Simulation movies of stratification
Introduction:
this page list some movies produced from numerical simulation attached to the
paper C. Doering, J. Wu, K. Zhao, X. Zheng, Long
time behavior of the two-dimensional Boussinesq equations
without buoyancy diffusion. Physics D: Nonlinear Phenomena, 2018.
The
governing equations are Boussinesq-Navier-Stokes
system:
For
the simulation presented in the paper, we have 3 videos here:
Movie
1: temperature evolution from time t=0 to t=100730 with time frequency 1000
Movie
2: velocity field evolution from time t=0 to t=100730 with time frequency 2500
Movie
3: evolution of two regions: {(x,y):
\theta(x,t) \in (0.3, 0.4)} and {(x,y):
\theta(x,y)\in (0.7.0.8)} from time t=0 to t=120630
with time frequency 1000
Beyond
the paper, we have another simulation whose evolution temperature is shown in
the following video.
The initial
condition of the temperature is of three constant regions, as shown in the
static picture. Following Boussinesq-Navier-Stokes
equations, the red region of high temperature rise to the top layer, the blue
region of low temperature sediments to the bottom, and the green region of
intermediate temperature chooses to stay in the middle. This video, in addition
to the above movies, demonstrates how the buoyancy drives the stratification of
temperature.
