Bulletin of the American Physical Society
77th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 24–26, 2024; Salt Lake City, Utah
Session L32: Stratified Flow and Thermal Instability |
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Chair: Stefan Llewellyn Smith, University of California, San Diego Room: 255 D |
Monday, November 25, 2024 8:00AM - 8:13AM |
L32.00001: Abstract Withdrawn
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Monday, November 25, 2024 8:13AM - 8:26AM |
L32.00002: Streak amplification in viscosity stratified wall-bounded flows Anagha Madhusudanan, Simon Illingworth, Rama Govindarajan We use the linearized Navier-Stokes equations to study streak amplification in viscosity stratified wall-bounded flows. For certain parameter regimes in channel flows, we observe that, while streak amplification is enhanced at the more viscous cold wall, it is diminished at the less viscous hot wall. Importantly, this is consistent with the observations of turbulence statistics from direct numerical simulations (Zonta et al., J. Fluid Mech. 697, 150 (2012)). Here, we show that, mathematically, there are two separate routes through which streak amplification occurs in viscosity stratified wall-bounded flows. In channel flows, while the two routes complement each other at the cold wall, thereby enhancing turbulence, at the hot wall these routes compete, and therefore diminish turbulence. |
Monday, November 25, 2024 8:26AM - 8:39AM |
L32.00003: ABSTRACT WITHDRAWN
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Monday, November 25, 2024 8:39AM - 8:52AM |
L32.00004: A Perturbative Correction to the Quasi-Linear Approximation for Stratified Turbulence David Darrow, Greg P Chini, Colm-Cille P Caulfield Recently, Chini et al. (JFM vol. 933, 2022) demonstrated that a quasilinear (QL) reduction of the Boussinesq equations is formally justified in the limit of strong stable density stratification (when the Froude number Fr→0). In this limit, there is a separation between the time scale of the fastest-growing stratified shear instabilities and the advection/vertical-shear time scale of the large-scale, layer-like horizontal flow, causing the QL instabilities to self-tune to a state of near-marginal stability. These features enabled the authors to develop a hybrid eigenvalue/initial-value algorithm for efficiently simulating the resulting slow-fast QL system. For small but finite Fr, however, fast modes with horizontal wavenumbers differing from that of the dominant mode may be excited nonlinearly, leading to a spectrally-local downscale energy cascade. Here, we show that these additional modes can be perturbatively incorporated via a weakly nonlinear analysis about the emergent marginal stability manifold. Computation of the higher harmonics, which are coupled to the marginal fundamental mode, requires only three times the total operation count of the single-mode algorithm. We demonstrate the efficacy of the extended-QL algorithm for 2D stratified Kolmogorov flow via direct comparisons with DNS. The systematic extension of QL theory developed herein should prove advantageous for other shear flows for which the QL reduction provides a useful point of departure. |
Monday, November 25, 2024 8:52AM - 9:05AM |
L32.00005: Modelling dispersion in stratified turbulent flows as a resetting process Nicolaos Petropoulos, Stephen M de Bruyn Kops, Colm-cille P Caulfield In stably stratified turbulent flows, numerical evidence shows that the horizontal displacement of Lagrangian tracers is diffusive while the vertical displacement converges towards a stationary distribution (Kimura and Herring JFM Vol 328 1996). We develop a stochastic model for the vertical dispersion of Lagrangian tracers in stably stratified turbulent flows that aims to replicate and explain the emergence of such a stationary distribution for vertical displacement. The dynamical evolution of the tracers results from the competing effects of buoyancy forces that tend to bring a vertically perturbed fluid parcel (carrying tracers) to its equilibrium position and turbulent fluctuations that tend to disperse tracers. When the density of a fluid parcel is allowed to change due to molecular diffusion, a third effect needs to be taken into account: irreversible mixing. Indeed, `mixing' dynamically and irreversibly changes the equilibrium position of the parcel and affects the buoyancy force that `stirs' it on larger scales. These intricate couplings are modelled using a stochastic resetting process (Evans and Majumdar, PRL, Vol 106 2011) with memory. We assume that Lagrangian tracers in stratified turbulent flows follow random trajectories that obey a Brownian process. In addition, their stochastic paths can be reset to a given position (corresponding to the dynamically changing equilibrium position of a density structure containing the tracers) at a given rate. The model parameters are constrained by analysing the dynamics of an idealised density structure. Even though highly idealised, the model has the advantage of being analytically solvable. We show the emergence of a stationary distribution for the vertical displacement of Lagrangian tracers, as well as identify some instructive scalings. |
Monday, November 25, 2024 9:05AM - 9:18AM |
L32.00006: Study of flow transition and boundary-layer asymmetry in non-Oberbeck-Boussinesq thermal convection flow Xiao Ji, Xin Wen, Lian-Ping Wang Thermal convection flow driven by large temperature differences between two vertical walls makes the Oberbeck-Boussinesq (OB) approximation invalid. This flow is governed by the compressible Navier-Stokes-Fourier equations, namely, flow with large density variations. In this study, the discrete unified gas-kinetic scheme (DUGKS) is used to simulate the non-Oberbeck-Boussinesq (non-OB) thermal convection flow. The transition of the flow field from steady to unsteady convection under different normalized temperature differences (0≤ε≤0.9) is studied. The results show that the critical Rayleigh number Ra decreases with increasing ε, due to different magnitudes of the buoyancy force associated with the hot and cold walls. In other words, at a given Ra number, a stable OB convection can become unstable under non-OB treatment. Here we explore this early transition in terms of thermal / momentum boundary-layer asymmetry and the resulting strength of the velocity and integral momentum inside the boundary layer, in order to provide a physical explanation. The DUGKS simulations will be used to quantify the maximum / minimum local velocity, the thermal and momentum boundary-layer thicknesses, and integral jet momentum magnitude, to build up a logical physical interpretation. |
Monday, November 25, 2024 9:18AM - 9:31AM |
L32.00007: Experimental Discovery of Early-Stage "Mushroom" Instability in Counter-Rotating Vortex pair in stratified fluid Shiyong Tan, Shijie Zhong, Christopher J Crowley, Qianwen Wu, Rui Ni A pair of parallel counter-rotating vortices represents one of the most elementary flow configurations found in the far wake of any lifting devices. In this study, we experimentally observe and analyze the dynamics and instabilities of two counter-rotating vortex lines in a stratified fluid. We report the first observation of a "mushroom" instability at the early stage of vortex movement when the Froude number around 1, characterized by a row of mushroom-like structures with a spacing of 0.37 times the initial distance between the vortex lines. Initial instability wavelength was set by the elliptic instability, which helps develop baroclinic torque that finally results in flow structure with lighter fluids invading the heavier fluids. Those mushrooms resemble the structures developed in Rayleigh Taylor instability. Additionally, we examine the effect of the density gradient on the characteristics of the elliptical instability, providing insights into the interplay between stratification and vortex dynamics. |
Monday, November 25, 2024 9:31AM - 9:44AM |
L32.00008: Multicelluar thermal convection in tall slot cavities: Influences of Prandtl number and abstract ratio on structure and stability Tyler Ried Kennelly, Sadegh Dabiri Vertical thermal convection in tall slot geometries gives rise to the onset and persistence of multicellular vortical structures, where multiple vertically stacked rolls exist upon each other. In this study, we investigate the mechanisms of the onset of multicellular vertical structures and roll-states in natural convection in a bounded geometry, focusing on the influences of the Prandtl and cavity aspect ratio. Through direct numerical simulations, we examine the flow, thermal transport phenomena, and number of cellular roll structures over a wide range of Prandtl and Rayleigh numbers and aspect ratios. |
Monday, November 25, 2024 9:44AM - 9:57AM |
L32.00009: Subcritical transition to chaos in liquid metal magnetoconvection Matthew McCormack, Andrei Teimurazov, Olga Shishkina, Moritz F Linkmann The motionless conducting state of liquid metal convection with an applied vertical magnetic field confined in a vessel with insulating side walls is known to become linearly unstable at a critical value of the dimensionless temperature difference given by the Rayleigh number Ra. Here, we will present direct numerical simulation results which show that finite-amplitude disturbances can give rise to stable equilibrium solutions beneath the linear stability threshold despite the linear onset branch bifurcating supercritically. Under increased thermal driving, solutions on the linear onset branch lose stability and are attracted to an invariant 2-torus born from a secondary Hopf bifurcation of the subcritical branch, which subsequently follows a Ruelle-Takens-Newhouse route to chaos. Thus, we show that the transition to turbulence is controlled by the subcritical branch, and chaotic solutions have no connection to linear stability theory. |
Monday, November 25, 2024 9:57AM - 10:10AM |
L32.00010: Spontaneous onset of three-dimensional motion with subsequent spatial and temporal reduction in convective flow systems Patrick Stofanak, Inanc Senocak, Cheng-Nian Xiao We numerically observe the spontaneous emergence of three-dimensional motion from a quiescent, purely conductive state in convective flows, which ultimately self-organizes into a two-dimensional steady state. Our study examines a stably-stratified fluid in a V-shaped valley heated from below. A dominant three-dimensional instability is identified through modal stability analysis. Direct numerical simulations show that after an initial period of spontaneous growth of three-dimensional motion, the flow self-organizes into a two-dimensional steady state over time on its own. This self-organization manifests consistently for any arbitrary infinitesimal three-dimensional disturbance. We demonstrate that the mechanism driving this self-organization is the increasing dominance of viscous dissipation over buoyant production of disturbance kinetic energy at later stages of flow evolution from the initial quiescent state. Our discovery reveals that the disturbance pathway to the final state can be more complex than the state itself, suggesting that the "fastest" route to the final state may involve transitioning through a higher-dimensional intermediate state. |
Monday, November 25, 2024 10:10AM - 10:23AM |
L32.00011: Direct numerical simulations of long-lived stable Ekman layers: impact of stratification mechanisms on turbulence Krishan Chand, Cheng-Nian Xiao, Inanc Senocak We investigate long-lived stable Ekman layers through direct numerical simulations (DNS), defining three dimensionless parameters (∏s, ∏w, and ∏f) for a fixed Prandtl number Pr=0.71. These parameters delineate "weakly stable" and "very stable" regimes within the atmospheric boundary layer (ABL). We explore two independent stratification mechanisms: surface cooling (Gw) and ambient stratification (Na2). The parameter ∏s (=Gw/Na2) quantifies the relative influence of these stratification mechanisms, while ∏w=Ug2/(ν Na), with Ug representing geostrophic wind and ν kinematic viscosity, is a measure of the significance of the flow's kinetic energy relative to its damping by the combined effects of viscosity and ambient stable stratification. Our findings reveal that for a constant ∏w, an increase in ∏s transitions the ABL to a "very stable" state, accompanied by turbulence rebirth at higher ∏s levels. Conversely, maintaining ∏s while increasing ∏w intensifies turbulence, characterizing a "weakly stable" ABL and preventing the collapse and resurgence of turbulence. Furthermore, our results indicate that simulations with higher ∏s require larger computational domains to accurately capture the dynamics of large-scale structures, a factor potentially overlooked in previous studies due to smaller domain sizes. |
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