ICTS

TBA

TBA

With the aim of assessing internal wave-driven mixing in the ocean, we develop a new technique for numerical simulations of stratified turbulence. Since the spatial scales of energetic ocean currents and internal gravity waves are typically much larger than that of turbulence, fully incorporating both in a model would require a high computational cost and is therefore out of our scope. Alternatively, we cut out a small domain periodically distorted by an unresolved large-scale flow field and locally simulate the energy cascade to the smallest scales. This technique enables us to concentrate the computational resources on resolving the breaking process of small-scale waves and the resulting turbulence while properly incorporating energy supply from large-scale flow components. This time, we demonstrate the results of two typical problems: the parametric subharmonic instability (PSI) of a plane internal gravity wave and the ageostrophic anticyclonic instability (AAI) of an elliptic vortex.

For the PSI case, we simulate the enhancement of a striped pattern of subharmonic internal waves in a tilted and oscillating coordinate system. When the disturbance amplitude grows sufficiently large, secondary instabilities arise and produce much smaller-scale fluctuations. Passing through these two stages, wave energy is transferred into turbulence energy and will be eventually dissipated. Different from the conventional scenarios of vertical shear-induced instabilities, a large part of turbulent potential energy is supplied from the outer wave and directly used for mixing. The mixing coefficient, defined as the dissipation rate of available potential energy divided by that of kinetic energy, is as large as 0.5 and tends to increase with the outer wave Froude number.

In the simulations of AAI, we rotate a model domain following elliptic streamlines of the gradient wind balance to assess the parametric excitation of inertia-gravity waves. From a series of experiments, we identify two different scenarios of wave breaking conditioned on the magnitude of the instability growth rate scaled by the buoyancy frequency. When this parameter is large, the primary wave amplitude excited by AAI quickly goes far beyond the overturning threshold and directly breaks. The resulting state is thus strongly nonlinear turbulence. If the instability parameter is small, weak wave–wave interactions begin to redistribute energy across frequency space before the primary wave reaches a breaking limit. Then, after a sufficiently long time, the system approaches a Garrett–Munk-like stationary spectrum, in which wave breaking occurs at finer vertical scales. In the two wave-breaking scenarios, the energy dissipation rates exhibit distinct scaling properties, similar to D’Asaro and Lien’s wave–turbulence transition model.

References and collaborators:
- Onuki, Yohei, Sylvain Joubaud, and Thierry Dauxois. "Simulating turbulent mixing caused by local instability of internal gravity waves." Journal of Fluid Mechanics 915 (2021): A77.
- Onuki, Yohei, Sylvain Joubaud, and Thierry Dauxois. "Breaking of internal waves parametrically excited by ageostrophic anticyclonic instability." Journal of Physical Oceanography 53.6 (2023): 1591-1613.

Baroclinic instability is a phenomenon in rotating stratified systems, and is known to play an important role in the Earth's atmosphere and ocean. The Eady problem is a text book example of baroclinic instability widely invoked for various applications (along with the Charney and Phillips problem). In the first part we recap some of the features of the standard geostrophic Eady problem (e.g., as described in most standard GFD textbooks), such as the linear instability characteristics, method of solution by analytical means, instability mechanism in terms of Counter-propagating Rossby Waves (CRWs), relations to baroclinic lifecycles, and its parameterisation in atmospheric and/or oceanic systems (e.g., works of Green, Gent-McWilliams and/or Greatbach-Lamb schemes). In the second part, we proceed to highlight and/or clarify some features of a modified Eady linear instability problem in the presence of a slope, namely (i) links of the Eady problem with quantum mechanics under the umbrella of non-Hermitian PT symmetric operators, (ii) a revised view of the CRW mechanism in the present sloped system that is more complete than existing attempts, with a rephrasing of the problem in terms of a dynamical system with a CRW basis, and (iii) analysis of the instability characteristics in terms of the GEOMETRIC framework, with some links to ocean eddy parameterisations. If time at the end, more speculative links of non-Hermitian PT symmetric operators, CRW basis and the more general shear instability problem will be provided.

We use the ocean-only global circulation model (gcm) ICON-O with very high horizontal (5km), vertical and temporal resolution including the astronomical tidal forcing to study the effects of mesoscale eddies on the low-mode internal tide. This is the first study using a high-resolution gcm to study these interactions.
The diagnosed lunar semidiurnal (M2) internal tide reveals wavy patterns with horizontally varying wavelengths, which do not correspond to plain waves.
We therefore propose a new modal decomposition method based on spatial empirical orthogonal functions. Using this method we observe enhanced dissipation of the internal tide kinetic energy inside and in the lee area of the eddy, which can be attributed to enhanced weakening of the low mode internal tide. We also observe that eddies can significantly alter the propagation pathways of the low-mode internal tide by refracting the beam southwards.
We also find that the high-modes of the internal tide are trapped inside and transported by the eddies following the eddy propagation path, thus do not necessarily stem from scattering processes of the low-mode internal tidal beams. Our findings agree with those published in idealised and observational studies and further improve the current understanding of eddy-internal tide interactions. They can be potentially used for a global quantification of their importance on vertical mixing.

Comprehending how submesoscale dynamics and their potential interplay with tides affect climate models is challenging due to their small scales and high computational demands. To address this challenge, our approach integrates modelling and observational methods. In this study, we investigate the impact of internal tides, eddies and submesoscale currents on the frequency energy spectrum of the ocean. To this end, we apply a novel simulation with telescopic grid refinement to achieve a horizontal resolution finer than 600 m over large regions of the South Atlantic. This refined resolution allows us to accurately capture submesoscale turbulence and a relatively large part of the internal wave spectrum under realistic atmospheric conditions. By comparing simulations with and without tides, we find that without tidal forcing there is significantly less energy at the high frequency end of the spectrum. Validation with mooring and Pressure Inverted Echo Sounder data sets deployed over a two year period in the Walvis Ridge region indicates that the simulation with tides is more accurate in terms of high frequency energy levels. Using an eddy tracking algorithm allows us to differentiate energy spectra within the Agulhas rings from a ring-absent background state. Within these eddies, we observe a substantial shift towards higher power spectral densities of approximately one order of magnitude across both small and large scales.

Submesoscale density fronts (1s-10s km wide) are a common feature of the ocean’s surface layer and are thought to be important for mediating buoyancy, heat, and energy exchanges which in turn have a substantial impact on the biogeochemistry. These fronts are challenging to observe due to their fast time and short length scales, so to date observations on regional and global scales have been limited. To fill this gap, this study uses a global database of along-track salinity and temperature data in combination with satellite data to identify 250,000 submesoscale density fronts across the globe.  On average, frontal buoyancy gradients scale with the frontal width, which is consistent with the expected dynamics. The submesoscale frontal gradients also exhibit global geographic variability that is correlated with the large scale density gradient, and inversely correlated with the large scale horizontal Turner angle and the mixed layer depth. Potential future research trajectories that could build off these observations are discussed, hopefully inspiring new ways of exploring submesoscale frontal dynamics through theory and modeling studies.

TBA

Atmosphere and ocean dynamics are dictated by balanced flows, such as mesoscale eddies, but determining a precise balanced state remains challenging in the presence of its nonlinear coupling with the unbalanced flows, such as internal gravity waves. The spontaneous loss of balance, resulting in nonlinear internal wave generation, challenges the existence of an invariant balanced state from a mathematical perspective, and at the same time has physical implications for the energy cycle of the atmosphere and ocean.

In this talk, I will discuss the recent progress in deriving and quantifying the balanced state in geophysical flows from nonlinear flow decomposition as well as the comparison of balanced states from different mathematical approaches: higher order balance and optimal balance . This decomposition is applied to varied oceanic regimes in a suite of idealized models to quantify spontaneous wave generation and assess its role in the energy cycle relative to other mechanisms. To diagnose these processes in complex flows, a new flow decomposition approach based on time averaging is presented for realistic applications, such as flows with boundaries. These developments provide new avenues to determine the balanced state and offer fresh insights into the energetics and dynamics of the atmosphere and ocean, that are central to understand the dynamics of the climate.

The principle dynamical components in the large scale ocean (i.e. spatial scales larger than O(100m)) are dominated by mesoscale eddies, submesoscale currents and interia gravity waves comprising both storm-forced Near-Inertial Waves (NIWs) and tidally generated internal waves (TIWs).  While mesoscale eddies (length scales of 10s of kms), generated primarily through baroclinic instability are the principal reservoir of kinetic energy in the world oceans, submesoscale currents (O(1-10 km)) comprising mixed layer eddies and fronts interact strongly with mesoscales and are critical for  regulating biogeochemical and air-sea fluxes. Here we use the so-called coarse-graining approach to compute cross-scale energy fluxes that shed light on dynamical interactions between these three components and their impact on the upper ocean. By first decomposing the oceanic velocity field into rotational and divergent components on one hand (i.e. a Helmholtz decomposition) and separately using an eddy-IGW decomposition, we obtain triadic components of energy fluxes which allow us to separately study mesoscale-submesoscale interactions and eddy-internal wave interactions. Among key findings employing this framework is that, in the absence of IGWs, the forward energy flux seen at small scales in the ocean is driven by frontogenesis, and that IGWs can induce a stimulated cascade in eddy-eddy energy interactions, thereby weakening them. We also explore other processes using this approach including the scattering of IGWs by mesoscales and submesoscales and the strength and importance of wave-wave energy cascades.

TBA

We focus on plane Poiseuille flow where an incompressible fluid is pushed between two parallel plates by maintaining a constant bulk velocity. Plane Poiseuille flow is a canonical wall-bounded shear flow where a subcritical transition to turbulence is observed. Assuming periodic boundary conditions in streamwise and spanwise directions, we classify invariant subspaces of the plane Poiseuille flow up to half-box shifts. Exploiting the interplay between symmetries and dynamics, we find new finite amplitude traveling wave solutions in some invariant subspaces, far below the linear stability threshold.

A fundamental model for large-scale ocean flow is two-dimensional (2D) turbulence above topography and has been studied since the 1970s. Ocean observations show that long-lived vortices sit astride prominent topographic features. Using a suite of numerical experiments, we illustrate the phenomenology of random topographic turbulence. As in two-dimensional turbulence, the energy of the flow is transferred towards larger scales of motion; after some rotation periods, however, the process is halted as the flow pattern becomes aligned along the topographic contours. It is found that global energy decays faster as the roughness of topography increases due to more effective viscous dissipation. The quasi-steady state reached by the flow is characterized by the relationship between potential vorticity and stream function which is found using minimum enstrophy arguments.

Eddy viscosity is employed throughout the majority of numerical fluid dynamical models, and has been the subject of a vigorous body of research spanning a variety of disciplines. It has long been recognized that the proper description of eddy viscosity uses tensor mathematics, but in practice it is almost always employed as a scalar due to uncertainty about how to constrain the extra degrees of freedom and physical properties of its tensorial form. This talk will introduce techniques from outside the realm of geophysical fluid dynamics that allow us to consider the eddy viscosity tensor using its eigenvalues and eigenvectors, establishing a new framework by which tensorial eddy viscosity can be tested. This is made possible by a careful analysis of an operation called tensor unrolling, which casts the eigenvalue problem for a fourth-order tensor into a more familiar matrix-vector form, whereby it becomes far easier to understand and manipulate. New constraints are established for the eddy viscosity coefficients that are guaranteed to result in energy dissipation, backscatter, or a combination of both. Finally, I will propose a testing protocol by which tensorial eddy viscosity can be systematically evaluated across a wide range of fluid regimes.

Permafrost can potentially release more than twice as much carbon than is currently in the atmosphere, and is warming at a rate twice as fast as the rest of the planet. Fundamentally, the thawing permafrost is a phase transition phenomenon, where a solid turns to liquid, albeit on large regional scales and over a period of time that depends on environmental forcing and other factors. In this talk, we present mathematical models that help to understand the processes on the interface "frozen ground-atmosphere" and investigate their criticality.

Lagrangian averaging plays an important role in the analysis of wave–mean-flow interactions and other multiscale fluid phenomena. The numerical computation of Lagrangian means, e.g. from simulation data, is, however, challenging. Traditional methods involve tracking a large number of particles to construct Lagrangian time series, which are then averaged using a low-pass filter. This approach has drawbacks including high memory demands, particle clustering, and complexities in parallelization.
To address these challenges, we have developed a novel approach for computing Lagrangian means of various fields, including particle positions, by solving partial differential equations (PDEs) integrated over successive averaging time intervals. We propose two distinct strategies based on their spatial independent variables. The first strategy utilizes the end-of-interval particle positions, while the second directly incorporates Lagrangian mean positions. These PDEs can be discretized in multiple ways, such as employing the same discretization as the governing dynamical equations, and can be solved on-the-fly to minimize the memory footprint.

The interannual-to-longer timescale (also referred to as low-frequency) variability in sea surface temperature (SST) of the Indian Ocean (IO) plays a crucial role in affecting the regional climate. This low-frequency variability can be caused by surface forcings and oceanic internal variability. Our study utilizes a high-resolution global model simulation to investigate the factors contributing to this observed variability and finds that internal oceanic variability plays a crucial role in driving the interannual to longer timescale variability in the southern IO. While previous studies have explored the impact of internal variability in the Indian Ocean, they have primarily focused on the tropical basin due to limitations imposed by the regional setup of the models used. However, our analysis reveals a notable southward shift in the latitude band of active internal variability for the interannual to longer period compared to earlier estimations based on coarser Indian Ocean regional models. By conducting an energy budget analysis, we show that baroclinic instability serves as the primary driver of the internal variability. This instability results from the modulation of isothermal tilts caused by the vertical shear of geostrophic zonal currents. It leads to an unstable upper water column, thereby enhancing the eddy kinetic energy (EKE) in the region. The slowly growing baroclinic instabilities, characterized by longer time and length scales, facilitate the generation of Rossby waves, which propagate the signals of SST and sea-level anomalies westward.

Surface currents modify wind driven Ekman pumping in the ocean both by modifying the stress itself and by modifying the relationship between the stress and the Ekman transport. The former effect results in a strong mesoscale structure in the wind stress curl, such as is evident from scatterometer data. This mesoscale forcing is anti-correlated with surface vorticity and thus produces a strong damping effect on ocean eddies and currents. Recent work, however, suggests that this damping effect is over-represented in common parameterizations of the air-sea wind stress. The latter effect is referred to as nonlinear Ekman dynamics. These dynamics take the stress as given and add advective terms to the linear balance. Specifically, cross terms involving the Ekman and non-Ekman components of the flow are added to the linear Ekman balance. This is known to produce small scale (e.g., submesoscale) structures in the pumping velocity.

Here, we first review both the ocean surface velocity dependence in formulations of the wind stress and how it relates to damping of geostrophic currents and eddies. We then propose a new formulation in which the surface velocity is not the velocity of an upper ocean grid cell, but rather is the velocity of a deformable rigid lid assumed to be lying between the atmosphere and ocean. The same boundary layer turbulence theory which gives the stress just above the boundary is also assumed to apply below, and matching the two stresses determines the surface velocity (and hence the stress). This formulation leads to a reduction in the damping of geostrophic eddies and currents. Next, we consider so-called nonlinear Ekman theory in submesoscale permitting simulations of wind driven ocean channel flow. A slowly varying part of near surface model vertical velocity is shown to agree well with the theory. When high frequency forcing is added, inertia-gravity waves interact with the slowly varying Ekman flow to produce a fast-time-scale analog to the Ekman velocity. Finally, we speculate that interactions between this fast Ekman flow and the waves themselves feed back on to the slowly varying Ekman-like flow. That is, we suggest that waves and (non-linear) Ekman dynamics can help to explain the rich structure seen in near-surface ocean vertical velocity fields.

The Bay of Bengal (bay) is a semi-enclosed tropical basin driven by seasonally reversing monsoon winds and a huge quantity of freshwater from rainfall and river runoff. The bay plays a fundamental role in controlling weather systems that make up the Asian summer monsoon system, including monsoon depressions and tropical cyclones. We have used a high resolution (~1 km) regional ocean model of the Bay of Bengal to explore the sub-mesoscale variability in the bay. Model simulations show that the East India Coastal Current (EICC) is extremely rich in submesoscale features compared to the open ocean and exhibit significant seasonal variations. Submesoscale activity over the EICC region is weakest during spring (March-May), slightly stronger during summer monsoon (June-September) and strongest during winter monsoon (November-January). Weak winds during spring and a huge fresh-water gain during summer monsoon tend to weaken submesoscale activity. Investigation of conversion rates of APE to KE revealed that the conversion rate is positive throughout the year over EICC region. The conversion rates are. highest in December which confirmed the highest rate of generation of submesoscale processes in the winter monsoon. The unique seasonal dynamics of submesoscale processes in the bay is determined by a combination of freshwater induced stratification and the state of EICC.

Critical behaviour associated with the occurrence of tipping points is one of the key aspects of the dynamics of the Earth system. Criticality occurs in many different forms and with different characteristic spatial and temporal scales. Past critical transitions have sometimes been associated with mass extinction events, and the snowball/warm Earth dichotomy has played a major role in the emergence of multicellular life. Currently, anthropogenic forcing to the climate system seem to be bringing some multi stable subcomponents of the climate closer to a bifurcation point, as in the case of the Atlantic meridional overturning circulation and the Greenland ice sheet. We will present here a general mathematical framework to look into critical behaviour in the Earth system. We will connect the analysis of the response of the system to perturbation in connection to its global stability properties and discuss ideas for creating robust early warning signals.

We present a data-driven framework for dimensionality reduction and causal inference in climate fields. Given a high-dimensional climate field, the methodology first reduces its dimensionality into a set of regionally constrained patterns. Causal relations among such patterns are then inferred in the interventional sense through the fluctuation-response formalism. To distinguish between true and spurious responses, we propose an analytical null model for the fluctuation-dissipation relation, therefore allowing us for uncertainty estimation at a given confidence level. The framework is then applied to understand the relation between sea surface temperature warming patterns and changes in the net radiative flux at the top of the atmosphere, the so-called "pattern effect". We present a set of new results on the pattern effect and discuss the role of different processes, active at different spatiotemporal scales, in establishing the causal linkages between warming at the surface and radiative balance.

Consider a system described by a multi-dimensional state vector X. The evolution of x is governed by a set of equations in the form of dx/dt=F(X(t)). x is a component of X. F(X(t)), the differential forcing of x, is a deterministic function of X. The solution of such a system often exhibits randomness, where the solution at one time is independent of the solution at another time. This study investigates the mechanism responsible for such randomness. We do so by exploring the integral forcing of x, G_T (t), a definite integral of F over the time span extending from t to t+T, which links the solution at two times, t and t+T.

We show that, for a system in equilibrium, G_T (t) can be expressed as G_T (t)=c_T+d_T x(t)+f_T (t), which consists of (apart from constant c_T) a dissipating component with strength d_T and a fluctuating component f_T (t), in line with the fluctuation-dissipation theorem that for a system in equilibrium, anything that generates fluctuations must also damp the fluctuations. Moreover, for a sufficiently large value of T, G_T (t) emerges as a unified forcing, characterized by d_T=-1 and a white-noise like fluctuating component f_T (t). The evolution of x from t to t+T, which is described by x(t+T)=x(t)+G_T (t) nominally, is then described by x(t+T)=c_T+f_T (t). This evolution is random, since x(t+T) is independent of x(t). This evolution is also irreversible, since the dissipating component of G_T (t) cancels with x(t) little by little and eventually completely by the time when G_T (t) emerges and generates x(t+T). The unified forcing results from interactions of x(t) with other components of X(t) that are completed during the forward integration over the time span [t,t+T], which cannot be included in the differential forcing F. In general, randomness and irreversibility are inherent features of a multi-dimensional physical system in equilibrium.

The Indian Ocean has been warming rapidly over the last few decades. However, this warming is not uniform, with the South Indian Ocean (SIO, south of 5S) exhibiting the strongest warming after 2000, an abrupt reversal from the cooling trend observed until the late 20th Century. Increased Indonesian throughflow (ITF) into the Indian Ocean during the recent climate hiatus was considered to be the primary reason for this SIO warming. Here, we show that the role of ITF on the IO decadal variability has reduced considerably after 2010. We find that the warming of the SIO during the climate hiatus (1998-2010) resulted in a weaker Mascarene High and decoupled it from the Southern Ocean atmospheric variabilities. Subsequently, while the Pacific Ocean subtropical gyre continued to migrate poleward in response to the anthropogenic warming in the Southern Ocean, it stalled in the Indian Ocean. This caused a three-fold increase in the Tasman inflows into the Indian Ocean, compensating for the weakened influence of ITF. The weakened Masacarene High also reduces the Agulhas outflow by ~20% from its peak, thus causing a heat convergence and continuing upper ocean warming in the SIO. This culminates in positive feedback, which continues to warm the SIO and, thereby, the rest of the Indian Ocean basin in recent decades. The rapid upper ocean warming in SIO significantly impacts the global climate systems and contributes to adverse weather extremes across the Indian subcontinents, Australia and Africa.

Atmospheric Cold Pools (ACP) or regions of large-scale masses of cold air are often observed beneath precipitating deep convective clouds as a result of rain evaporation. An ACP is typically identified as a drop in air temperature that is greater than 10C within a period of 30 minutes to an hour at a given location. The dense air pockets relative to warmer surroundings sink and lead to low-level outflows that may propagate as gravity currents. It has been postulated that propagating ACPs could trigger secondary convection when ensuing gravity currents undercut and mechanically lifts warm air to the level of free convection. Detailed understanding of ACP dynamics has been stymied by the lack of high-resolution field data or numerical simulations, in particular in cases where a cold-pool induced gravity current is propagating in an ambience with a mean flow. As such, and motivated by observations of ACPs in the Bay of Bengal during recent MISO-BOB field studies, laboratory experiments were conducted to mimic the evolution of ACP downdrafts in the presence of cross flows, wherefore a dense gravity current (salt water) was made to interact with an oncoming mean flow (water) in a recirculating water tunnel.

The resulting updraft flows are measured using particle image velocimetry (PIV). Scales for height (Hu) and velocity (Vu) of updraft triggered by the outflow are formulated for Reynolds numbers ranging from Re = 700 to 1500. The laboratory scales, Hu = 1.4h and Vu = C1 $\Delta$ U (where $\Delta$ U is velocity shear, h is the depth of gravity current, and C1 is a constant dependent on shear strength), are applied to MISO-BOB field cases to understand the conditions necessary for an ACP to trigger updraft and secondary convection. This modeling effort contributes to understanding the conditions necessary for ACPs to induce updrafts and subsequent secondary convection, offering valuable insights into the dynamics of ACPs and mechanisms fostering development of convective cells.

TBA