Dissipation
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Dissipation is the result of irreversible processes that take place in inhomogeneous systems. These processes produce entropy (see entropy production) at a certain rate. The entropy production rate times ambient temperature gives the dissipated power. Important examples of irreversible processes are: heat flow through a thermal resistance, fluid flow through a flow resistance, diffusion (mixing), chemical reactions, and electrical current flow through an electrical resistance (Joule heating). The concept of dissipation was introduced in the field of thermodynamics by William Thomson (Lord Kelvin) in 1852.
Dissipating forces are those that can not be described by Hamiltonian formalism. Loosely speaking, this includes friction, and all similar forces that result in decoherency of energy—that is, conversion of coherent or directed energy flow into an indirected or more isotropic distribution of energy.
Waves or oscillations, lose energy over time, typically from friction or turbulence. In many cases the "lost" energy raises the temperature of the system. 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, numerical dissipation (also known as "numerical diffusion") refers to certain side-effects that may occur as a result of a numerical solution to a differential equation. When the pure advection equation, which is free of dissipation, is solved by a numerical approximation method, the energy of the initial wave may be reduced in a way analogous to a diffusional process. Such a method is said to contain 'dissipation'. In some cases, "artificial dissipation" is intentionally added to improve the numerical stability characteristics of the solution.
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.
In water engineering
Dissipation is the process of converting mechanical energy of downward-flowing water into thermal and acoustical energy. Various devices are designed in streambeds to reduce the kinetic energy of flowing waters to reduce their erosive potential on banks and river bottoms. Very often these devices look like small waterfalls or cascades, where water flows vertically or over riprap to lose some of its kinetic energy.
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