated in high-resolution three-dimensional spectral element simulations in a closed cylindrical cell with an aspect ratio of one and are compared to previous turbulent convection simulations in air. We compare the scaling of global momentum and heat transfer. The scaling exponents are found to be in agreement with experiments. Mean profiles of the root-mean-square velocity as well as the thermal and kinetic energy …
High-amplitude events of the out-of-plane vorticity component $ω_z$ are analyzed by stereoscopic particle image velocimetry (PIV) in the bulk region of turbulent Rayleigh-Bénard convection in air. The Rayleigh numbers ${\rm Ra}$ vary from $1.7 \times 10^4$ to $5.1 \times 10^5$. The experimental investigation is connected with a comprehensive statistical analysis of long-term time series of $ω_z$ and individual velocity derivatives $\partial u_i/\partial x_j$. A statistical convergence for derivative moments up to an order of 6 is demonstrated. Our results are found to agree well with existing …
One of the most prominent dynamical features of turbulent, rapidly-rotating convection is the formation of large-scale coherent structures, driven by Reynolds stresses resulting from the small-scale convective flows. In spherical geometry, such structures consist of intense zonal flows that are invariant along the rotation axis. In planar geometry, long-lived, depth-invariant structures also form at large scales, but, in the absence of horizontal anisotropy, they consist of vortices that grow to the domain size. In this work, through the introduction of horizontal anisotropy into a numerical m…
Combined measurements of velocity components and temperature in a turbulent Rayleigh-Bénard convection flow at a low Prandtl number of $\mathit{Pr}= 0.029$ and Rayleigh numbers between $10^6 \le \mathit{Ra} \le 6 \times 10^7$ are conducted in a series of experiments with durations of more than a thousand free-fall time units. Multiple crossing ultrasound beam lines and an array of thermocouples at mid-height allow for a detailed analysis and characterization of the complex three-dimensional dynamics of the single large-scale circulation (LSC) roll in the cylindrical convection cell of unit asp…
Numerical simulations of 3D, rapidly rotating Rayleigh-Benard convection are performed using an asymptotic quasi-geostrophic model that incorporates the effects of no-slip boundaries through (i) parameterized Ekman pumping boundary conditions, and (ii) a thermal wind boundary layer that regularizes the enhanced thermal fluctuations induced by pumping. The fidelity of the model, obtained by an asymptotic reduction of the Navier-Stokes equations that implicitly enforces a pointwise geostrophic balance, is explored for the first time by comparisons of simulations against the findings of direct nu…
Technische Universität Ilmenau（伊尔默瑙工业大学）；Friedrich-Schiller-Universität Jena（耶拿弗里德里希·席勒大学）；New York University（纽约大学）
A combined convolutional autoencoder-recurrent neural network machine learning model is presented to analyse and forecast the dynamics and low-order statistics of the local convective heat flux field in a two-dimensional turbulent Rayleigh-Bénard convection flow at Prandtl number ${\rm Pr}=7$ and Rayleigh number ${\rm Ra}=10^7$. Two recurrent neural networks are applied for the temporal advancement of flow data in the reduced latent data space, a reservoir computing model in the form of an echo state network and a recurrent gated unit. Thereby, the present work exploits the modular combination…
Local regions of anomalous particle dispersion, and intermittent events that occur in turbulent flows can greatly influence the global statistical description of the flow. These local behaviors can be identified and analyzed by comparing the growth of neighboring convex hulls of Lagrangian tracer particles. Although in our simulations of homogeneous turbulence the convex hulls generally grow in size, after the Lagrangian particles that define the convex hulls begin to disperse, our analysis reveals short periods when the convex hulls of the Lagrangian particles shrink, evidence that particles …
We study the connection between extreme events of thermal and kinetic energy dissipation rates in the bulk of three-dimensional Rayleigh-Bénard convection and the wall shear stress patterns at the top and the bottom planes that enclose the layer. Zero points of this two-dimensional vector field stand for detachments of strong thermal plumes. If their position at the opposite planes and a given time is close then they can be considered as precursors for high-amplitude bulk dissipation events triggered by plume collisions or close passings. This scenario requires a breaking of the synchronicity …
In this paper, we experimentally study the influence of large-scale Taylor rolls on the small-scale statistics and the flow organization in fully turbulent Taylor-Couette flow {for Reynolds numbers up to $\text{Re}_S=3\times 10^5$}. The velocity field in the gap confined by coaxial and independently rotating cylinders at a radius ratio of $η=0.714$ is measured using planar {particle image velocimetry} in horizontal planes at different cylinder heights. Flow regions with and without prominent Taylor vortices are compared. We show that the local angular momentum transport (expressed in terms of …
