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. 

How to cite: Caulfield, C., Petropoulos, N., and de Bruyn Kops, S.: Modelling dispersion in stratified turbulent flows as a resetting process , EGU General Assembly 2025, Vienna, Austria, 27 Apr–2 May 2025, EGU25-14086, https://doi.org/10.5194/egusphere-egu25-14086, 2025.

The energy transfers in the meso- to submesoscale regime in the ocean yield both up-scale and down-scale components from a complex pattern of flow structures which impact scale-dependent ocean turbulence and mixing that is not yet correctly parameterised in climate models.
The Walvis Ridge region in the South Atlantic is characterized by strong tidal beams and lies in the path of the Agulhas eddies and hence also features large mesoscale energy with associated submesoscale fronts and filaments.
Here, we quantify lateral mixing in the mixed layer using surface drifter observations from two observational campaigns with a unique deployment of two drifter types at two different depth levels simultaneously, one at the very surface and one at 15m depth. We quantify the contribution of the different motions that show up in the drifter trajectories at various time and space scales ranging from hours to months and 100m to 1000s of km and how they influence the applicability of the eddy-diffusion model.                                    

We find that large scale mean flow removal plays a critical role in achieving convergence in the components of the diffusivity tensor and in the major axis component after diagonalization. Writing the diffusivities as the product of time scales and kinetic energy, the significant anisotropy in the diffusivity tensor is mainly explained by the anisotropy in the Lagrangian integral time scales, while the major axis component of the velocity variance tensor is comparable to the minor axis component. The details of this anisotropy depend on scale. Motions on scales smaller than the Rossby Radius contribute significantly to the diffusivities. We discuss how the results relate to what kind of energy cascade exists at which scale.

How to cite: Griesel, A., Dräger-Dietel, J., Aravind, A., Breunig, E., Carrasco, R., Carpenter, J., Horstmann, J., and Leimann, I.: Investigating vertical dependence of turbulence regimes and lateral mixing in the mixed layer from drifter observations in the South Atlantic, EGU General Assembly 2025, Vienna, Austria, 27 Apr–2 May 2025, EGU25-20207, https://doi.org/10.5194/egusphere-egu25-20207, 2025.

Buoyancy-driven exchange flows in geophysical contexts, such as flows through straits, often create a partially-mixed intermediate layer through mixing between the two stratified counterflowing turbulent layers. We present a three-layer hydraulic analysis of such flows, highlighting the dynamical importance of the intermediate layer. Our model is based on the viscous, shallow water, Boussinesq equations and includes the effects of mixing as a non-hydrostatic pressure forcing. We apply this shallow-water formulation to direct numerical simulations of stratified inclined duct (SID) exchange flows where turbulence is controlled by a modest slope of the duct. We show that the nonlinear characteristics of the three-layer model correspond to linear long waves perturbing the three-layer mean flow, and predict, in agreement with recent experimental observations in SID, hydraulically-controlled regions in the middle of the duct, linked to the onset of instability and turbulence. We also provide the first evidence of long-wave resonance, as well as resonance between long and short waves, and their connection to transitions from intermittent to fully developed turbulence. These results challenge current parameterisations for turbulent transport in stratified exchange flows, which typically overlook long waves and internal hydraulics induced by streamwise variations of the flow.

How to cite: Linden, P., Atoufi, A., Lefauve, A., and Zhu, L.: Hydraulic control, turbulence and mixing in stratified buoyancy-driven exchange flows, EGU General Assembly 2025, Vienna, Austria, 27 Apr–2 May 2025, EGU25-3191, https://doi.org/10.5194/egusphere-egu25-3191, 2025.

Internal gravity waves (IGWs) shape the ocean through their interactions with e.g. eddies and other waves. These interactions can lead to wave breaking and density mixing, which influence large-scale mean flows. The resulting energy transfers shape the spectral shape of IGWs, which is surprisingly similar throughout the oceans - the universal Garrett-Munk (GM) spectrum. A key mechanism shaping this continuous energy spectrum is nonlinear wave-wave interaction. We study the scattering of IGWs via wave-wave interactions under the weak-interaction assumption, using the kinetic equation derived from a non-hydrostatic Boussinesq system with constant rotation and stratification. The kinetic equation and coupling coefficients derived from Eulerian and Lagrangian equations are identical under the resonance condition. By developing Julia-native numerical codes, we evaluate the energy transfers for resonant and non-resonant interactions, including inertial and buoyancy oscillations. Our findings confirm that resonant triads dominate the energy transfers, while non-resonant interactions are negligible in isotropic spectra but may become relevant in anisotropic conditions. These findings provide convergent results at reduced computational costs, improving the efficiency and reliability of energy transfer evaluations in oceanic IGW spectra.

How to cite: Sebastia Saez, P., Eden, C., Olbers, D., and Chouksey, M.: Wave-wave interactions within a typical internal gravity wave spectrum in the ocean, EGU General Assembly 2025, Vienna, Austria, 27 Apr–2 May 2025, EGU25-19040, https://doi.org/10.5194/egusphere-egu25-19040, 2025.

Internal wave dynamics play a critical role in understanding ocean diapycnal diffusivity and associated mixing processes, particularly in the deep ocean context. Building upon prior analyses of internal wave breaking and its influence on diapycnal diffusivity, in this study we employ a high-resolution regional ocean model to infer ocean diapycnal diffusivity due to internal wave (IW) breaking [Momeni et al., 2025]. Our work leverages the Bouffard-Boegman parameterization, which distinguishes between reversible and irreversible mixing components. This framework provides a robust methodology to infer diapycnal diffusivity profiles from turbulent dissipation rates, improving upon earlier KPP-based approaches that lacked this critical distinction. This inference is made possible through the work of Skitka et al. [2024], which directly measured dissipation rates from numerical simulations.

The findings reinforce and expand on earlier results from dynamically downscaled simulations in the northeast Pacific, which revealed a pronounced wave-turbulence cascade and highlighted the suppression of higher-order IW modes due to the background component of KPP. By deactivating this component, higher-order modes engage in triad resonance interactions with lower-order modes and are effectively energized; they subsequently undergo shear instability, enhancing mixing rates and aligning diffusivity profiles with empirical observations. This mechanism is discussed in detail in Momeni et al. [2024].

Our results underscore KPP’s limitations in distinguishing mixing processes and its tendency to overestimate shear contributions to diffusivity. These insights pave the way for improving diapycnal diffusivity parameterizations in low-resolution climate models by emphasizing mechanisms rooted in internal wave breaking rather than simplified parameterizations. Future work will focus on higher-resolution simulations to refine these findings and address basin- and latitude-dependent variations.

References

Kayhan Momeni, Yuchen Ma, William R Peltier, Dimitris Menemenlis, Ritabrata Thakur, Yulin Pan, Brian K Arbic, Joseph Skitka, and Matthew H Alford. Breaking internal waves and ocean diapycnal diffusivity in a high-resolution regional ocean model: Evidence of a wave-turbulence cascade. Journal of Geophysical Research: Oceans, 129(6):e2023JC020509, 2024.

Kayhan Momeni, W Richard Peltier, Joseph Skitka, Yuchen Ma, Brian K Arbic, Dimitris Menemenlis, and Yulin Pan. An alternative buoyancy reynolds number-based inference of ocean diapycnal diffusivity due to internal wave breaking: results from a high-resolution regional ocean model. Geophysical Research Letters, 2025. Submitted for publication.

Joseph Skitka, Brian K Arbic, Yuchen Ma, Kayhan Momeni, Yulin Pan, William R Peltier, Dimitris Menemenlis, and Ritabrata Thakur. Internal-wave dissipation mechanisms and vertical structure in a high-resolution regional ocean model. Geophysical Research Letters, 51(17):e2023GL108039, 2024.

How to cite: Momeni, K., Peltier, W. R., Skitka, J., Ma, Y., Arbic, B. K., Pan, Y., and Menemenlis, D.: Wave-Turbulence Cascades and Deep Ocean Mixing: Inferring Diapycnal Diffusivity in High-Resolution Ocean Models, EGU General Assembly 2025, Vienna, Austria, 27 Apr–2 May 2025, EGU25-4591, https://doi.org/10.5194/egusphere-egu25-4591, 2025.

Oceanic mesoscale eddy mixing plays a crucial role in the Earth’s climate system by redistributing heat, salt and carbon. Eddy mixing is impacted by various physical factors, one of which is the oceanic bottom slope. Within a barotropic framework, it can be shown analytically that bottom slopes suppress the cross-slope eddy mixing. Unfortunately, adding baroclinic effects greatly increases the complexity of the problem. To understand how bottom slopes influence eddy mixing in a baroclinic framework, we study eddy fields in a quasi-geostrophic two-layer model with a linear bottom slope. We investigate the eddy mixing by releasing and tracking virtual particles in the flow fields and analysing how they spread in the cross-slope direction. This is done for a range of bottom slope magnitudes and for prograde as well as retrograde slopes. The goal is to figure out how eddy mixing depends on the steepness and direction of the bottom slope and on the position in the water column. We find that for steep bottom slopes, the baroclinic instability is suppressed, the eddy field gets weaker, and the spreading of particles in the cross-slope direction decreases. This suppression is comparable for prograde and retrograde slopes. Moreover, the suppression is observed not only in the bottom layer, where the slope is located, but also in the upper layer. This indicates that the suppression of eddy mixing by oceanic bottom slopes can have an impact throughout the water column.

How to cite: Sterl, M., Palóczy, A., LaCasce, J., Groeskamp, S., and Baatsen, M.: The influence of oceanic bottom slopes on eddy mixing in a two-layer model, EGU General Assembly 2025, Vienna, Austria, 27 Apr–2 May 2025, EGU25-5953, https://doi.org/10.5194/egusphere-egu25-5953, 2025.

One of the main factors characterizing the dynamics of the atmosphere is its vertical density stratification. Gravity waves arising under these conditions play an essential role in large-scale energy transport through upwards propagation and breaking in the middle atmosphere, manifesting in phenomena such as the cold summer mesopause. Moreover, it was recently found that the summer mesopause is also home to the strongly stratified turbulence regime occurring at extremely high buoyancy Reynolds and low horizontal Froude numbers. Direct observation or numerical simulation of these processes with high resolution proves difficult however, due to the remoteness of the region combined with the mesoscale horizontal and small vertical scales that have to be resolved for a detailed analysis of the emerging dynamics. 

To deepen our knowledge of the these processes in this region, we employ a combined approach of state-of-the-art radar observations using the MAARSY and SIMONe systems and the physics-informed machine learning method HYPER. The first step and the main topic of the current study is to reconstruct high-resolution 3D wind fields from the line-of-sight measurements in the summer mesosphere. The resulting fields closely capture the observed data and produce high-fidelity, Navier-Stokes-compliant predictions of the surrounding flow beyond measuring points. Building on this, we aim to provide an analysis of the first high-resolution radar observations of strongly stratified turbulence in the middle atmosphere.

How to cite: Peterhans, V. J., Urco, J. M., Avsarkisov, V., and Chau, J. L.: Analysis of Mesoscale Dynamics in the Mesosphere using Radar Observations and Machine Learning, EGU General Assembly 2025, Vienna, Austria, 27 Apr–2 May 2025, EGU25-6814, https://doi.org/10.5194/egusphere-egu25-6814, 2025.

The rotation rate and the magnetic field play a key role, in the geodynamo models, for understanding the convective flow behavior in the Earth’s outer core where dynamic MAC balance of forces occurs frequently and is affected by the diffusion processes. Due to the presence of buoyancy, Lorentz and Coriolis forces, the turbulent eddies in the core get deformed and elongated in the direction parallel to the rotation axis and magnetic field in BM anisotropy or are affected by gravity (buoyancy) direction in SA anisotropy. Hence the turbulence is highly anisotropic. The turbulent small-scale eddies are diffusers of momentum and heat, and thus, the effective viscosity and thermal diffusion are also anisotropic. The effect of anisotropic thermal diffusion coefficient on the stability of horizontal fluid planer layer heated from below and cooled from above, rotating about its vertical axis and subjected to a uniform horizontal magnetic field, is analyzed in the present study. The cross, oblique and parallel rolls assumed to make an angle (θ), 90°, 0° < θ < 90° and 0°, respectively, with the axis of the magnetic field. These rolls are calculated for different range of control parameters arising in the system. The linear stability analysis is investigated by using the normal mode method. The appearance of rolls for stationary modes as well as oscillatory modes depends on the SA (Stratification Anisotropy) parameter, α (the ratio of horizontal and vertical thermal diffusivities). The stabilizing/destabilizing effect strongly depends on the Chandrasekar (Q) and Taylor (Ta) numbers. The obtained results for isotropic cases coincide with those obtained by pioneers in the literature. The two-dimensional anisotropic complex Ginzburg-Landau (ACGL) equation with cubic nonlinearity is used to study the weakly nonlinear behaviour near the primary instability threshold. This equation, derived using the multiple scale analysis, is similar to the one found in the literature. The numerical simulation of this ACGL equation with periodic boundary conditions has been carried out using the pseudo-spectral method in Fourier space with exponential time differencing. The formation of spatiotemporal patterns strongly depends on α, Ta and Q. For fixed Q, as Ta increases, the Coriolis force intensifies, more stable and organized spiral patterns showed their presence. Further for increasing Ta, the size or scale of spiral patterns decreases, while the number of patterns get increased. 

How to cite: Nayak, K., Rani, H. P., Devanuri, J. K., Rameshwar, Y., and Brestenský, J.: Pattern Formation of Rotating Magnetoconvection with Anisotropic Thermal Diffusivity Effect in the Earth's Outer Core, EGU General Assembly 2025, Vienna, Austria, 27 Apr–2 May 2025, EGU25-437, https://doi.org/10.5194/egusphere-egu25-437, 2025.

Stratified shear flows are commonplace in the ocean and the atmosphere. Understanding the mechanisms by which such flows become turbulent and lead to irreversible mixing due to the ultimate break down of different types of primary instabilities is vital in understanding diapycnal fluxes of heat and other important scalars such as salt and carbon. We consider numerically the Lagrangian view of turbulent mixing in stably stratified parallel shear flow where both the initial velocity field and initial density departure from the base hydrostatic state have a hyperbolic tangent profile in the vertical coordinate with the same point of inflection. By varying the ratio of velocity interface thickness and density interface thickness, these initial conditions permit two types of instabilities: Kelvin-Helmholtz instability (KHI) and Holmboe wave instability (HWI). These instabilities lead to two distinct types of mixing; overturning motions within the density interface, and scouring by turbulence on the edges of the density interface. Here, we examine mixing from a Lagrangian perspective using direct numerical simulations (DNS) for initial conditions that are unstable to KHI and HWI. Lagrangian particles are tracked in the simulations, and the fluid buoyancy sampled along particle paths provides a Lagrangian measure of mixing. The timing of mixing events experienced by particles inside and outside the interface is different in simulations exhibiting KHI and HWI. The particles exhibit aggregation in buoyancy space when there is sustained overturning motion within the interface. The root mean square (RMS) buoyancy for a set of particles that start with the same buoyancy is larger for HWI than KHI for the same bulk Richardson number, implying heterogeneous mixing along particle paths for HWI. Finally, the number of particles starting close to the mid-plane of the interface which experience a change in sign in the local fluid buoyancy and end on the opposite side of the mid-plane is compared for KHI and HWI for several values of the bulk Richardson number. Surprisingly, for HWI with a large bulk Richardson number, more than half of the particles that start near the mid-plane end on the opposite side of the mid-plane. We explain this result in terms of localisation of mixing.

How to cite: Zhou, X., Taylor, J., and Caulfield, C.: A Lagrangian view of mixing in stratified shear flows, EGU General Assembly 2025, Vienna, Austria, 27 Apr–2 May 2025, EGU25-7453, https://doi.org/10.5194/egusphere-egu25-7453, 2025.