In

physicsPhysics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

,

**dissipation** embodies the concept of a

dynamical systemA dynamical system is a concept in mathematics where a fixed rule describes the time dependence of a point in a geometrical space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, and the number of fish each springtime in a...

where important mechanical models, such as

waveIn physics, a wave is a disturbance that travels through space and time, accompanied by the transfer of energy.Waves travel and the wave motion transfers energy from one point to another, often with no permanent displacement of the particles of the medium—that is, with little or no associated mass...

s or

oscillationOscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. Familiar examples include a swinging pendulum and AC power. The term vibration is sometimes used more narrowly to mean a mechanical oscillation but sometimes...

s, lose

energyIn physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...

over

timeTime is a part of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify rates of change such as the motions of objects....

, typically from

frictionFriction is the force resisting the relative motion of solid surfaces, fluid layers, and/or material elements sliding against each other. There are several types of friction:...

or

turbulenceIn fluid dynamics, turbulence or turbulent flow is a flow regime characterized by chaotic and stochastic property changes. This includes low momentum diffusion, high momentum convection, and rapid variation of pressure and velocity in space and time...

. The lost energy converts into

heatThermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...

, which raises the

temperatureTemperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

of the system. Such systems are called

dissipative systemA dissipative system is a thermodynamically open system which is operating out of, and often far from, thermodynamic equilibrium in an environment with which it exchanges energy and matter....

s.

For example, a

waveIn physics, a wave is a disturbance that travels through space and time, accompanied by the transfer of energy.Waves travel and the wave motion transfers energy from one point to another, often with no permanent displacement of the particles of the medium—that is, with little or no associated mass...

that loses

amplitudeAmplitude is the magnitude of change in the oscillating variable with each oscillation within an oscillating system. For example, sound waves in air are oscillations in atmospheric pressure and their amplitudes are proportional to the change in pressure during one oscillation...

is said to

**dissipate**. The precise nature of the effects depends on the nature of the wave: an

atmospheric waveAn atmospheric wave is a periodic disturbance in the fields of atmospheric variables which may either propagate or not . Atmospheric waves range in spatial and temporal scale from large-scale planetary waves to minute sound waves...

, for instance, may dissipate close to the surface due to

frictionFriction is the force resisting the relative motion of solid surfaces, fluid layers, and/or material elements sliding against each other. There are several types of friction:...

with the land mass, and at higher levels due to

radiative coolingRadiative cooling is the process by which a body loses heat by thermal radiation.- Earth's energy budget :In the case of the earth-atmosphere system it refers to the process by which long-wave radiation is emitted to balance the absorption of short-wave energy from the sun.The exact process by...

.

Dissipating forces are those that can not be described by

HamiltonianHamiltonian mechanics is a reformulation of classical mechanics that was introduced in 1833 by Irish mathematician William Rowan Hamilton.It arose from Lagrangian mechanics, a previous reformulation of classical mechanics introduced by Joseph Louis Lagrange in 1788, but can be formulated without...

formalism. Loosely speaking, this includes friction, and all similar forces that result in decoherency of energy—that is, conversion of

coherentIn physics, coherence is a property of waves that enables stationary interference. More generally, coherence describes all properties of the correlation between physical quantities of a wave....

or directed energy flow into an indirected or more isotropic distribution of energy.

In

computational physicsComputational physics is the study and implementation of numerical algorithms to solve problems in physics for which a quantitative theory already exists...

, 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

advectionAdvection, in chemistry, engineering and earth sciences, is a transport mechanism of a substance, or a conserved property, by a fluid, due to the fluid's bulk motion in a particular direction. An example of advection is the transport of pollutants or silt in a river. The motion of the water carries...

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 stabilityIn the mathematical subfield of numerical analysis, numerical stability is a desirable property of numerical algorithms. The precise definition of stability depends on the context, but it is related to the accuracy of the algorithm....

characteristics of the solution.

A formal, mathematical definition of dissipation, as commonly used in the mathematical study of

measure-preserving dynamical systemIn mathematics, a measure-preserving dynamical system is an object of study in the abstract formulation of dynamical systems, and ergodic theory in particular.-Definition:...

s, is given in the article

*wandering set*In those branches of mathematics called dynamical systems and ergodic theory, the concept of a wandering set formalizes a certain idea of movement and mixing in such systems. When a dynamical system has a wandering set of non-zero measure, then the system is a dissipative system...

.

## In river hydrology

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 potentialErosion is when materials are removed from the surface and changed into something else. It only works by hydraulic actions and transport of solids in the natural environment, and leads to the deposition of these materials elsewhere...

on banks and

river bottomsA stream bed is the channel bottom of a stream, river or creek; the physical confine of the normal water flow. The lateral confines or channel margins, during all but flood stage, are known as the stream banks or river banks. In fact, a flood occurs when a stream overflows its banks and flows onto...

. Very often these devices look like small

waterfallA waterfall is a place where flowing water rapidly drops in elevation as it flows over a steep region or a cliff.-Formation:Waterfalls are commonly formed when a river is young. At these times the channel is often narrow and deep. When the river courses over resistant bedrock, erosion happens...

s or cascades, where water flows vertically or over

riprapRiprap — also known as rip rap, rubble, shot rock or rock armour or "Rip-rap" — is rock or other material used to armor shorelines, streambeds, bridge abutments, pilings and other shoreline structures against scour, water or ice erosion.It is made from a variety of rock types, commonly granite or...

to lose some of its

kinetic forceThe kinetic energy of an object is the energy which it possesses due to its motion.It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes...

.