Boussinesq approximation may refer to several modelling concepts – as introduced by
Joseph Valentin Boussinesq
Joseph Valentin Boussinesq (; 13 March 1842 – 19 February 1929) was a French mathematician and physicist who made significant contributions to the theory of hydrodynamics, vibration, light, and heat.
Biography
From 1872 to 1886, he was appoi ...
(1842–1929), a French mathematician and physicist known for advances in fluid dynamics:
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Boussinesq approximation (buoyancy)
In fluid dynamics, the Boussinesq approximation (, named for Joseph Valentin Boussinesq) is used in the field of buoyancy-driven flow (also known as natural convection). It ignores density differences except where they appear in terms multiplied b ...
for buoyancy-driven flows for small density differences in the fluid
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Boussinesq approximation (water waves)
In fluid dynamics, the Boussinesq approximation for water waves is an approximation valid for weakly non-linear and fairly long waves. The approximation is named after Joseph Boussinesq, who first derived them in response to the observation by ...
for long waves propagating on the surface of a fluid layer under the action of gravity
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Turbulence modeling
Turbulence modeling is the construction and use of a mathematical model to predict the effects of turbulence. Turbulent flows are commonplace in most real life scenarios, including the flow of blood through the cardiovascular system, the airflow o ...
and
eddy viscosity
The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water.
Viscosity quantifies the inte ...
: in modelling the turbulence
Reynolds stresses
In fluid dynamics, the Reynolds stress is the component of the total stress tensor in a fluid obtained from the averaging operation over the Navier–Stokes equations to account for turbulent fluctuations in fluid momentum.
Definition
The velocit ...
, the Boussinesq approximation results in the use of an eddy viscosity concept
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