Barocline

The baroclicinity is a term of Mécanique fluids. It is said that one deals with fluid barocline , when the lines of equal Pression cross those of equal Densité ( isopycne ) in this one. This qualifier is used in several fields of which the Météorologie, the physical Océanographie and the Astrophysique to describe gases or liquids of which propriétées vary with the thickness.

Consequences

The image of right-hand side, in top, shows the crossing according to the vertical of the density (

\, \ rho

) and of the pressure (P) in a fluid barocline. Moreover, the density is proportional to the temperature (T).

The baroclinicity is thus = $\, \ nabla P \ times \ nabla \ rho \ propto \ nabla P \ times \ nabla T$ .

Notice that one gave a slope to these lines. If one made a cut according to the horizontal one of has towards B, one would find a crossing of the Isobare S and Isotherme S as on the section of bottom. It is what one observes in a chart on constant level, like a chart of surface of the weather systems in a frontal zone, where one changes mass of air.

This wants to say:

that the Température (T) varies when one moves along a pressure level (P)
that a flow with a given pressure level changes the temperature on this level
that a disturbance barocline is a disturbance which converts potential energy thermal into kinetic energy

Vector baroclinic

In a fluid of which the density changes with a given pressure level, one must have a source term which causes this change. In the Navier-Stokes equations, whose atmospheric primitive equations are the expression in meteorology and oceanography, that amounts introducing a term of change of the swirl geostrophic (

\, \ zeta

). The term of source is called the vector baroclinic and becomes:

$\, \ frac {\ share \ vec \ zeta} {\ share T} = \ frac {1} {\ rho^2} \ nabla \ rho \ times \ nabla P$

This vector is of interest as well for the compressible fluids as those incompressible but inhomogenous. The internal waves of gravity and the unstable modes of Rayleigh-Taylor can be analyzed thanks to this vector. It is also important in the creation of swirl at the time of the passage of shocks in inhomogenous mediums like the instability of Richtmeyer-Meshkov .

As the density is proportional to the temperature (T). The vector of baroclinicity becomes:

$\, \ frac {\ share \ vec \ zeta} {\ share T} \ propto \ nabla P \ times \ nabla T$

Use of the baroclinicity

The plunger S are familiar with the internal waves of very long period which can be exitées with the Thermocline, a zone of density switching. Similar waves can be generated with the interface between a layer of water and one of oil when the interface is not horizontal. One is then almost with the hydrostatic balance with the vertical Gradient of pressure. However, the gradient of density has an angle with this last. The value of the vector of baroclinicity is thus nonnull what creates a horizontal and vertical displacement to find balance. Naturally, this movement is propagated, exceeded the horizontal one and possibly creates an undertow, therefore a Oscillation.

The internal waves of gravity produitent by this process do not need a very marked interface. For example, a very gradual gradient of density of temperature or salinity will produce this vector. This process is that which controls the behavior of several fields of the everyday life:

In meteorology, the atmosphere is a medium where exists intense zones baroclines. They are the frontal zones of change of temperature. The numerical Prévision of time must take account of the baroclinicity of the atmosphere by taking of account the thermodynamic structure of this one. That gives an analysis and a forecast to several very complex levels. Here some phenomena generated along the zones baroclines:

vertical Movement of the air.
thermal Wind: the wind is a balance between the Force of Coriolis and that of the pressure. The latter varies according to hydrostatic balance with the density of the air according to the height and thus with the average temperature of the layer. As the temperature varies with telling pressure level, the wind will vary with altitude in an atmosphere barocline and one obtains a thermal wind.
Jet-stream: this one is the result direct of the baroclinicity of the air.

In oceanography for the modeling more real of the current sailors, the Thermocline, etc similar to those in meteorology.

Like in other fundamental fields:

Astrophysical: the zones baroclines are important in the study of the fluids of stars and the interstellar environments.
Geophysical: the concept is important in the study of the magma under the earth's crust.

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