Dissipation

From Exampleproblems

In physics, dissipation embodies the concept of a dynamical system where important mechanical modes, such as waves or oscillations, lose energy over time, typically due to the action of friction or turbulence. The lost energy is converted into heat, raising the temperature of the system. Such systems are called dissipative systems.

For example, a wave that loses amplitude is said to dissipate. The precise nature of the effects depends on the nature of the wave: an atmospheric wave, for instance, may dissipate close to the surface due to friction with the land mass, and at higher levels due to radiative cooling.

In computational physics, a numerical dissipation is also known as "artificial dissipation" or "artificial diffusion" or "numerical diffusion". They all mean this: when the pure advection equation--which, by definition, is free of dissipation--is solved by a numerical approximation method that reduces the amplitude and changes the shape of the initial wave in a way analogous to a diffusional process, the method is said to contain 'dissipation'.

A formal, mathematical definition of dissipation, as commonly used in the mathematical study of measure-preserving dynamical systems, is given in the article wandering set.nl:Dissipatie