Turbulent convection in a vertical column of PPD

URL: https://github.com/evgenykurbatov/kp23-turb-conv-ppd

Abstract

A model for the transport of anisotropic turbulence in an accretion disk is presented. This model is based on the mean field approximation and is designed to study turbulence of various nature and its role in the redistribution of the angular momentum of the accretion disk. The mean field approach makes it possible to take into account various types of instabilities by adding appropriate sources in the form of moments of fluctuations of hydrodynamic quantities. We used the model to study the role of convective instability in a gaseous and dusty circumstellar disk in the framework of a one-dimensional approximation. To do this, it was combined with the calculation of radiative transfer and with the calculation of the convective flow in the mixing length theory approximation. Within this framework, we confirm the conclusions of other authors that the turbulence generated by convection does not provide the observable disk accretion rates and sufficient heat source for which convection would be self-sustaining. The reasons for this are the strong anisotropy of turbulence in the disk, as well as the fact that convection turns out to be too weak source for turbulence.

This code is suitable for calculating the evolution of gas density, temperature, IR radiation field, convection and turbulence stress tensor in the vertical column of protoplanetary disk.

Features of the Cologne engine

Hydrostatics
- Star gravity + self gravity
- Turbulent pressure
Non-statonary radiative transfer (diffusive approximation) + thermal balance
- Heating by external sources
- Opacity model for a mixture of graphite and silicate dust particles
External heating sources: star, interstellar radiation, and accretion
Convection in MLT approximation
- Canuto flux model
- Hansen & Kawaler flux model
Turbulence transfer (Reynolds stress tensor approach)
- Simplified dissipation model (eps~K/tau)
- Full dissipation model - not yet

Requirements

Python3 with Numpy, Scipy, Matplotlib, Numba.
Cologne v1.2.0 - the engine (included in this package).

The models were ran on Python 3.7, tested on 3.9.

Code

The cologne/ directory contains the engine Cologne.

Each model is represented by a directory MODEL/ and a script MODEL.py. The model parameters are read from MODEL/params.py.

Models:

dry_*.py -- no convection, no turbulence
conv_*.py -- just convection, no turbulence
turb_*.py -- both convection and turbulence

In the models with the '_plus' suffix, the surface density of the column is increased by four times.

The hydrostatics and radiative transfer modules in the Cologne engine are remake of the code by Ya. N. Pavlyuchenkov (originally in Fortran).

Publications

E. P. Kurbatov, Ya. N. Pavlyuchenkov. The turbulent convection in protoplanetary disks and its role in the angular momentum transfer, arXiv

Authors

Author of the code

Evgeny P. Kurbatov Institute of Astronomy, Russian Academy of Sciences / Moscow, Russia (ORCID iD)

Co-author of the Paper

Yaroslav N. Pavlyuchenkov Institute of Astronomy, Russian Academy of Sciences / Moscow, Russia

[email protected]

References

Original code

Ya. N. Pavlyuchenkov, A. V. Tutukov, L. A. Maksimova, and E. I. Vorobyov. Evolution of a Viscous Protoplanetary Disk with Convectively Unstable Regions, 2020, Astronomy Reports, Vol. 64, No. 1, pp. 1-14 // ADS | arXiv
E. I. Vorobyov and Ya. N. Pavlyuchenkov. Improving the thin-disk models of circumstellar disk evolution. The 2+1-dimensional model, 2017, A&A, Vol. 606, p. A5 // ADS | arXiv

Modules and methods

G. Van Rossum and F. L. Drake. Python 3 Reference Manual, 2009, CreateSpace // DOI
Array programming with NumPy, 2020, Nature, Vol. 585, No. 7825, pp. 357-362 // DOI
L. Petzold. Automatic Selection of Methods for Solving Stiff and Nonstiff Systems of Ordinary Differential Equations, 1983, SIAM Journal on Scientific and Statistical Computing, Vol. 4, No. 1, pp. 136-148 // DOI
SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python, 2020, Nature Methods, Vol. 17, pp. 261-272 // DOI
S. K. Lam, A. Pitrou, and S. Seibert. Numba: A llvm-based python jit compiler. in Proceedings of the Second Workshop on the LLVM Compiler Infrastructure in HPC, 2015, pp. 1-6
N. Wogan and C. Rackauckas. Nicholaswogan/numbalsoda: numbalsoda v0.3.5, 2022 // DOI

Just because of fun and stars and a little bit of interest in science

I didn't try your project myself. But how about a real life test regarding the
motion of angular momentum in a plate of star pasta soup?
Angular momentum transport by heat and turbulence can be incredibly efficient
and happens a lot faster than e.g. heat conduction and there is an pretty nice
and simple test of this.
Just get take a plate of star pasta soup and stir the center of that with a spoon.
After a very short time the outer regions are rotating faster then the center!
This happens even faster in case of a hot soup which has a much lower viscosity.
If viscosity would be important thing then the center wouldn't ever rotate slower
than the outer regions at all and the angular momentum transport would be also
slower in case of a higher temperature. It's not the viscosity that counts but
the Brownian motion of the water molecules is responsible for the transport
of the angular momentum.
On all particles which moving in rotation direction faster than the surrounding
ones act higher centrifugal forces which are driving them to the outer regions of the
plate. If particles move in opposite direction then the centrifugal forces are lowering
and the particles move towards the center.
It's the most likely reason of differential rotation of the sun and the gas planets as well.
Does your model already care the centrifugal forces on the particles because of the
temperature and the interaction of the inner and outer particles for forwarding
angular momentum and energy to the outer regions?
If not then you should add this because it's the important thing. I know that it's
hard to do calculate because you have to care the movement and interaction of
random moving particles for that.
Light particles like hydrogen molecules are moving faster at the same temperature.
For this they should be much more efficient than other stuff or even rocks if it
comes to the transport of angular momentum towards the outer regions of an
accretion disk. This also drives the light hydrogen particles faster to the center of
an accretion disk or a galaxy. What else are the young stars in the center of our
galaxy come from? Of course this is just a guess.
But first of all I hope you enjoy the playing with your soup (or a some water) for
watching the transport of angular momentum inside your plate for discovering the
science of a star pasta soup and it's hidden relation to the stars and planets above us!
😉

evgenykurbatov / kp23-turb-conv-ppd Goto Github PK

kp23-turb-conv-ppd's Introduction

Turbulent convection in a vertical column of PPD

Abstract

Features of the Cologne engine

Requirements

Code

Publications

Authors

Author of the code

Co-author of the Paper

References

Original code

Modules and methods

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