Acoustic analogies are applied mostly in numerical aeroacoustics to reduce aeroacoustic sound sources to simple emitter types. They are therefore often also referred to as aeroacoustic analogies. In general, aeroacoustic

analogies Analogy (from Greek ''analogia'', "proportion", from ''ana-'' "upon, according to" lso "against", "anew"+ ''logos'' "ratio" lso "word, speech, reckoning" is a cognitive process of transferring information or meaning from a particular subject ...

are derived from the compressible

Navier–Stokes equations In physics, the Navier–Stokes equations ( ) are partial differential equations which describe the motion of viscous fluid substances, named after French engineer and physicist Claude-Louis Navier and Anglo-Irish physicist and mathematician Geo ...

(NSE). The

compressible In thermodynamics and fluid mechanics, the compressibility (also known as the coefficient of compressibility or, if the temperature is held constant, the isothermal compressibility) is a measure of the instantaneous relative volume change of a f ...

NSE are rearranged into various forms of the inhomogeneous acoustic

wave equation The (two-way) wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields — as they occur in classical physics — such as mechanical waves (e.g. water waves, sound waves and seism ...

. Within these equations, source terms describe the acoustic sources. They consist of pressure and speed fluctuation as well as stress tensor and force terms.

Approximations An approximation is anything that is intentionally similar but not exactly equal to something else. Etymology and usage The word ''approximation'' is derived from Latin ''approximatus'', from ''proximus'' meaning ''very near'' and the prefix ...

are introduced to make the source terms independent of the acoustic variables. In this way, linearized equations are derived which describe the propagation of the acoustic waves in a homogeneous, resting medium. The latter is excited by the acoustic source terms, which are determined from the turbulent fluctuations. Since the aeroacoustics are described by the equations of classical acoustics, the methods are called aeroacoustic analogies. The Lighthill analogy considers a free flow, as for example with an engine jet. The nonstationary fluctuations of the stream are represented by a distribution of

quadrupole A quadrupole or quadrapole is one of a sequence of configurations of things like electric charge or current, or gravitational mass that can exist in ideal form, but it is usually just part of a multipole expansion of a more complex structure refl ...

sources in the same volume. The Curle analogy is a formal solution of the Lighthill analogy, which takes hard surfaces into consideration. The Ffowcs Williams–Hawkings analogy is valid for aeroacoustic sources in relative motion with respect to a hard surface, as is the case in many technical applications for example in the automotive industry or in air travel. The calculation involves

dipole In physics, a dipole () is an electromagnetic phenomenon which occurs in two ways: *An electric dipole deals with the separation of the positive and negative electric charges found in any electromagnetic system. A simple example of this system ...

and monopole terms.

References

Further reading