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 A28: Geophysical Fluid Dynamics: Stratified Flows I |
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Chair: Justin Burton, Emory University Room: 251 F |
Sunday, November 24, 2024 8:00AM - 8:13AM |
A28.00001: Buoyancy-pressure correlations in stably stratified turbulence Young Ro Yi, Jeffrey R Koseff, Elie R Bou-Zeid A defining aspect of stably stratified turbulence is the damping of vertical velocity fluctuations by the buoyancy force. This increasingly promotes large-scale anisotropy as flow stability increases from near-neutral to very stable conditions. Consequently, both the pressure-strain redistribution mechanism and the vertical buoyancy flux play key roles in how energy is exchanged among the three components of turbulent kinetic energy (TKE) and turbulent potential energy (TPE). Here, we focus specifically on the pressure fluctuations caused by density fluctuations and their correlations with the diagonal components of the rate-of-strain tensor (pressure-strain redistribution) and the density gradients (pressure scrambling). We present closed-form expressions for the (i) buoyancy pressure-strain redistribution (source/sink in both the horizontal and vertical TKE budgets); and (ii) buoyancy pressure scrambling (source/sink in the vertical buoyancy flux budget). These expressions reveal the connections between (i) the buoyancy pressure-strain redistribution and the vertical buoyancy flux and (ii) buoyancy pressure scrambling and density variance. We study these relationships using a dataset of direct numerical simulations (DNS) of forced, stably stratified turbulence. In this dataset, we observe more frequent counter-gradient (CG) buoyancy fluxes as stability is increased, which drive the reduction in the conversion of vertical TKE into TPE. These CG fluxes also promote large-scale anisotropy in the flow through increased conversion of vertical TKE into horizontal TKE by the buoyancy pressure-strain redistribution, which is contrary to the physical concepts underlying return-to-isotropy models. |
Sunday, November 24, 2024 8:13AM - 8:26AM |
A28.00002: The dynamics of stacked density-stratified shear layers Adhithiya Sivakumar, Alexis K Kaminski, Colm-Cille P Caulfield Geophysical flows sometimes contain multiple vertically stacked stratified shear layers at close proximity to each other. Interactions between neighbouring layers can excite new instabilities and have non-trivial effects on the ensuing turbulence. We therefore consider the stability of a 2D stably stratified three-layer fluid. The fluid is sheared symmetrically over a distance 2h across each density interface and the shear layers are separated by a quiescent region of depth 2H. In the limits of zero and infinite shear layer separation, we recover two classic configurations. When H/h = 0, our basic state reduces to a single shear layer encompassing both density interfaces (in which both Holmboe wave instabilities and the Taylor-Caulfield instability are predicted to arise for sufficiently strong stratification). On the other hand, layer interaction effects weaken as H/h → ∞, implying only independent Holmboe wave instabilities localised in each layer. At finite, but small, H/h, inviscid linear stability analysis reveals the existence of new instabilities and regime transitions relative to the zero-separation case. We explore the effects of diffusion on these new features and study their nonlinear evolution using direct numerical simulations. |
Sunday, November 24, 2024 8:26AM - 8:39AM |
A28.00003: Turbulent spectrum of 2D internal gravity waves Michal Shavit, Oliver Bühler, Jalal Shatah Our work contributes to a nearly 60-year quest to derive the turbulent spectrum of weakly interacting internal gravity waves from first principles. |
Sunday, November 24, 2024 8:39AM - 8:52AM |
A28.00004: Layering in Stratified Rotating Turbulent Flows Jim McElwaine, Cecile Le-Dizes, Claudia Cenedese, Pascale Garaud Layering is ubiquitous throughout the world's oceans yet it is poorly understood except in the double diffusive case. The presence of layers is profoundly important for understanding ocean mixing and hence the transport of heat and carbon dioxide. Understanding the rate at which the ocean can store these is critically important for the accurate modelling of climate change. We report the first laboratory experiments to study layer formation in a rotating stratified tank mixed by traversing vertical bars and show how rotation can influence layer formation. |
Sunday, November 24, 2024 8:52AM - 9:05AM |
A28.00005: Turbulence generated by an isolated topography in stratified rotating flows Jinyuan Liu, Pranav Suresh Puthan Naduvakkate, Sutanu Sarkar Kármán wakes are frequently observed behind islands in satellite images. This phenomenon akin to two-dimensional bluff-body wakes is a result of strong stratification. With the presence of rotation, the vortex dynamics are further enriched and various types of instabilities are possible. In order to quantify turbulence, identify the mechanisms responsible for its generation as well as its dependence on stratification and rotation, a series of large-eddy simulations are conducted. The vertical Froude number, Fr = U/Nh, varies from 0.075 to 0.40, where U is the freestream velocity, N is the buoyancy frequency, and h is the height of the submerged conical obstacle. For each Fr, three different Rossby numbers (Ro = U/fcD, where fc is the Coriolis frequency and D is the base diameter) are used, representative of mesoscale and submesoscale dynamics. For all simulations, the buoyancy-scale based Reynolds number, ReN = U2/νN = ReDFr(h/D), is kept constant at 900, resulting in a range of ReD = UD/ν from 7500 to 40000. It is found that, in the near wake where turbulence and its dissipation are strong, both vertical shear instability and centrifugal instability are active, indicated by unstable gradient Richardson number and unstable horizontal component of potential vorticity, respectively. Implications for the variability of turbulent dissipation rate will be discussed. |
Sunday, November 24, 2024 9:05AM - 9:18AM |
A28.00006: Reynolds stresses and budgets in temporally-evolving stratified wakes Jiaqi Li, Robert F Kunz, Xiang I. A. Yang We present detailed analyses of the Reynolds stresses and their budgets in temporally evolving stratified wakes using direct numerical simulation. Ensemble averaging is employed to mitigate statistical errors in the data, and the results are presented as functions of both the transverse and vertical coordinates---at multiple time instants across the near-wake, non-equilibrium, and quasi-two-dimensional regimes for wakes in weakly and strongly stratified environments. We first study the spatial structures of the Reynolds stresses as well as their budget terms. Key findings include the identification of dominant terms in the Reynolds stress transport equations, the generation and destruction processes of the Reynolds stresses, the role of spatial and inter-component redistribution of the Reynolds stresses, and the energy transfer between the Reynolds stress and the mean flow. The study also examines the effects of the Reynolds number and the Froude number. Additionally, we assess the validity of the eddy-viscosity-type models and some existing closures for the Reynolds stress model, highlighting the limitations of isotropy and return-to-isotropy hypotheses in stratified flows. |
Sunday, November 24, 2024 9:18AM - 9:31AM |
A28.00007: Pathways to turbulence from internal waves in stratified horizontal shear flows Sam Lewin, Miles MP Couchman, Arun Balakrishna, Alexis K Kaminski We use direct numerical simulations to study the behaviour of a monochromatic internal wave packet incident on a horizontal shear layer in a uniform vertical density stratification. The interaction of the wave and shear flow is controlled primarily by two fundamental limiting mechanisms, namely the advection of momentum across the shear layer by the wave and the Doppler shifting of the wave frequency by the shear. When Doppler shifting is weak, wave advection of momentum creates enhanced local vertical shear. On the other hand, when Doppler shifting is strong, the wave becomes trapped within the shear layer when its intrinsic frequency becomes equal to the buoyancy frequency and may overturn convectively. By varying the relative importance of stratification and horizontal shear (the Froude number) and the dimensionless wave vector k, we demonstrate that the properties of the turbulence produced by wave breaking depend sensitively on the the relative importance of the two mechanisms outlined above. There are significant implications for the parameterization of stratified turbulent mixing and dissipation in oceanographic flows. |
Sunday, November 24, 2024 9:31AM - 9:44AM |
A28.00008: Propagation and interaction of gravity currents resulting from successive release of two lock fluids Khem P Bhattarai, Subhas K Venayagamoorthy Gravity currents are ubiquitous in the natural environment. This study investigates the interaction of gravity currents generated by successive releases of two lock-fluids using highly resolved numerical simulations. We examined three distinct scenarios: (a) simultaneous release of two lock fluids, (b) sequential release of two lock fluids, and (c) the release of a single lock fluid with a density equal to the average of the two lock fluids. Results show that mixing is significantly enhanced in the case of sequential release of lock fluids. Specifically, as the denser (trailing) current catches up with the lighter (leading) current, enhanced mixing of fluids is observed. This is mainly due to complex interaction that ensues leading to elevated shear at the head of the combined currents resulting in Kelvin-Helmholtz like instabilities. Analysis of the interaction between two currents is done as a function of the time of release (TR), the time to catch (TC) of the lighter current, and the ratios of the density of the lock fluids to the ambient fluid (ϒ1, ϒ2). |
Sunday, November 24, 2024 9:44AM - 9:57AM |
A28.00009: Exact coherent structures in two-dimensional strongly stratified Kolmogorov flow Khalid F ALqahtani, Baole Wen, Greg P Chini Stably stratified turbulence is a primary agent for diabatic mixing in atmospheric and oceanic flows but occurs on scales that are too small to be resolved in regional circulation much less climate models. In the limit of strong stratification, a highly anisotropic, layer-like horizontal flow develops with emergent vertical shear sufficiently strong to trigger spatially-localized regions of instability. To better understand the spatial structure of these instabilities, their nonlinear saturation, and the diabatic mixing they drive, we employ tools from modern dynamical systems theory. Specifically, we develop a Newton-Krylov iterative solver to compute “exact coherent structures” (ECS), i.e., fully nonlinear, invariant solutions, in the idealized and well-controlled setting of two-dimensional stratified Kolmogorov flow. Unlike prior related studies, we investigate the physically-relevant regime of small Froude and large Reynolds number. We explore the dependence of the numerically computed ECS on these parameters and the domain size, and compare our results with DNS and with predictions from a recently-derived quasilinear reduction of the governing Boussinesq equations in this regime. |
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