Bulletin of the American Physical Society
75th Annual Meeting of the Division of Fluid Dynamics
Volume 67, Number 19
Sunday–Tuesday, November 20–22, 2022; Indiana Convention Center, Indianapolis, Indiana.
Session T14: Geophysical Fluid Dynamics: Stratified Flows I |
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Chair: Colm-Cille Caulfield, Univ of Cambridge Room: 141 |
Monday, November 21, 2022 4:10PM - 4:23PM |
T14.00001: Turbulent disruption of density staircases in stratified shear flows Nicolaos Petropoulos, Ali Mashayek, Colm-Cille P Caulfield Formation of step-like `density staircase' distributions induced by stratification and turbulence has been widely studied and can be explained by the `instability' of a sufficiently strongly stably stratified turbulent flow due to the decrease of the turbulent density flux with increasing stratification via the `Phillips mechanism' (O. M. Phillips, Deep Sea Res. vol 19, pp 79-81, 1972) . However, such density staircases are not often observed in ocean interiors, except in regions where double diffusion processes are important, leading to thermohaline staircases. Using reduced order models for the evolution of velocity and density gradients, we analyse staircase formation in stratified and sheared turbulent flows. Under the assumption of inertial scaling U3/L for the kinetic energy dissipation rate ε, where U and L are characteristic velocity and length scales, we determine ranges of bulk Richardson numbers Rib and turbulent Prandtl numbers PrT for which staircases can potentially form and show that the Phillips mechanism only survives for sufficiently small turbulent Prandtl numbers. For relevant oceanic parameters, the system is not prone to staircases for PrT > PrTc ≈ 0.5 - 0.7. Since several studies indicate that ocean interiors are usually above this threshold, this result supports the empirical observation that staircases are not favoured in ocean interiors in the presence of ambient turbulence. We also show that our analysis is robust to other scalings for ε such as U2N where N is the a characteristic value of the buoyancy frequency, supporting our results in both shear-dominated and buoyancy-dominated turbulent regimes. |
Monday, November 21, 2022 4:23PM - 4:36PM |
T14.00002: Analysis of intermittent turbulence in stably stratified channel flow Haoyang Cen, Artem Korobenko, Qi Zhou Under sufficiently strong stratification, fully developed turbulent channel flows could transition to intermittent flows where laminar and turbulent patches coexist. Intermittency complicates the conventional statistics approach when describing turbulence. Using direct numerical simulations, we analyze the turbulence quantities under the effect of intermittency. The numerical simulations cover a range of friction Reynolds and Richardson numbers, which enables us to investigate the boundary at which transitions from fully turbulent to intermittent occur in the parameter space for stably stratified channel flow. The volume fraction of turbulent patches in each simulation is quantified, based on which we attempt to predict the occurrence of intermittency in the parameter space. Our results suggest that the intermittency criterion documented for stratified plane Couette flow (Deusebio et al., J. Fluid Mech., volume 781, 2015) does not apply to channel flows. Alternative criteria for the intermittency boundary are sought. |
Monday, November 21, 2022 4:36PM - 4:49PM |
T14.00003: Transport across stable density interfaces in forced stratified turbulence Miles M Couchman, Steve M de Bruyn Kops, Colm-Cille P Caulfield Understanding how turbulence enhances irreversible scalar mixing in density-stratified fluids is a central problem in geophysical fluid dynamics. Unstable vertical density inversions are often assumed to be an indirect proxy for mixing when direct measurements of scalar diffusion are unavailable. We here investigate this assumption by using a forced direct numerical simulation of stratified turbulence to consider spatial correlations between the vertical density gradient ∂ρ/∂z and the dissipation rates of kinetic energy ε and scalar variance χ, the latter quantifying scalar mixing. The computational domain develops a vertical density staircase, characterized by relatively well-mixed layers separated by sharp, stable gradients that are correlated with sheared velocity interfaces. While density inversions are most prevalent within the mixed layers, much of the scalar mixing is localized to the intervening interfaces, a phenomenon not apparent if considering local static instability or ε alone. We highlight that while the majority of the domain is indeed characterized by the canonical flux coefficient Γ≡χ/ε=0.2, often assumed in ocean mixing parameterizations, extreme values of χ within the statically-stable interfaces, associated with elevated Γ, strongly skew the bulk statistics. |
Monday, November 21, 2022 4:49PM - 5:02PM |
T14.00004: Predictability of Stratified Turbulence Martin F Diaz, Michael L Waite In the study of geophysical fluid dynamics, predictability still stands in the foreground of interest as one of the primary challenges. Following Lorenz's pioneering framework, several results from homogeneous and isotropic turbulence have suggested that flows with many scales of motion present limited predictability due to the inevitable contamination of error from small to large scales, even if initially confined to small scales. In this work, we investigate the predictability of freely decaying stratified turbulence, which is representative of small-scale geophysical turbulence where Coriolis effects are weak. Predictability of stratified turbulence is studied using direct numerical simulations by analyzing the error growth in pairs of realizations of velocity fields departing from almost indiscernible initial conditions. Previous studies have indicated that the finite range of predictability is determined by to the slope of the flow's kinetic energy spectrum. In stratified turbulence, the shape of the energy spectrum depends on the buoyancy Reynolds number, as long as it is not too large. We perform a comparative analysis of spectra and perturbation upscale growth behaviour in different regimes of stratified turbulence from large to unitary order of buoyancy Reynolds number. |
Monday, November 21, 2022 5:02PM - 5:15PM |
T14.00005: Integration of slow-fast quasilinear models of turbulent shear flows Alessia Ferraro, Gregory Chini, Tobias M Schneider The quasilinear (QL) reduction, which retains fluctuation-fluctuation nonlinearities only where they feed back onto mean fields, is often employed as a model reduction strategy. This approximation can be justified in the limit of temporal scale separation between the mean and fluctuation dynamics as arises in the asymptotic description of strongly stratified shear turbulence. Here, we utilize carefully constructed model problems to derive two important extensions to our recently introduced formalism for integrating slow-fast QL systems, which exploits the tendency of these systems to self-organize about a marginal stability manifold and slaves the amplitude of the (marginal) fluctuations to the slowly-evolving mean field. The first extension accommodates large-amplitude bursting events, in which temporal scale separation is transiently lost until marginal stability is re-established. The second extension yields a slow equation for the wavenumber of the marginal mode. Together, these extensions enable scale-selective adaptivity in both space and time. Our formalism is consistent with the idea that shear flow turbulence tracks low-dimensional state-space structures during slow evolutionary phases punctuated by intermittent bursting events. |
Monday, November 21, 2022 5:15PM - 5:28PM |
T14.00006: Stratified mixing in mean shear free homogeneous isotropic turbulence: An experimental study Arefe Ghazi Nezami, Blair Johnson Stratified turbulent flow has an important role in the dynamics of aquatic and atmospheric environments. The interaction of turbulence with a buoyancy gradient is complicated and has been studied for several decades, but there remain unknowns in quantifying the primary drivers of interfacial dynamics and mass transport. We perform experiments to investigate mixing at a stable density interface with a sharp gradient in which the upper layer is turbulent and the bottom dense layer is quiescent. We generate homogeneous isotropic turbulence with negligible mean shear by randomly actuating an array of synthetic jets located at the top of a tank. We use particle image velocimetry to acquire the flow velocity, in order to compute turbulence statistics such as the integral length scale, turbulent kinetic energy, and dissipation. Simultaneously, we use laser induced fluorescence to measure the fluid density field, and to determine the location and thickness of the density interface. We also quantify the mass transport across the interface, and identify various types of instabilities and entertainment events. By changing the Richardson number, the turbulent Reynolds number, and the Prandtl number, we determine under what conditions different mixing rates and interfacial dynamics occur. |
Monday, November 21, 2022 5:28PM - 5:41PM |
T14.00007: On the Motion of Hairpin Filaments in the Atmospheric Boundary Layer Abhishek Paraswarar Harikrishnan, Marie Rodal, Rupert Klein, Nikki Vercauteren Recent results from Harikrishnan et al. [arXiv:2110.02253 (2021)] have revealed that an abundance of hairpin-like structures oriented in a similar direction can be observed in the turbulent patches of a stably stratified Ekman flow. Understanding the dynamics of these inclined features are of immediate importance as they could lead to better subgrid-scale models for large eddy simulation (LES) of stably stratified atmospheric boundary layers (ABL). In this work, we use the corrected thin-tube model of Klein and Knio [J. Fluid Mech. (1995)] to compute the motion of hairpin filaments with the ABL as a background flow. The influence of the mean background flow on the motion of hairpin filaments is examined under neutral, weak and strong stratification. These simulations are then compared to feature tracking of Q-criterion structures performed directly on the direct numerical simulation (DNS) data. Finally, an extension of the asymptotic analysis of Callegari and Ting [J. App. Math. (1978)] is carried out to include the influence of gravity. The results show that a contribution from the gravity term occurs only when the tail of a infinitely long filament is tilted at an angle relative to the wall. |
Monday, November 21, 2022 5:41PM - 5:54PM |
T14.00008: Development and long-term evolution of layers in turbulent stratified fluids Paul E Pruzina, David W Hughes, Sam Pegler A fascinating aspect of stratified turbulence is the spontaneous formation of density staircases, consisting of layers with nearly uniform density separated by narrow interfaces with large density gradients. For example, double diffusive staircases appear in regions of the ocean where the overall stratification is stable, and layers can also be induced experimentally by stirring a fluid with a stable salt gradient. One leading theory for layering is the Phillips Effect: layering occurs due to the dependence of the turbulent density flux on the density gradient. If the flux is a decreasing function of the gradient for a finite range of gradients, then negative diffusion causes perturbations to grow into systems of layers and interfaces. We present a model for stirred stratified layering derived from the Boussinesq equations encapsulating the Phillips effect. Solutions to the model produce layered regions which evolve indefinitely through layer mergers. We include molecular and viscous diffusion, both of which act to stabilise the system. A novel investigation into the long-term dynamics of solutions reveals a simple scaling law for the time dependence of the number of layers, suggesting a self-similar structure to merger dynamics, and a link to Cahn-Hilliard models of layering. |
Monday, November 21, 2022 5:54PM - 6:07PM |
T14.00009: Simulation of stratified turbulent wakes at very high Reynolds numbers Nidia Reyes, Nidia Reyes-Gil, Greg N Thomsen, Peter J Diamessis, Kris Rowe A series of implicit large-eddy simulations is conducted to study the dynamics of turbulent wakes operating in the strongly stratified regime, as a continuation of the work presented in Zhoud & Diamessis (Phys. Rev. 2019). Particular attention is paid to aspects of the code design/implementation, as well as the selection of the spatial discretization scheme, aimed to obtain simulations of sphere wakes at a body-based Reynolds number Re ~ O(10^6). |
Monday, November 21, 2022 6:07PM - 6:20PM |
T14.00010: On the effects of differential diffusion and equation of state in stably stratified turbulent channel flow Steven Thompson, Reetesh Ranjan Stably stratified turbulent flows observed in underwater naval applications have density stratification dependent upon two scalar fields, namely, temperature and salinity through an equation of state (EoS). The differences in the molecular diffusivity of these scalar fields, which are characterized in terms of Lewis number (Le = Sc/Pr) lead to the occurrence of the differential diffusion phenomenon. Here, Sc and Pr denote the Schmidt and Prandtl numbers, respectively. In this study, direct numerical simulations of turbulent channel flow at a frictional Reynolds number of 395 and at two values of the frictional Richardson number 0 (neutral) and 60 (stratified) are performed to examine the role of EoS, differential diffusion, and density stratification on the flow field. The effects of EoS are characterized in terms of the use of a linear and a nonlinear EoS and the effects of differential diffusion are analyzed for Le = 1, and 4 by considering flow under neutral and stably stratified conditions. The results are analyzed in terms of the behavior of the instantaneous flow field, turbulence statistics, and other quantities of interest such as the buoyancy frequency, gradient Richardson number, length scales, etc., which are relevant to the broader class of stratified flows. |
Monday, November 21, 2022 6:20PM - 6:33PM Author not Attending |
T14.00011: Enhanced diffusion induced in a tilted pipe: the role of diffusion-driven flow in enhancing mixing Lingyun Ding, Richard M McLaughlin In this work, we identify and isolate an unexplored mechanism of solute dispersion in an inclined capillary pipe. Cracked micro channels may experience diffusion induced flows in the presence of density stratification. Here, we explore the role of such flows in quantifiying the mixing they may produce. We present a combination of theoretical and experimental anaylsis to calculated the effective Taylor diffusivity induced by such flows as a function of the various physical parameters including inclination angle, cross-sectional area, molecular diffusivity, fluid viscosity, and solute density gradient. |
Monday, November 21, 2022 6:33PM - 6:46PM |
T14.00012: Intermittency and spontaneous interface formation in stratified open channel flow Vassili Issaev, Nicholas J Williamson, Steven Armfield We investigate and quantify the effects of spatio-temporal intermittency resulting from stable stratification in stratified open channel flow through direct numerical simulations. We find that due to the vertical inhomogeneity of the momentum and buoyancy flux profiles in our flow configuration, intermittency spontaneously manifests as a deformed horizontal interface between the upper quiescent flow where ReB ≤ Ο(1) and the lower bulk turbulent flow where ReB ≥ Ο(10) , where ReB is the buoyancy Reynolds number. We hence adapt the local unstable density criterion of Portwood et al 2016 to robustly identify the turbulent and quiescent regions within instantaneous realisations of the flow. We quantify local intermittency through a depth varying `turbulent' volume fraction which we find is well predicted by a local Monin-Obhukov length normalized in viscous wall-units Λ+, such that intermittency is observed within the range of 2.5 ≤ Λ+ ≤ 260. We find that the region of intermittency is defined by vigorous and efficient mixing through Kelvin-Helmholtz type overturning instabilities that form due to the critical conditions at the turbulent/quiescent interface and accordingly find that the thickness of the interfacial layer scales with the Ellison length LE. This region of critical intermittency is described by a constant gradient Richardson number of Rig ≈ 0.2, and where the local stream-wise velocity and density gradients develop such that the `turbulent' and `quiescent' flow are defined by Rig marginally lower and higher than the critical value respectively. Similarly we find that irrespective of the external parameter set, the turbulent Froude number approaches a clear lower limit at the turbulent/quiescent interface of Fr ≈ 0.3. Hence, we investigate and quantify the effects of intermittency within this region on a Fr based parametrization of the flux coefficient Γ. |
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