The Rayleigh-Taylor Instability

Problem Background

The Rayleigh-Taylor instability arises when a fluid pushes against another fluid of different density. The simplest way to imagine this situation is to consider a heavy fluid sitting atop a light fluid. The system is in hydrostatic equilibrium with gravity pointing downwards. A small perturbation at the interface between the two fluids will disturb this unstable equilibrium, and the heavy fluid will sink while the light fluid rises.

Initial Conditions

The problem setup is adapted from the Athena test suite page: ​http://www.astro.virginia.edu/VITA/ATHENA/rt.html This page has information on both 2D and 3D simulations, Hydro and MHD, but the 2D Hydro case is the relevant one here.

Simulations

All of the following simulation movies show density. (Red = 2 and Blue = 1)

This simulation is run with a fixed grid of 100 x 300.

• RT Movie

For this run, all parameters are the same. The grid is now 50 x 150, and there are 3 levels of AMR which yields an effective resolution that is 4x the previous run.

• RT Movie (Higher Resolution)​

I realized that uniform gravity was not working properly in the first two simulations, so here is one in which it is working. Also, this simulation is a 50 x 150 grid with 2 levels of AMR.

• RT Movie (Gravity Working)​

The previous simulation has asymmetry that is especially noticable in late time frames. After going back to my problem module, I noticed that the perturbation had some z dependence which it should not since this is a 2D simulation. Fixing that yielded a nice symmetric simulation.

• RT Movie (symmetric)​

Tracking the Interface

• Interface Movie​
• Log(interface_position) Plot​

Calculating the Growth Rate

Results