Talks

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.

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 th...

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 e...

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 m...

Turbulence reconstruction poses significant challenges in a wide range of fields, including geophysics, astronomy, and even the natural and social sciences. The complexity of these challenges is largely due to the non-trivial geometrical and statistical properties observed over decades of time and spatial scales. Recent advances in machine learning, such as generative adversarial networks (GANs), have shown notable advantages over classical methods in addressing these challenges[1,2]. In addition, the success of generative diffusion models (DMs), particularly in computer vision, has opened up new avenues for tackling turbulence problems. These models use Markovian processes that progressively add and remove noise scale by scale, which naturally aligns with the multiscale nature of turbulence. In this presentation we discuss a conditional DM tailored for turbulence reconstruction tasks. The inherent stochasticity of DM provides a probabilistic set of predictions based on known measureme...

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 multipl...

The Indian Ocean (IO) coastline which houses a large population from the continents of Africa, Asia and Australia is vulnerable to a plethora of climatic hazards that are brought on by sea-level rise. The global mean sea level has risen at a rate of ~3.6 mm/yr over the last two decades and is projected to increase by more than 1m by the end of this century. A thorough assessment of the dynamics of the regional sea-level change is vital for effective policymaking to mitigate natural calamities associated with the rising sea levels. We use a suit of 27 models from phase six of the coupled model intercomparison project (CMIP6) simulations to study their representation of dynamic sea level (DSL) and the factors that influence DSL variability in the basin. We show that the multi-model mean DSL exhibits a good correlation with observation with few notable biases consistent across the models. There is a positive bias in the DSL across the basin with a west to east gradient and a pronounced bi...

We develop a Machine-Learning Renormalization Group (MLRG) algorithm to explore and analyze many-body lattice models in statistical physics. Using the representation learning capability of generative modeling, MLRG automatically learns the optimal renormalization group (RG) transformations from self-generated spin configurations and formulates RG equations without human supervision. The algorithm does not focus on simulating any particular lattice model but broadly explores all possible models compatible with the internal and lattice symmetries given the on-site symmetry representation. It can uncover the RG monotone that governs the RG flow, assuming a strong form of the $c$-theorem. This enables several downstream tasks, including unsupervised classification of phases, automatic location of phase transitions or critical points, controlled estimation of critical exponents, and operator scaling dimensions. We demonstrate the MLRG method in two-dimensional lattice models with Ising symmetry and show that the algorithm correctly identifies and characterizes the Ising criticality.

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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.

Internal gravity waves pervade the oceans, profoundly shaping their dynamics. Their interactions with eddies and other waves govern energy transfers and can lead to wave breaking, and density mixing, thus influencing large-scale mean flows. Despite their significance, the relative importance of wave-mean flow interactions vis-à-vis wave-wave interactions remains elusive. We investigate internal gravity wave-mean flow interactions with the novel numerical Internal Wave Energy Model (IWEM) based on the six-dimensional radiative transfer equation. We simulate wave interactions with local coherent mesoscale eddies, to find a wave energy loss at the eddy rim akin to critical layer behavior. We investigate internal gravity wave-wave interactions by numerically evaluating the kinetic equation derived from weak interaction assumptions. Our findings unveil a predominantly forward energy cascade from wave-wave interactions

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.