Baroclinity

In fluid dynamics, the baroclinity (sometimes called baroclinicity) of a stratified fluid is a measure of how misaligned the gradient of pressure is from the gradient of density in a fluid. In meteorology a baroclinic atmosphere is one for which the density depends on both the temperature and the pressure; contrast this with a 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 latitudes, or tropics, whereas the baroclinic areas are generally found in the mid-latitude/polar regions.

Whether a fluid counts as rapidly rotating 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, become more relevant.

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.

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.

Meteorology is the interdisciplinary scientific study of the atmosphere. The study of meteorology dates back millennia, though significant progress in meteorology did not occur until the 18th century. The 19th century saw modest progress in the field after weather observation networks were formed across broad regions. Prior attempts at prediction of weather depended on historical data. It wasn't until after the elucidation of the laws of physics and, more particularly, the development of the computer, allowing for the automated solution of a great many equations that model the weather, in the latter half of the 20th century that significant breakthroughs in weather forecasting were achieved.

Meteorological phenomena are observable weather events that are explained by the science of meteorology. Meteorological phenomena are described and quantified by the variables of Earth's atmosphere: temperature, air pressure, water vapor, mass flow, and the variations and interactions of those variables, and how they change over time. Different spatial scales are used to describe and predict weather on local, regional, and global levels.

Ptolemy wrote on the atmospheric refraction of light in the context of astronomical observations. In 1021, Alhazen showed that atmospheric refraction is also responsible for twilight; he estimated that twilight begins when the sun is 19 degrees below the horizon, and also used a geometric determination based on this to estimate the maximum possible height of the Earth's atmosphere as 52,000 passim (about 49 miles, or 79 km).

St. Albert the Great was the first to propose that each drop of falling rain had the form of a small sphere, and that this form meant that the rainbow was produced by light interacting with each raindrop. Roger Bacon was the first to calculate the angular size of the rainbow. He stated that a rainbow summit can not appear higher than 42 degrees above the horizon. In the late 13th century and early 14th century, Kam?l al-D?n al-F?ris? and Theodoric of Freiberg were the first to give the correct explanations for the primary rainbow phenomenon. Theoderic went further and also explained the secondary rainbow. In 1716, Edmund Halley suggested that aurorae are caused by "magnetic effluvia" moving along the Earth's magnetic field lines.
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