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Dissipation
 
 
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In physics
Physics

Physics is the natural science which examines basic concepts such as energy, force, and spacetime and all that derives from these, such as mass, charge, matter and its Motion ....
, dissipation embodies the concept of a dynamical system
Dynamical system

The dynamical system concept is a mathematics formalization for any fixed "rule" which describes the time dependence of a point's position in its ambient space....
 where important mechanical modes, such as wave
Wave

A wave is a disturbance that propagates through space and time, usually with transference of energy. While a mechanical wave exists in a medium , waves of electromagnetic radiation can travel through vacuum, that is, without a medium....
s or oscillation
Oscillation

Oscillation 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 Alternating current power....
s, lose energy
Energy

In physics, energy is a scalar physical quantity that describes the amount of Work_ that can be performed by a force. Energy is an attribute of objects and systems that is subject to a conservation law....
 over time
Time

Time is a component of the measurement used to sequence events, to compare the durations of events and the intervals between them, and to quantify the motions of objects....
, typically due to the action of friction
Friction

File:Friction alt.svgFriction is the force resisting the relative lateral motion of solid surfaces, fluid layers, or material elements in contact....
 or turbulence
Turbulence

In fluid dynamics, turbulence or turbulent flow is a fluid regime characterized by chaotic, 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 is converted into heat
Thermodynamics

In physics, thermodynamics is the study of the conversion of heat energy into different forms of energy ; different energy conversions into heat energy; and its relation to macroscopic variables such as temperature, pressure, and volume....
, raising the temperature
Temperature

In physics, temperature is a physical property of a Physical system that underlies the common notions of hot and cold; something that feels hotter generally has the greater temperature....
 of the system. Such systems are called dissipative system
Dissipative system

A dissipative system is a thermodynamically open system which is operating far from thermodynamic equilibrium in an environment with which it exchanges energy and matter....
s.

For example, a wave
Wave

A wave is a disturbance that propagates through space and time, usually with transference of energy. While a mechanical wave exists in a medium , waves of electromagnetic radiation can travel through vacuum, that is, without a medium....
 that loses amplitude
Amplitude

Amplitude is the magnitude of change in the oscillating variable, with each oscillation, within an oscillating system. For instance, sound waves 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 wave
Atmospheric wave

An 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 friction
Friction

File:Friction alt.svgFriction is the force resisting the relative lateral motion of solid surfaces, fluid layers, or material elements in contact....
 with the land mass, and at higher levels due to radiative cooling
Radiative cooling

Radiative cooling is the condition in which a body loses more energy by thermal radiation than it gains from its surroundings....
.

Dissipating forces are those which can not be described by Hamiltonian
Hamiltonian

Hamiltonian may refer toIn mathematics:* Hamiltonian system* Hamiltonian path, in graph theory* Hamiltonian group, in group theory* Hamiltonian ...
 formalism.






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In physics
Physics

Physics is the natural science which examines basic concepts such as energy, force, and spacetime and all that derives from these, such as mass, charge, matter and its Motion ....
, dissipation embodies the concept of a dynamical system
Dynamical system

The dynamical system concept is a mathematics formalization for any fixed "rule" which describes the time dependence of a point's position in its ambient space....
 where important mechanical modes, such as wave
Wave

A wave is a disturbance that propagates through space and time, usually with transference of energy. While a mechanical wave exists in a medium , waves of electromagnetic radiation can travel through vacuum, that is, without a medium....
s or oscillation
Oscillation

Oscillation 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 Alternating current power....
s, lose energy
Energy

In physics, energy is a scalar physical quantity that describes the amount of Work_ that can be performed by a force. Energy is an attribute of objects and systems that is subject to a conservation law....
 over time
Time

Time is a component of the measurement used to sequence events, to compare the durations of events and the intervals between them, and to quantify the motions of objects....
, typically due to the action of friction
Friction

File:Friction alt.svgFriction is the force resisting the relative lateral motion of solid surfaces, fluid layers, or material elements in contact....
 or turbulence
Turbulence

In fluid dynamics, turbulence or turbulent flow is a fluid regime characterized by chaotic, 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 is converted into heat
Thermodynamics

In physics, thermodynamics is the study of the conversion of heat energy into different forms of energy ; different energy conversions into heat energy; and its relation to macroscopic variables such as temperature, pressure, and volume....
, raising the temperature
Temperature

In physics, temperature is a physical property of a Physical system that underlies the common notions of hot and cold; something that feels hotter generally has the greater temperature....
 of the system. Such systems are called dissipative system
Dissipative system

A dissipative system is a thermodynamically open system which is operating far from thermodynamic equilibrium in an environment with which it exchanges energy and matter....
s.

For example, a wave
Wave

A wave is a disturbance that propagates through space and time, usually with transference of energy. While a mechanical wave exists in a medium , waves of electromagnetic radiation can travel through vacuum, that is, without a medium....
 that loses amplitude
Amplitude

Amplitude is the magnitude of change in the oscillating variable, with each oscillation, within an oscillating system. For instance, sound waves 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 wave
Atmospheric wave

An 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 friction
Friction

File:Friction alt.svgFriction is the force resisting the relative lateral motion of solid surfaces, fluid layers, or material elements in contact....
 with the land mass, and at higher levels due to radiative cooling
Radiative cooling

Radiative cooling is the condition in which a body loses more energy by thermal radiation than it gains from its surroundings....
.

Dissipating forces are those which can not be described by Hamiltonian
Hamiltonian

Hamiltonian may refer toIn mathematics:* Hamiltonian system* Hamiltonian path, in graph theory* Hamiltonian group, in group theory* Hamiltonian ...
 formalism. Loosely speaking, friction and all similar forces which result in decoherency of energy, that is, conversion of coherent or directed energy flow into an indirected or more isotropic distribution of energy.

In computational physics
Computational physics

Computational physics is the study and implementation of numerical algorithms in order to solve problems in physics for which a quantitative theory already exists....
, a numerical dissipation is also known as "artificial dissipation" or "artificial diffusion" or "numerical diffusion". They all mean this: when the pure advection
Advection

Advection, in mechanical and chemical engineering, is a transport mechanism of a substance or a conserved property with a moving fluid. The fluid motion in advection is described mathematically as a vector field, and the material transported is typically described as a scalar concentration of substance, which is contained in the fluid....
 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 system
Measure-preserving dynamical system

In mathematics, a measure-preserving dynamical system is an object of study in the abstract formulation of dynamical systems, and ergodic theory in particular....
s, is given in the article wandering set
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....
.

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 potential
Erosion

For morphological image processing operations, see Erosion 'For use of in dermatopathology, see Erosion Erosion is the removal of solids in the natural environment....
 on banks and river bottoms
Stream bed

A 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....
. Very often these devices look like small waterfall
Waterfall

A waterfall is usually a geology geologic formation resulting from water, often in the form of a stream, flowing over an erosion-resistant rock formation that forms a nickpoint, or sudden break in elevation....
s or cascade
Cascade

A cascade is a type of waterfall or a series of waterfalls.Cascade may also refer to:...
s, where water flows vertically or over riprap
Riprap

Riprap ? also known as rip rap, rubble, shot rock or rock armour ? is Rock or other material used to armor shorelines and streambeds against water and sometimes ice erosion....
 to lose some of its kinetic force
Kinetic energy

The kinetic energy of an object is the extra energy which it possesses due to its motion. It is defined as the mechanical work needed to accelerate a body of a given mass from rest to its current velocity....
.

See also

  • Flood control
    Flood control

    In communications, flood control is a feature of many communication protocols designed to prevent overwhelming of a destination receiver. Such controls can be implemented either in software or in hardware, and will often request that the message be resent after the receiver has finished processing....
  • Two dimensional gas