Barotropic fluid

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Barotropic fluid stratification of pressure and density

In fluid dynamics, a barotropic fluid is a fluid whose density is a function of only pressure.^[1] Barotropic fluids are useful model for fluid behavior in a wide variety of scientific fields, from meteorology to astrophysics.

Most liquids have a density which varies weakly with pressure or temperature, i. e., the density of a liquid is nearly constant, so to a first approximation liquids are barotropic. To greater precision, they are not barotropic. For example, the density of seawater depends on temperature, salinity, and pressure, but only by a few percent at most.

In astrophysics, barotropic fluids are important in the study of stellar interiors or of the interstellar medium. One common class of barotropic model used in astrophysics is a polytropic fluid. Typically, the barotropic assumption is not very realistic.

In meteorology, a barotropic atmosphere is one in which the density depends only on pressure, so that isobaric surfaces (constant-pressure surfaces) are also isopycnic surfaces (constant-density surfaces). The isobaric surfaces will also be isothermal surfaces, hence (from the thermal wind equation) the geostrophic wind is independent of height. Hence the motions of a rotating barotropic air mass or fluid are strongly constrained. The tropics are more nearly barotropic than mid-latitudes because temerpature is more nearly horizontally uniform in the tropics.

A barotropic flow is a generalization of the barotropic atmosphere. It is a flow in which the pressure is a function of the density only and vice versa. In other words, it is a flow in which isobaric surfaces are isopycnic surfaces and vice versa. One may have a barotropic flow with a non-barotropic fluid, but a barotropic fluid must always follow a barotropic flow. Examples include barotropic layers of the oceans, an isothermal ideal gas or an isentropic ideal gas.

A situation which is not barotropic is baroclinic, i. e., pressure is not enough to specify density. For a barotropic fluid or a barotropic flow (such as a barotropic atmosphere), the baroclinic vector is zero.

References

↑ Shames, Irving H. (1962). Mechanics of Fluids. McGraw-Hill. p. 159. LCCN 61-18731. Retrieved 8 November 2012. "It $\rho {}$ is expressible as a function of $p$ only, that is, $\rho =\rho {}(p)$ , the [ $\int _{0}^{p}{\frac {dp}{\rho {}}}$ in Eq. 5-66] is integrable. Fluids having this characteristic are called barotropic fluids."

James R Holton, An introduction to dynamic meteorology, ISBN 0-12-354355-X, 3rd edition, p77.
Marcel Lesieur, "Turbulence in Fluids: Stochastic and Numerical Modeling", ISBN 0-7923-0645-7, 2e.
D. J. Tritton, "Physical Fluid Dynamics", ISBN 0-19-854493-6.

v t e Meteorological data and variables

General	Adiabatic processes Lapse rate Lightning Surface solar radiation Surface weather analysis Visibility Vorticity Wind

Condensation	Cloud Cloud condensation nuclei Fog Lifted condensation level (LCL) Precipitation Water vapor

Convection	Convective available potential energy (CAPE) Convective inhibition (CIN) Convective instability Convective temperature (T_c) Equilibrium level (EL) Helicity Level of free convection (LFC) Lifted index (LI) Bulk Richardson number (BRN)

Temperature	Dew point (T_d) Equivalent temperature (T_e) Forest fire weather index Haines Index Heat index Humidex Humidity Potential temperature (θ) Equivalent potential temperature (θ_e) Sea surface temperature (SST) Wet-bulb temperature Wet-bulb potential temperature Wind chill

Pressure	Atmospheric pressure Baroclinity Barotropicity

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Barotropic fluid

See also

References