Originally Posted by

**ldenk** Hi!

I don't understand the following:

F = 1/tf * V

F... vector quantity, represents the friction

tf ... friction timescale

V ... velocity of an air parcel V= (u,v,w), also called wind velocity

In the Article "Ray tracing volume densities" Kajiya and Von Herzen (1984) writes:

"Frictional effects are approximated by a simple relation yielding an exponential decay of wind velocities with time"

(the wind velocities are described by a simplified equation of motion and also

change at every time step)

Why is this a exponential decay ?!

hope you can help me

ldenk

The friction on the parcel should be in the opposite direction to the

velocity so you should have:

$\displaystyle F = -V/t_f$

Then Newton tells us that:

$\displaystyle \frac{dV}{dt}\ =\ m.F$

which is:

$\displaystyle \frac{dV}{dt}\ =\ -m.V/t_f$

and as both $\displaystyle m$ and $\displaystyle t_f$ are positive the solution

of the differential equation has the form of exponential

decay.

(I would also assume that at some point things have been normalised

so that F is the frictional force per unit mass, and so the value of

$\displaystyle m$ that appears here should be $\displaystyle 1$.)

RonL