Projects |

Inertial Modes

Mon, 01 Jan 0001 00:00:00 +0000

Inertial modes are global oscillations of a rotating fluid, restored by the Coriolis force. I’ve studied where they come from and how they show up across very different systems: in a laboratory spherical Couette experiment, where my simulations reproduced modes seen at BTU Cottbus; in the Sun, where eigenmodes computed with the linear code (the same code used to map the onset of convection itself) match recent observations of solar Rossby and HFR vorticity waves; and, more fundamentally, in 3D convection simulations, which show that these modes emerge naturally from rotationally constrained turbulence once the convective Rossby number drops below about one-half - without any external forcing.

Related publications:

- The Astrophysical Journal (2026)
- Earth and Space Science (2023)
- The Astrophysical Journal Letters (2022)
- Surveys in Geophysics (2022)
- Journal of Fluid Mechanics (2018)

Turbulence

Mon, 01 Jan 0001 00:00:00 +0000

How does smooth, ordered flow break down into turbulence? In a laboratory spherical Couette experiment, we traced a sudden transition to turbulence to a centrifugal instability of the inner sphere’s boundary layer, which seeds small-scale structures that grow into turbulence dominated by inertial waves and drive efficient angular momentum transport.

On a very different scale, turbulence also governs whether Europa’s deep ocean can reach its icy surface: simulations of turbulent water flow through cracks in the ice shell show that rapid cooling forms frazil ice that clogs the pathway within hours, limiting direct exchange between the ocean and the shallow subsurface.

Related publications:

- Nature Astronomy (2026)
- Journal of Fluid Mechanics (2024)

Planetary Dynamos

Mon, 01 Jan 0001 00:00:00 +0000

Planets that generate (or once generated) their own magnetic fields do so through a dynamo: convective motion of an electrically conducting fluid in their interior. Observed fields are rarely simple dipoles, though. I’ve used 3D dynamo simulations to explain Mars’ lopsided ancient field, reproduced by imposing a hemispheric heat flux variation at the core-mantle boundary, and to help constrain the interiors of Jupiter and Saturn, whose dilute “fuzzy” cores and stably stratified layers must be included to reproduce their observed fields.

Related publications:

- Geophysical Research Letters (2025)
- The Planetary Science Journal (2023)
- Journal of Geophysical Research: Planets (2022)

Scientific Software

Mon, 01 Jan 0001 00:00:00 +0000

Simulating and analyzing planetary and stellar magnetohydrodynamics requires purpose-built tools. Here are the codes and packages I develop and maintain.

MagIC

MagIC is a numerical code that can simulate fluid dynamics in spherical geometry. It solves for the Navier-Stokes equation including Coriolis force, optionally coupled with an induction equation for Magneto-Hydro Dynamics (MHD), a temperature (or entropy) equation and an equation for chemical composition under both the anelastic and the Boussinesq approximations.

MagIC has been used in 174 publications (170 refereed) since 2002, according to .

MagIC is pseudo-spectral and makes use of spherical harmonics $Y_\ell^m(\theta,\phi)$ in the angular directions. In the radial direction, it offers two options: one can either make use of Chebyshev polynomials or finite differences.

I am one of the developers of MagIC, so feel free to reach out if you plan to use it for your work! For more information, visit: .

Links: ·

Kore

Kore is a numerical code that can solve for wave-like solutions in rotating spheres and spherical shells. It solves for solutions to the combination of linearized Navier-Stokes, magnetic induction equation, a temperature (or entropy) equation and an equation for chemical composition under both the anelastic and the Boussinesq approximations.

Kore is fully spectral and makes use of spherical harmonics $Y_\ell^m(\theta,\phi)$ in the angular directions. In the radial direction, it expands every spherical harmonic coefficient in Chebyshev polynomials while using Gegenbauer polynomials to compute radial derivatives.

I am one of the developers of Kore, so feel free to reach out if you plan to use it for your work! Kore is free and open source.

Links:

Kaiju

Kaiju (formerly GAMERA) is written in modern Fortran and provides a flexible, portable, and exascale-capable MHD code. It uses the finite volume method to simulate magnetospheric dynamics.

I was involved in adapting it to in order to accurately compute the field-aligned currents (FACs) and better correct the MESSENGER data.

Links:

planetMagFields

planetMagFields is a package that provides an easy interface to plot and analyze planetary magnetic field data. It provides very easy access to the Gauss coefficients of a planet’s magnetic field obtained from inversion of planetary mission data, and an easy interface to plot, analyze and even produce files for 3D visualization of a planet’s magnetic field.

To learn more, check out the documentation here:

If you’re using this package for your work, please cite the paper in Journal of Open Source Software (JOSS):

Barik et al., (2024). planetMagFields: A Python package for analyzing and plotting planetary magnetic field data. Journal of Open Source Software, 9(97), 6677,

Or bibtex:

 @article{Barik2024,
 doi = {10.21105/joss.06677},
 url = {https://doi.org/10.21105/joss.06677},
 year = {2024},
 publisher = {The Open Journal},
 volume = {9},
 number = {97},
 pages = {6677},
 author = {Barik, Ankit and Angappan, Regupathi},
 title = {planetMagFields: A Python package for analyzing and plotting planetary magnetic field data},
 journal = {Journal of Open Source Software}
 }

Links: · ·

inermodz

A fluid rotating with solid body rotation (rotation rate $\Omega$ ) is stably stratified in angular momentum. It can be shown that a small perturbation to this fluid gives rise to a wave solution that oscillates with frequency $|\omega|\leq2\Omega$ . In the absence of boundaries (or far away from them), such a wave propagates as plane waves called “inertial waves”. In the presence of boundaries, the solution must satisfy boundary conditions (for example, impenetrability, $\boldsymbol{u}\cdot\hat{\boldsymbol{n}}=0$ ) and the solutions are global modes called “inertial modes”. These modes can be computed analytically for some container shapes such as a cylinder and a sphere. This Python package allows one to compute the analytical mode frequencies and solutions in a sphere.

Links:

Magnetic Data

Mon, 01 Jan 0001 00:00:00 +0000

Not all planetary magnetic fields come from simulations - some come from carefully inverting the sparse, noisy measurements that spacecraft actually recorded. The illustrate this well: their 66 satellites carry magnetometers too coarse to be useful individually, but together sample each point on Earth every nine minutes, and this dense repeated sampling significantly increases the signal to noise ratio for studying Earth’s internal and external magnetic fields.

Related publications:

- Geochemistry, Geophysics, Geosystems (2021)

Unpublished

Mon, 01 Jan 0001 00:00:00 +0000

Not everything makes it into a journal. A few threads I’ve worked on are either still in progress, or were reported through a project report, a code repository, or a thesis rather than a paper.

The Moon’s dynamo

Paleomagnetic analysis of Apollo rock samples shows the Moon once had a magnetic field stronger than present-day Earth’s, which then decayed to zero. No single proposed dynamo mechanism - thermochemical convection, a basal magma ocean, or mechanical driving by precession - explains the full history on its own.

We found that a mix of convection and precession has the potential to explain the strength, decline, and eventual disappearance of the lunar field together.

External Fields (Mercury)

MESSENGER observations of Mercury’s magnetotail provided details of the planet’s field, but existing corrections for field-aligned currents (FACs) relied on empirical models.

Along with , I adapted the MHD code (formerly GAMERA) to map the currents through Mercury’s magnetosphere and solve for the FACs directly, aiming to better correct the MESSENGER data.

Stellar angular momentum transport

Angular momentum transport from the core to the envelope of massive stars is a subject of active research. During the , I supervised student Hachem Dhouib in studying this in a 3-solar-mass ZAMS star using the MagIC code. We found that internal gravity waves emanating from the radiative zone transport angular momentum through the star.

The video shows an equatorial section through the star with colors representing radial velocity: red (blue) is outward (inward).

Read the full project report .

Uranus’s magnetic field from Voyager 2

Uranus has been visited by a spacecraft exactly once: Voyager 2’s 1986 flyby, which returned the only in-situ magnetic field measurements we have of the planet. I revisited that magnetometer data (from the Planetary Data System archives) to invert it for a spherical harmonic model of Uranus’s internal field, using a regularized least-squares inversion with an L-curve criterion to pick the optimal regularization strength.

The recovered field agrees well with previously published models by Connerney et al. (1987), Holme & Bloxham (1996), and Herbert (2009). Code and figures are available at .