Homework 1
Qing Zou
Boussinesq equations:
2
+ (v )2 = 4 + g ,
t
x
T
+ (v ) =
+ 2 .
t
H x
(1.30)
= A sin(x/L) sin(z/H),
= B cos(x/L) sin(z/H) C sin(2z/H).
(1.31)
And
whats more, we know that
2 = = ,
4 = (2 )2 = ()2 ,
and
=
In this case,
2 2 2
+
+
.
x
1
DERIVATION OF THE LORENZ EQUATIONS
I.
GOVERNING EQUATIONS
Consider the incompressible Navier-Stokes equations within the Boussinesq approximation, modeling
the thermal convection between two parallel horizontal flat plates separated by a distance d and
Differential Dynamical Systems Errata (2nd & 3rd Printings)
J.D. Meiss
October 2, 2013
Errors are listed by page and line number. The symbol = means replace with. A negative
line number means count from the bottom of the page. Each equation line is counte