Convection of a Line

Description

The Convection Equation is

where

is a constant. For an initial condition of a line

substitution of

gives

which, since

and

are both constants, can be integrated from the initial time to give

This applet graphs the initial condition and the value at a later time,

. Two arrows indicate the change. One arrow indicates the change in

and the other indicates the line movement in the

direction. Several sliders are available to change all of the parameters.

Observe what happens as you adjust each slider. Particularly interesting is what happens to the

displacement as the slope

is changed. A curve can be considered as a set of short connected line segments so how would a curve 'move'?