LORENTZ EQUATIONS

 

dx/dt = S*(y-x)

 

dy/dt = R*x - y - x*z

 

dz/dt = x*y -B*z

 

Is a system of 3 coupled, non-linear differential equations for the three variables x(convective flow), y(horizontal temperature), z(vertical temperature).

 

USE:

S (Prandtl Number) = 10,

R (Rayleigh Number) = 28,

B (vertical to horizontal size ratio) = 8/3,

 

Initial values: x0 = z0 = 0, y0 =1

 

Note: The equations cannot be "solved" analytically,only numerically (using, for instance, Euler's method, with D="delta"):

 

dx/dt = "xdot"= lim (Dt-->0) {Dx/Dt}=

=approx. Dx/Dt ---->

 

x(t +Dt) =approx. x(t) + xdot*Dt