Fluid whose density is a function of pressure only
Barotropic fluid stratification of pressure and density
In fluid dynamics, a barotropic fluid is a fluid whose density is a function of pressure only.[1] The barotropic fluid is a useful model of fluid behavior in a wide variety of scientific fields, from meteorology to astrophysics.
The density of most liquids is nearly constant (isopycnic), so it can be stated that their densities vary only weakly with pressure and temperature. Water, which varies only a few percent with temperature and salinity, may be approximated as barotropic. In general, air is not barotropic, as it is a function of temperature and pressure; but, under certain circumstances, the barotropic assumption can be useful.
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 that for which the density of the air depends only on pressure, as a result isobaric surfaces (constant-pressure surfaces) are also constant-density surfaces. Such isobaric surfaces will also be isothermal surfaces, hence (from the thermal wind equation) the geostrophic wind will not vary with depth. Hence, the motions of a rotating barotropic air mass is strongly constrained. The tropics are more nearly barotropic than mid-latitudes because temperature is more nearly horizontally uniform in the tropics.
A barotropic flow is a generalization of a 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 of a non-barotropic fluid, but a barotropic fluid will always follow a barotropic flow. Examples include barotropic layers of the oceans, an isothermal ideal gas or an isentropic ideal gas.
A fluid which is not barotropic is baroclinic, i. e., pressure is not the only factor to determine density. For a barotropic fluid or a barotropic flow (such as a barotropic atmosphere), the baroclinic vector is zero.
^Shames, Irving H. (1962). Mechanics of Fluids. McGraw-Hill. p. 159. LCCN 61018731. Retrieved 8 November 2012. If is expressible as a function of only, that is, , the in Eq. 5-66 is integrable. Fluids having this characteristic are called barotropic fluids.
In fluid dynamics, a barotropicfluid is a fluid whose density is a function of pressure only. The barotropicfluid is a useful model of fluid behavior...
density. Thus, in a barotropicfluid (which is defined by zero baroclinity), these surfaces are parallel. In Earth's atmosphere, barotropic flow is a better...
not be homentropic. A homentropic and perfect gas is an example of a barotropicfluid where the pressure and density are related by P ( ρ ) = K ρ γ , {\displaystyle...
which the barotropic term cannot be neglected. For inviscid fluids, the viscosity tensor τ is zero. Thus for an inviscid, barotropicfluid with conservative...
to nondissipative fluids. Take the simple example of a barotropic, inviscid vorticity-free fluid. Then, the conjugate fields are the mass density field...
the pressure depends only on density and vice versa, the fluid dynamics are called barotropic. In the atmosphere, this corresponds to a lack of fronts...
intersect. This is in contrast to a barotropicfluid, in which the density is only a function of pressure. For this barotropic case, isobars and isopycnals are...
incompressible and barotropicfluids". "Interpretation of the vorticity equation". "Kelvin's vorticity theorem for incompressible or barotropic flow". "Spherepack...
term is also called the "solenoid term". Under the condition of a barotropicfluid with a constant projection area A e {\displaystyle A_{e}} , the Bjerknes...
The barotropic vorticity equation assumes the atmosphere is nearly barotropic, which means that the direction and speed of the geostrophic wind are independent...
reason, this model may also be called barotropic (density depends only on pressure). For the isothermal-barotropic model, density and pressure turn out...
continuity equation. The shallow water equations assume a homogeneous and barotropicfluid. For simplicity, the system is limited by means of a weak and uniform...
pressure-gradient force and the gravitational force, hydrostatic balance occurs. In a barotropic atmosphere, where density is a function only of pressure, a horizontal...
group velocity. The terms "barotropic" and "baroclinic" are used to distinguish the vertical structure of Rossby waves. Barotropic Rossby waves do not vary...
part of the Earth. The different types of models run are thermotropic, barotropic, hydrostatic, and nonhydrostatic. Some of the model types make assumptions...
with a barotropic relation p = p ( ρ ) {\displaystyle p=p(\rho )} between pressure p and density ρ; and (iii) any body forces acting on the fluid are conservative...
Kelvin published his circulation theorem, which states that a barotropic, ideal fluid with conservative body forces conserves the circulation around...
systems approach to the equations of a linearly viscous compressible barotropicfluid". Proceedings of the ICM, 2002, Beijing. Vol. 3. pp. 295–304. arXiv...
assumed is just a linear approximation to the generic barotropic equation of state of the fluid. However, even after the above deliberations, it is still...
They used a simplified form of atmospheric dynamics based on solving the barotropic vorticity equation over a single layer of the atmosphere, by computing...
normal/Newtonian matter, but a false vacuum can violate it. Consider the linear barotropic equation state p = w ρ , {\displaystyle p=w\rho ,} where ρ {\displaystyle...
of the wind. The Sverdrup relation can be derived from the linearized barotropic vorticity equation for steady motion: β v g = f ∂ w / ∂ z {\displaystyle...
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