Density lines and isobars cross in a baroclinic fluid (top). As density is related to temperature, on a surface map, isobars and isotherms cross too

In fluid dynamics, the baroclinity (sometimes called baroclinicity) is a measure of the stratification in a fluid. A baroclinic atmosphere is one for which the density depends on both the temperature and the pressure; contrast this with barotropic atmosphere, for which the density depends only on the pressure. In atmospheric terms, the barotropic zones of the Earth are generally found in the central lattitudes, or tropics, whereas the baroclinic areas are generally found in the mid-lattitude/polar regions. Image File history File links Download high-resolution version (599x633, 82 KB) File links The following pages on the English Wikipedia link to this file (pages on other projects are not listed): Baroclinity ... Image File history File links Download high-resolution version (599x633, 82 KB) File links The following pages on the English Wikipedia link to this file (pages on other projects are not listed): Baroclinity ... The word isobar derives from the two ancient Greek words, ισος (isos), meaning equal, and βαρος (baros), meaning weight. In meteorology, an isobar is a line of equal or constant pressure on a graph, plot, or map; an isopleth of pressure. ... An isotherm is a line of equal or constant temperature on a graph, plot, or map; an isopleth of temperature. ... Fluid dynamics is the sub-discipline of fluid mechanics dealing with fluids (liquids and gases) in motion. ... Stratification gooberini went to lousville to dance on a praire and then he went down the hill to hang out with jarry. ... A barotropic atmosphere is one in which the density depends only on the pressure, so that isobaric surfaces are also surfaces of constant density. ... A noontime scene from the Philippines on a day when the sun is almost directly overhead. ...

Baroclinity is proportional to

which again is proportional to the angle between surfaces of constant pressure and surfaces of constant density. Thus, in a barotropic fluid (which is defined by zero baroclinity), these surfaces are parallel. The use of water pressure - the Captain Cook Memorial Jet in Lake Burley Griffin in Canberra, Australia. ... In physics, density is mass m per unit volume V. For the common case of a homogeneous substance, it is expressed as: where, in SI units: ρ (rho) is the density of the substance, measured in kg·m-3 m is the mass of the substance, measured in kg V is...

Areas of high atmospheric baroclinity are characterized by the frequent formation of cyclones. Radar image of a tropical cyclone in the northern hemisphere. ...

Baroclinic instability

Baroclinic instability is a fluid dynamical instability of fundamental importance in the atmosphere and in the oceans. In the atmosphere it is the dominant mechanism shaping the cyclones and anticyclones that dominate weather in mid-latitudes. In the ocean it generates a field of mesoscale (100 km or smaller) eddies that play various roles in oceanic dynamics and the transport of tracers. Baroclinic instability is a concept relevant to rapidly rotating, strongly stratified fluids. View of Jupiters active atmosphere, including the Great Red Spot. ... Ocean (Okeanos, a Greek god of sea and water; Greek ωκεανός) covers almost three quarters (71%) of the surface of the Earth. ... Radar image of a tropical cyclone in the northern hemisphere. ... In meteorology, an anticyclone (that is, opposite to a cyclone) is a weather phenomenon in which there is a descending movement of the air and a high pressure area over the part of the planets surface affected by it. ... Weather is a term that encompasses phenomena in the atmosphere of a planet. ... The term mesoscale is a size scale referring to weather systems smaller than synoptic scale systems but larger than storm-scale systems. ... In fluid dynamics, an eddy is the swirling of a fluid and the reverse current created when the fluid flows past an obstacle. ... There are several uses for Tracer: Tracer ammunition Tracer isotope or radioactive tracers as used in positron emission tomography, SPECT and autoradiography. ... Atmospheric stratification is the division of the atmosphere into distinct layers, each with specific properties such as temperature or humidity. ...

Whether one is rapidly rotating or not is determined in this context by the Rossby number, which is a measure of how close the flow is to solid body rotation. More precisely, a flow in solid body rotation has vorticity that is proportional to its angular velocity. The Rossby number is a measure of the departure of the vorticity from that of solid body rotation. The Rossby number must be small for the concept of baroclinic instability to be relevant. When the Rossby number is large, other kinds of instabilities, often referred to as inertial, becomes more relevant. The Rossby number, named for Carl-Gustav Arvid Rossby, is a dimensionless number used in describing fluid flow, usually in geophysical phenomena in the oceans and atmosphere. ... Vorticity is a mathematical concept used in fluid dynamics. ... Angular velocity describes the speed of rotation and the orientation of the instantaneous axis about which the rotation occurs. ...

The simplest example of a stably stratified flow is an incompressible flow with density decreasing with height. In a compressible gas such as the atmosphere, the relevant measure is the vertical gradient of the entropy, which must increase with height for the flow to be stably stratified. One measures the strength of the stratification by asking how large the vertical shear of the horizontal winds has to be in order to destabilize the flow and produce the classic Kelvin-Helmholtz instability. This measure is the Richardson number. When the Richardson number is large, the stratification is strong enough to prevent this shear instability. Ice melting - classic example of entropy increasing[1] described in 1862 by Rudolf Clausius as an increase in the disgregation of the molecules of the body of ice. ... Stratification gooberini went to lousville to dance on a praire and then he went down the hill to hang out with jarry. ... A KHI on the planet Saturn, formed at the interaction of two bands of the planets atmosphere Kelvin-Helmholtz instability can occur when velocity shear is present within a continuous fluid or when there is sufficient velocity difference across the interface between two fluids. ... The Richardson number is named after Lewis Fry Richardson (1881 - 1953). ...

Before the classic work of Jule Charney and Eric Eady on baroclinic instability in the late 1940's, most theories trying to explain the structure of mid-latitude eddies took as their starting points the high Rossby number or small Richardson number instabilities familiar to fluid dynamicists at that time. The most important feature of baroclinic instability is that it exists even in the situation of rapid rotation (small Rossby number) and strong stable stratification (large Richardson's number) typically observed in the atmosphere. Jule Gregory Charney (January 1, 1917 – June 16, 1981) was an American meteorologist who played an important role in developing weather prediction. ...

The energy source for baroclinic instability is the potential energy in the environmental flow. As the instability grows, the center of mass of the fluid is lowered. In growing waves in the atmosphere, cold air moving downwards and equatorwards displaces the warmer air moving polewards and upwards. {{Portal|Energy}Potential energy is the energy available within a physical system due to an objects position in conjunction with a conservative force which acts upon it (such as the gravitational force or Coulomb force). ... In physics, the center of mass of a system of particles is a specific point at which, for many purposes, the systems mass behaves as if it were concentrated. ...

Baroclinic instability can be investigated in the laboratory using a rotating, fluid filled annulus. The annulus is heated at the outer wall and cooled at the inner wall, and the resulting fluid flows give rise to baroclinically unstable waves. An annulus In mathematics, an annulus (the Latin word for little ring, with plural annuli) is a ring-shaped geometric figure, or more generally, a term used to name a ring-shaped object. ...

The term "baroclinic" refers to the mechanism by which vorticity is generated. Vorticity is the curl of the velocity field. in general, the evolution of vorticity can be broken into contributions from advection (as vortex tubes move with the flow), stretching and twisting (as vortex tubes are pulled or twisted by the flow) and baroclinic vorticity generation, which occurs whenever there is a density gradient along surfaces of constant pressure. Baroclinic flows can be contrasted with barotropic flows in which density and pressure surfaces coincide and there is no baroclinic generation of vorticity. Vorticity is a mathematical concept used in fluid dynamics. ... A barotropic atmosphere is one in which the density depends only on the pressure, so that isobaric surfaces are also surfaces of constant density. ...

The study of the evolution of these baroclinic instabilities as they grow and then decay is synonymous in dynamical meteorology with the problem of developing theories for the fundamental characteristics of midlatitude weather.

Baroclinic vector

Beginning with the equation of motion for a fluid (say, the Euler equations or the Navier-Stokes equations) and taking the curl, one arrives at the equation of motion for the curl of the fluid velocity, that is to say, the vorticity. The Navier-Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, are a set of equations which describe the motion of fluid substances such as liquids and gases. ... The vorticity equation is an important prognostic equation in the atmospheric sciences. ... Vorticity is a mathematical concept used in fluid dynamics. ...

In a fluid that is not all of the same density, a source term appears in the vorticity equation whenever surfaces of constant density (isopycnic surfaces) and surfaces of constant pressure (isobaric surfaces) are not aligned. This term (denoted by the subscript below) is known as the baroclinic vector. (Note that is the vorticity vector, P is pressure, and ρ is density): Isopycnic means of the same density. ... isobaric (meaning of the same weight or pressure) may refer to: in thermodynamics, an isobaric process, i. ...

This vector is of interest both in compressible fluids and in incompressible (but inhomogenous) fluids. Internal gravity waves as well as unstable Rayleigh-Taylor modes can be analyzed from the perspective of the baroclinic vector. It is also of interest in the creation of vorticity by the passage of shocks through inhomogenous media, such as in the Richtmeyer-Meshkov instability. Ocean wave Wave clouds over Theresa, Wisconsin, USA Atmospheric gravity waves as seen from space. ...

Divers may be familiar with the very slow waves that can be excited at a thermocline or a halocline; these are internal waves. Similar waves can be generated between a layer of water and a layer of oil. When the interface between these two surfaces is not horizontal and the system is close to hydrostatic equilibrium, the gradient of the pressure is vertical but the gradient of the density is not. Therefore the baroclinic vector is nonzero, and the sense of the baroclinic vector is to create vorticity to make the interface level out. In the process, the interface overshoots, and the result is an oscillation which is an internal gravity wave. Unlike surface gravity waves, internal gravity waves do not require a sharp interface. For example, in bodies of water, a gradual gradient in temperature or salinity is sufficient to support internal gravity waves driven by the baroclinic vector.