Line of greatest slope

In topography, the line of greatest slope is a curve following the steepest slope. It is always orthogonal to the contour lines. Mathematically it is determined by the gradient of the height, taken as a potential field, so the lines of greatest slope are the analogon of lines of force.

If inertial forces and terrain roughness are set side, a ball rolling down a slope, or water flowing down, will follow the line of greatest slope.

In geomorphology the line of continuous, maximum descent from any point on a land surface is known as a thalweg.