Waves and Modes |

Kore

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

Kore is a numerical code that can solves 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 and is available at : .

Spherical Couette flow

Sun, 01 Jan 2017 00:00:00 +0000

The spherical Couette system is the spherical analogue of the classic Taylor-Couette setup, with two concentric coaxial differentially rotating spherical spheres. The space between the spheres is filled with a fluid which is viscously driven. This is the setup used by the new generation of dynamo experiments such as the three meter experiment in College Park, Maryland and the DTS Experiment in Grenoble, France. This provides a more accurate geometry akin to planetary and stellar interiors and provides a relatively simpler system to study various fluid instabilities and turbulence in spherical shells.

I studied this system during my PhD (see thesis ). My simulations successfully reproduced experimental observations in the experiments at Cottbus by . There are a number of interesting questions that we attempted to answer in our work. First was the onset of global inertial modes by differential rotation itself. Second is the transition to turbulence at a critical differential rotation. Our addresses the first question while the second is under review which addresses the second question.

Sun

Mon, 01 Jan 2024 00:00:00 +0000

The recent observations of Rossby waves by caused quite a stir in the solar physics community and a renewed interest in inertial waves. Subsequent observations of High Frequency Retrograde (HFR) vorticity waves by raised a question of whether they are related to any theoretical known waves. We used the linear MHD code to compute inertial eigenmodes of spherical shells and found that the aspect ratio of the solar convective shell r_i/r_o = 0.71 , both sets of eigenmodes matched rather well with the observations. What is surprising is that our model did not have any density stratification, unlike the Sun.

Onset of convection in rotating spherical shells

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

Convection in rotating spherical shells is ubiquitous in planets and stars. Before fully understanding the nonlinear process, we must make efforts in understanding the linear part - the onset of convection. Though this has been an active area of research since the times of Chandrasekhar, very little work had been done in understanding how the critical parameters of convection vary with the aspect ratio of a spherical shell $\chi=r_i/r_o$ . We used the eigenvalue code to compute the critical onset of convection across four decades in rotation rate (Ekman number) and for $0.05\leq\chi\leq 0.95$ , spanning almost all possible cases in astrophysical objects. The database has been made openly available and is being used by other publications to understand where in the physical regime their simulations are. For more information, you can read the (open access) publication.

Transport of angular momentum in stars

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

Angular momentum transport from core the envelope of massive stars has been a subject of active research. During the , I supervised student Hachem Dhouib from CEA Saclay to study this in a 3 solar mass ZAMS star using the MagIC code. The star has a convective zone in the center, followed by a stably stratified layer at the top. We found that the emanation of internal gravity waves in the radiative zone leads to an angular momentum transport in the star. Read the full project report .

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