Session A23: Turbulent Convection

Transition to the ultimate regime in Rayleigh-Bénard turbulence

We will try to reconcile the various experimental observations for very large Rayleigh number Rayleigh-Bénard (RB) turbulence, where different effective scaling exponents γ in the relation Nu ~ Ra^γ between the Nusselt number Nu and the Rayleigh number Ra have been observed. Here the analogy between RB flow and parallel flow along a flat plate is illuminating. In turbulent RB convection, the core part of the flow (“bulk”) is always turbulent, while the kinetic boundary layers (BLs) can vary from scaling-wise laminar Prandtl-Blasius type boundary layer (“classical regime”, γ<1/3) to fully turbulent Prandtl-von Karman type boundary layer, leading to an enhanced heat transport (“ultimate regime”, γ>1/3). The nature of the transition may be of subcritical nature and be in analogy to the transition in parallel shear flow along a flat plate, which undergoes a  transition between laminar and turbulent boundary layers that have different dependences of the skin friction coefficient on the Reynolds number. There is a similar analogy between RB flow and pipe and channel flows and Taylor-Couette flow.

    

Turbulent natural convection in a differentially heated vertical channel: A theoretical study

To understand thermally driven wall-bounded turbulent flows, the model system of turbulent natural convection in a differentially heated vertical channel is often studied. One important question is how the heat flux depends on the control parameters of the flow. We have carried out a theoretical study in the large aspect-ratio limit, where the height and width of the vertical walls of the channel are much larger than their separation. In this limit, the mean flow quantities depend only on the coordinate along the direction normal to the vertical walls. Our theoretical analysis, which is based on the mean momentum balance and mean energy balance equations and makes the minimal closure approximations needed, yields the dependence of the heat flux and wall shear stress, as measured by the Nusselt number (Nu) and the shear Reynolds number (Re_τ) on the Rayleigh (Ra) and Prandtl (Pr) numbers:

Nu≈[C²f(Pr)]^1/3Pr^-(1-2ε)/3Ra^1/3 and Re_τ≈[f(Pr)/C]^1/3Pr^-(1+ε)/3Ra^1/3 in the high-Ra limit. Here, C is a constant, f(Pr) is a function of Pr that is not in the form of a power law and ε = 1/3 and 1, respectively for Pr ≫ 1 and Pr ≪ 1. We have tested our theoretical results using available direct numerical simulation (DNS) data for Pr≥1 and an excellent agreement is found. In contrast, the DNS data do not support the asymptotic laws of heat transfer and the mean maximum velocity obtained by a scaling approach in previous theoretical studies.   

Split energy cascade induced by spontaneous flow transition in two-dimensional thermal turbulence

Two-dimensional turbulence is characterized by an inverse energy cascade from small scales to large ones, in contrast to the direct downscale energy cascade in three dimensions. Here, we report a split energy cascade in purely 2D thermal turbulence, i.e. the coexistence of direct and inverse energy cascades separated at intermediate scales. This phenomenon is induced by a spontaneous transition in the flow topology, during which the domain-sized circulatory roll is squeezed and intense randommoving eddies that provide a channel for downscale energy flux emerge. The flow mode analysis and orientation order of velocity field reveal that this flow transition is a critical behavior with bi-stability.   

Resolution Requirements for Numerical Simulations of Buoyant Plumes

High-fidelity computational predictions of buoyant plumes in natural and built environments are constrained by the difficulty of modeling complex physics across wide temporal and spatial scale ranges. Plume structure and dynamics are governed by coupled nonlinear interactions between turbulence, buoyancy-driven flow, and, in the case of reacting flows, flame chemistry. These multi-physics phenomena typically span an enormous range of spatial and temporal scales and are intricately connected to various canonical flow instabilities, including Rayleigh Taylor and Kelvin Helmholtz instablities. In this talk, we outline recent efforts to use adaptive mesh refinement (AMR), where the grid is resolved at small scales only in regions of high dynamical and physical significance, for the study of buoyant plume structure, dynamics, and evolution in a range of contexts. We place particular focus on the fundamental changes in flow dynamics that occur with different levels of spatial resolution, specifically related to the accurate representation of Rayleigh Taylor instablities. These instablities affect the frequency at which many buoyant plumes oscillate, or "puff", and we show that simulations with insufficient resolution are likely to incorrectly predict the resulting puffing frequency. We end by highlighting challenges faced in the application of AMR to simulations of buoyant plumes, including future research directions.   

The robust wall modes and their interplay with bulk turbulence in confined rotating Rayleigh-Bénard convection

In confined rotating convection, a strong zonal flow can develop close to the side wall with a modal structure that precesses along the wall counter to the applied rotation. It is surmised that this is a robust non-linear evolution of the wall modes observed before the onset of bulk convection. We perform direct numerical simulations of cylindrically confined rotating convection at high rotation rates and strong turbulent forcing. We find a fit-parameter-free relation that links the angular drift frequency of the robust wall mode observed far into the turbulent regime with the critical wall mode frequency at onset, firmly substantiating the connection between the observed boundary zonal flow and the wall modes. Deviations from this relation at stronger turbulent forcing suggest that the bulk turbulence hampers the development of the wall mode. By studying the interactive flow between wall mode and bulk turbulence, we identify radial jets penetrating from the wall mode into the bulk. These jets induce a large scale multipolar vortex structure in the bulk, dependent on the wavenumber of the wall mode. In a narrow cylinder the entire bulk flow is dominated by a quadrupolar vortex driven by the radial jets, whereas in a wider cylinder the jets are found to have a finite penetration length and the vortices do not cover the entire bulk.   

Compressible Turbulent Convection in Highly Stratified Adiabatic Background

Buoyancy-driven turbulent convection leads to a fully compressible flow with a prominent top-down asymmetry of first- and second-order statistics when the adiabatic equilibrium profiles of temperature, density and pressure change very strongly across the convection layer. We report  a series of highly resolved three-dimensional fully compressible direct numerical simulations  for dimensionless dissipation numbers, $0.1 le D le0.8 $ at fixed Rayleigh number $Ra = 10^6$ and superadiabaticity $epsilon = 0.1$. Strong stratification leads to  the formation of an increasingly thicker stabilized sublayer with a slightly negative mean convective heat flux  $J_{c}left(z ight)$ at the top of the convection zone. A transition is observed  for $D > Dcrit approx 0.65$, when density fluctuations collapse to those of pressure; it is characterized by an up to nearly 50\% reduced global turbulent heat transfer and a sparse network of focused thin and sheet-like thermal plumes falling through the top  sublayer deep into the bulk. A systematic comparison of   boundary  characteristics at top and bottom walls and  trends with higher Rayleigh numbers might also be discussed.   

Exploring Jump Rope Vortex Dynamics in Turbulent LiquidMetal Rayleigh-BÅLenard Convection Under Diverse MechanicalBoundary Conditions

The large-scale circulation (LSC) is a crucial dynamical feature of turbulent thermal convection, shaping the appearance of various geophysical and astrophysical systems, such as solar granulation or cloud streets (Akashi et al., (2022),footnote{Akashi et al., extit{J. Fluid Mech.} extbf{932}, 27 (2022)} and Vogt and Horn et al., (2018)footnote{Vogt and Horn et al., extit{PNAS}. extbf{115}, 50 (2018)}). This study investigates the Jump Rope Vortex, one of the fundamental modes within turbulent Rayleigh-B'enard convection, besides torsion and sloshing. This mode is distinguished by its fully three-dimensional (3D) motion, reminiscent of a twirling jump rope. Through the application of high-resolution direct numerical simulations (DNS), we seek to elucidate the dynamics of the jump rope vortex under a diverse set of boundary conditions, encompassing rigid (no-slip), free-slip, periodic, and mixed configurations.

Existing research has primarily focused on no-slip boundary conditions on the characteristics of turbulent thermal convection. However, a comprehensive understanding of the role of various boundary conditions in modulating the fully 3D motion of the jump rope vortex, remains elusive. Each boundary condition, no-slip, free-slip, periodic, and mixed impose unique constraints on the flow, which consequently affects the LSCs and jump rope vortex dynamics, as well as the heat and momentum transport. In this study, we systematically quantify the effects of these diverse boundary conditions on the morphology, stability, and heat transfer properties of the jump rope vortex. We will present results from an array of DNS in liquid metal with $Pr=0.025$, covering Rayleigh numbers in the range of $Ra = 1.0 imes10^4$ to $1.0 imes10^6$. Furthermore, we explore variations in the domain's aspect ratio, ranging from $Gamma = 2$ to $5$ with both square and rectangle bases. 

This knowledge can be invaluable for the development of theoretical models and the interpretation of observational data in the context of convective systems.   

Boundary-layer disruption and heat-transfer enhancement in convection turbulence by oscillating deformations of boundary

Turbulent convection driven by unstable temperature gradients in the direction of gravity exists in many natural flows and engineering applications, such as atmosphere, mantle and indoor temperature control, etc. The way to regulate and enhance the convective heat transfer efficiency has important theoretical and practical value. Here we report a new mechanism for improving the efficiency of turbulent convective heat transfer, saying by using boundary vibration deformation. Specifically, vibration deformations in the form of standing waves are introduced at boundaries. The results indicate that, to significantly increase the heat transfer, the boundary vibration amplitude needs to be comparable to the boundary layer thickness. And this enhancement happens when the wavenumber is large enough. For a moderate frequency, the nondimensional heat flux, i.e. the Nusselt number can be more than doubled compared to the uncontrolled flow. Since boundary layer is the bottleneck of heat transfer for the parameters explored here, the method proposed here can strongly disturb the original boundary layer and enhance the heat flux. This also leads to the dependence of the Nusselt number on the Rayleigh number approaching the scaling law for the so-called ultimate regime.