This simulation, conducted using Modular Ocean Model 6, represents an oversized "swimming pool" that spans from \(-25^\circ\)E to \(0^\circ\)E and \(10^\circ\)N to \(60^\circ\)N, roughly the size of the North Atlantic basin. In the video, sea surface height is shown in grayscale, while vorticity is depicted in red (cyclonic) and blue (anticyclonic), viewed from above. The circulation is driven by the large-scale temperature difference between the equator and the poles. The video highlights the mesoscale eddies, or vortices, that emanate from the eastern boundary. In my Ph.D. dissertation, I demonstrated that these eddies served a dual role. First, they acted to trap a narrow eastern boundary current, which flowed poleward at the surface and equatorward at depth. Second, they broadened the sinking limb of the overturning circulation by transporting warm water away from the eastern boundary.

Typically, one would expect a narrow boundary current along the eastern boundary to broaden and eventually dissipate westward due to Rossby waves. However, trapping occurred because eddies were absent within approximately \(\sim 2\) Rossby radii (or \(10-30\,\)km) of the boundaries. In coarse-resolution models, which do not resolve these eddies, the Gent-McWilliams diffusivity is often used to represent their effect on the large-scale flow. My research showed that this diffusivity needed to be tapered near the oceanic boundaries to effectively trap narrow eastern boundary currents in the absence of topography.

The closed geometry of this basin also allowed for the analysis of the zonal overturning circulation. I found that these eddies broadened the vertical branches of the overturning circulation. Specifically, the sinking limb of the circulation was located in the northeastern quadrant of the basin. A key observation was the predominance of anticyclonic eddies originating from the eastern boundary. These eddies were responsible for transporting warm water from the eastern boundary current toward the interior. As they moved into the interior, they lost heat to the atmosphere, dissipated, and their water-mass became denser, thereby broadening the area of sinking beyond just the eastern boundary.

In summary, my research demonstrated how eddies could both trap boundary currents and broaden the sinking branch of the overturning circulation.

Enceladus and Europa are icy moons orbiting Saturn and Jupiter, respectively. These moons are characterized by thick ice shells, ranging from \(10\) to \(100\,\)km in thickness, which cover global oceans of liquid water that may potentially support life. However, due to the ice shells, we cannot directly observe these oceans from space. The primary goal of this study was to explore the likely ocean circulation by focusing on quantities that can be more easily measured or estimated remotely, such as rotation rate, bottom heating, and ocean depth.

I conducted simulations using MITgcm and Oceananigans.jl, with uniform heating from below and cooling at the surface. One such simulation is shown here, with three panels displaying meridional sections of zonal velocity (blue indicating westward flow, red indicating eastward flow), temperature, and the evolution of particles initially released at the ocean's bottom. The ocean is continuously energized by bottom heating from the moon's core, while the surface is capped by a rigid ice shell maintained at freezing temperatures, which removes heat from the ocean. The east-west velocity patterns observed are similar to those found on gas giants like Jupiter and Saturn. In the temperature plot, small convective plumes near the poles and convectively-driven Rossby waves (rolls) near the equator are evident.

The question arises: which of these mechanisms transports bottom heat more efficiently to the ice shell? I found that in oceans where plumes were unresolved (due to coarse resolution or high viscosity), heat was predominantly transferred to the ice shell near the equator via rolls, leading to thinner equatorial ice sheets. In contrast, oceans with well-resolved plumes transferred heat more effectively to the ice shell near the poles, resulting in thinner polar ice sheets. This difference provides a potential way to infer ocean circulation from ice sheet observations.

Additionally, I performed numerical simulations of hydrothermal plumes emerging from the bottom of Enceladus and found that heat flux and salinity significantly affected the height to which the plumes could rise. Importantly, the plumes could not reach the ice shell on Enceladus due to its weak gravity and low thermal expansion coefficient.

Over the years, I've come to recognize the limitations of numerical models. As a result, I've started integrating them with data-driven approaches to address some of these shortcomings. Currently, my research at the Centre for Climate Studies at IIT Bombay focuses on developing data-driven emulators for numerical ocean models. These emulators can significantly outperform traditional models by requiring fewer parameters to represent the same processes. However, this comes at the cost of violating basic conservation principles. Thus, my current challenge is not only to develop these emulators but also to identify scenarios where they can replace costly large-scale numerical models. Additionally, I aim to explore ways of combining data-driven methods with traditional numerical models. Since traditional models cannot explicitly represent processes smaller than the grid size, we need to find ways to account for the effects of small-scale processes using large-scale resolved ones. Data-driven methods offer a promising path to achieve this.