A Model of Atmospheric Circulation

time t

10.

cross-latitude heating contrast F

7.

ocean-continents heating contrast G

4.

angular frequency ω

0.1

This Demonstration illustrates a mathematical model of atmospheric circulation, represented by the equations:

dx

dt

=-

2

y

-

2

z

-ax+aFcos(ωt)

,

dy

dt

=xy-bxz-y+bGcos(ωt)

,

dz

dt

=bxy+xz-z

,

with initial conditions

x(0)=y(0)=z(0)=1

,

Here

t

represents time,

x

stands for the strength of the symmetric, globally averaged westerly wind current, and

y

and

z

are the cosine and sine phases of a chain of superposed waves transporting heat toward the poles.

F

and

G

are thermal forcings:

F

is the symmetric cross-latitude heating contrast and

G

accounts for the asymmetric heating contrast between oceans and continents;

ω

is the angular frequency. The parameters of interest are the thermal forcings and their angular frequency; the values of the parameters

a

and

b

are set to 20 and 18.