## Monday, February 23, 2009

### GALACTIC DYNAMICS IN THE LIGHT OF METEOROLOGICAL THEORY

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Summary --Equations for the motions in a galaxy which is controlled by gravitational forces and inertial effects are formulated. It is found that for the motions relative to the rotating system formulae analogous, and of similar form, to the geostrophie wind equations may be written. From these formulae and from the distribution of the relative gravitational potential in the disc of the galaxy, it is found that a spiral tendency in the mass distribution carries the implication of an inward flux of angular momentum by advective processes. This is to be compared with an outward flux through gravitational torques obtained in previous studies in which the writer participated.

1. Introduction --A large tract of Newtonian theory can be more compactly and conveniently discussed in terms of the gravitational potential % a concept introduced subsequent to the time of Newton. The fundamental equation relating ~ to the spacial distribution of mass is the familiar equation of Poisson, namely, (1) V2~ = 4rsGp
where G is the universal constant of gravitation and p is the density of mass in space.
It is well known that certain philosophical difficulties arise in an attempt to apply (1) to the entire universe as was pointed out notably by EINSTEIN (1917), and modern cosmological theory may be said to have had its beginning in this source. If the mass density ~ is taken over some finite region of space, one property- of equation (1) is that it alone does not possess the competence to specify the motion of a given interior mass point. The solution of (1), speaking mathematically, consists of two parts, namely, a complimentary function which is not uniquely fixed by the interior mass, and a particular integral which is so determined.

For the specification of the complimentary function one must apply as a boundary condition added information, let us say, concerning the value of the potential at an infinite distance from the given mass distribution if it is one that is isolated in space, as we shall for our present purpose now assume. Under these conditions the subject takes on a simple form owing to the fact that the complimentary function, since it is a solution of (]) with the right hand member zero (i.e., of Laplace's.

by VICTOn P. STARR(*)

## Thursday, February 19, 2009

### Wind shear

Wind shear refers to the variation of wind over either horizontal or vertical distances. Airplane pilots generally regard significant windshear to be a horizontal change in airspeed of 30 knots (15 m/s) for light aircraft, and near 45 knots (22 m/s) for airliners.[2] Vertical speed changes greater than 4.9 knots (2.5 m/s) also qualify as significant wind shear for aircraft. Low level wind shear can affect aircraft airspeed during take off and landing in disastrous ways.[3] It is also a key factor in the creation of severe thunderstorms. The additional hazard of turbulence is often associated with wind shear.

Wind shear, sometimes referred to as windshear or wind gradient, is a difference in wind speed and direction over a relatively short distance in the atmosphere. Wind shear can be broken down into vertical and horizontal components, with horizontal wind shear seen across weather fronts and near the coast, and vertical shear typically near the surface, though also at higher levels in the atmosphere near upper level jets and frontal zones aloft.

Wind shear itself is a microscale meteorological phenomenon occurring over a very small distance, but it can be associated with mesoscale or synoptic scale weather features such as squall lines and cold fronts. It is commonly observed near microbursts and downbursts caused by thunderstorms, weather fronts, areas of locally higher low level winds referred to as low level jets, near mountains, radiation inversions that occur due to clear skies and calm winds, buildings, wind turbines, and sailboats. Wind shear has a significant effect during take-off and landing of aircraft due to their effects on control of the aircraft, and was a significant cause of aircraft accidents involving large loss of life within the United States.

Sound movement through the atmosphere is affected by wind shear, which can bend the wave front, causing sounds to be heard where they normally would not, or vice versa. Strong vertical wind shear within the troposphere also inhibits tropical cyclone development, but helps to organize individual thunderstorms into living longer life cycles which can then produce severe weather. The thermal wind concept explains with how differences in wind speed with height are dependent on horizontal temperature differences, and explains the existence of the jet stream.[1]

## References :

http://en.wikipedia.org/wiki/Wind_shear

### Turbulence

In fluid dynamics, turbulence or turbulent flow is a fluid regime characterized by chaotic, stochastic property changes. This includes low momentum diffusion, high momentum convection, and rapid variation of pressure and velocity in space and time. Flow that is not turbulent is called laminar flow. The (dimensionless) Reynolds number characterizes whether flow conditions lead to laminar or turbulent flow; e.g. for pipe flow, a Reynolds number above about 4000 (A Reynolds number between 2100 and 4000 is known as transitional flow) will be turbulent. At very low speeds the flow is laminar, i.e., the flow is smooth (though it may involve vortices on a large scale). As the speed increases, at some point the transition is made to turbulent flow. In turbulent flow, unsteady vortices appear on many scales and interact with each other. Drag due to boundary layer skin friction increases. The structure and location of boundary layer separation often changes, sometimes resulting in a reduction of overall drag. Because laminar-turbulent transition is governed by Reynolds number, the same transition occurs if the size of the object is gradually increased, or the viscosity of the fluid is decreased, or if the density of the fluid is increased.

Turbulence causes the formation of eddies of many different length scales. Most of the kinetic energy of the turbulent motion is contained in the large scale structures. The energy "cascades" from these large scale structures to smaller scale structures by an inertial and essentially inviscid mechanism. This process continues, creating smaller and smaller structures which produces a hierarchy of eddies. Eventually this process creates structures that are small enough that molecular diffusion becomes important and viscous dissipation of energy finally takes place. The scale at which this happens is the Kolmogorov length scale.

In two dimensional turbulence (as can be approximated in the atmosphere or ocean), energy actually flows to larger scales. This is referred to as the inverse energy cascade and is characterized by a k − (5 / 3) in the power spectrum. This is the main reason why large scale weather features such as hurricanes occur.

Turbulent diffusion is usually described by a turbulent diffusion coefficient. This turbulent diffusion coefficient is defined in a phenomenological sense, by analogy with the molecular diffusivities, but it does not have a true physical meaning, being dependent on the flow conditions, and not a property of the fluid, itself. In addition, the turbulent diffusivity concept assumes a constitutive relation between a turbulent flux and the gradient of a mean variable similar to the relation between flux and gradient that exists for molecular transport. In the best case, this assumption is only an approximation. Nevertheless, the turbulent diffusivity is the simplest approach for quantitative analysis of turbulent flows, and many models have been postulated to calculate it. For instance, in large bodies of water like oceans this coefficient can be found using Richardson's four-third power law and is governed by the random walk principle. In rivers and large ocean currents, the diffusion coefficient is given by variations of Elder's formula.

When designing piping systems, turbulent flow requires a higher input of energy from a pump (or fan) than laminar flow. However, for applications such as heat exchangers and reaction vessels, turbulent flow is essential for good heat transfer and mixing.

While it is possible to find some particular solutions of the Navier-Stokes equations governing fluid motion, all such solutions are unstable at large Reynolds numbers. Sensitive dependence on the initial and boundary conditions makes fluid flow irregular both in time and in space so that a statistical description is needed. Russian mathematician Andrey Kolmogorov proposed the first statistical theory of turbulence, based on the aforementioned notion of the energy cascade (an idea originally introduced by Richardson) and the concept of self-similarity. As a result, the Kolmogorov microscales were named after him. It is now known that the self-similarity is broken so the statistical description is presently modified [1]. Still, the complete description of turbulence remains one of the unsolved problems in physics. According to an apocryphal story Werner Heisenberg was asked what he would ask God, given the opportunity. His reply was: "When I meet God, I am going to ask him two questions: Why relativity? And why turbulence? I really believe he will have an answer for the first."[2] A similar witticism has been attributed to Horace Lamb (who had published a noted text book on Hydrodynamics)—his choice being quantum mechanics (instead of relativity) and turbulence. Lamb was quoted as saying in a speech to the British Association for the Advancement of Science, "I am an old man now, and when I die and go to heaven there are two matters on which I hope for enlightenment. One is quantum electrodynamics, and the other is the turbulent motion of fluids. And about the former I am rather optimistic."[3]

## Wednesday, February 18, 2009

the small-diameter column of violently rotating air developed within a convective cloud and in contact with the ground. Tornadoes occur most often in association with thunderstorms during the spring and summer in the mid-latitudes of both the Northern and Southern Hemispheres. These whirling atmospheric vortices can generate the strongest winds known on Earth: wind speeds in the range of 500 km (300 miles) per hour have been measured in extreme events. When winds of this magnitude strike a populated area, they can cause fantastic destruction and great loss of life, mainly through injuries from flying debris and collapsing structures. Most tornadoes, however, are comparatively weak events that occur in sparsely populated areas and cause minor damage.

Records of tornado occurrences are fragmentary for many areas, making estimates of global tornado frequency difficult. Insurance records show that tornadoes have caused significant losses in Europe, India, Japan, South Africa, and Australia. Rare but deadly tornadoes have occurred in many other countries, including Bangladesh, China, and Argentina. There are few tornado reports from either the Arctic or the equatorial tropics.

In the United Kingdom almost all reported tornadoes are associated with vigorous convection occurring in advance of and along a cold frontal boundary. Large temperature differences are associated with early winter cold fronts that move rapidly across the country from the north and west, at times spawning widespread outbreaks of small tornadoes. For example, the passage of a very strong frontal boundary across the United Kingdom on November 23, 1981, produced 105 documented tornadoes. Similar phenomena occur in other European countries such as France and Belgium.

Most Southern Hemisphere tornadoes occur in Australia. Many reports come from New South Wales, where there were 173 reported tornadoes from 1901 to 1966. In addition, South Africa and Argentina both reported 191 tornadoes from 1930 to 1979. Because tornado formation is closely tied to the speed and directional shear of the wind with height, tornadoes in the Southern Hemisphere almost exclusively rotate clockwise, opposite to the rotation of their Northern Hemisphere counterparts.

### Temperature and layer

Exosphere
From 500–1,000 km (310–620 mi; 1,600,000–3,300,000 ft) up to 10,000 km (6,200 mi; 33,000,000 ft), contain free-moving particles that may migrate into and out of the magnetosphere or the solar wind.
Exobase
Also known as the 'critical level', it is the lower boundary of the exosphere.
Ionosphere
The part of the atmosphere that is ionized by solar radiation stretches from 50 to 1,000 km (31 to 620 mi; 160,000 to 3,300,000 ft) and typically overlaps both the exosphere and the thermosphere. It plays an important part in atmospheric electricity and forms the inner edge of the magnetosphere. Because of its charged particles, it has practical importance because it influences, for example, radio propagation on the Earth. It is responsible for auroras.
Thermopause
The boundary above the thermosphere, it varies in height from 500–1,000 km (310–620 mi; 1,600,000–3,300,000 ft).
Thermosphere
From 80–85 km (50–53 mi; 260,000–280,000 ft) to over 640 km (400 mi; 2,100,000 ft), temperature increasing with height. Although the temperature can rise to 1,500 °C (2,730 °F), a person would not feel warm because of the extreme low pressure. The International Space Station orbits in this layer, between 320 and 380 km (200 and 240 mi).
Mesopause
The temperature minimum at the boundary between the thermosphere and the mesosphere. It is the coldest place on Earth, with a temperature of −100 °C (−148.0 °F; 173.1 K).
Mesosphere
From the Greek word "μέσος" meaning middle. The mesosphere extends from about 50 km (31 mi; 160,000 ft) to the range of 80–85 km (50–53 mi; 260,000–280,000 ft). Temperature decreases with height, reaching −100 °C (−148.0 °F; 173.1 K) in the upper mesosphere. This is also where most meteors burn up when entering the atmosphere.
Stratopause
The boundary between the mesosphere and the stratosphere, typically 50 to 55 km (31 to 34 mi; 160,000 to 180,000 ft). The pressure here is 1/1000th sea level.
Stratosphere
From the Latin word "stratus" meaning spreading out. The stratosphere extends from the troposphere's 7–17 km (4.3–11 mi; 23,000–56,000 ft) range to about 51 km (32 mi; 170,000 ft). Temperature increases with height. The stratosphere contains the ozone layer, the part of the Earth's atmosphere which contains relatively high concentrations of ozone. "Relatively high" means a few parts per million—much higher than the concentrations in the lower atmosphere but still small compared to the main components of the atmosphere. It is mainly located in the lower portion of the stratosphere from approximately 15–35 km (9.3–22 mi; 49,000–110,000 ft) above Earth's surface, though the thickness varies seasonally and geographically.
Ozone Layer
Though part of the Stratosphere, the ozone layer is considered as a layer of the Earth's atmosphere in itself due to the fact that its physical and chemical composition is far different to the Stratosphere. Ozone (O3) in the earth's stratosphere is created by ultraviolet light striking oxygen molecules containing two oxygen atoms (O2), splitting them into individual oxygen atoms (atomic oxygen); the atomic oxygen then combines with unbroken O2 to create O3. O3 is unstable (although, in the stratosphere, long-lived) and when ultraviolet light hits ozone it splits into a molecule of O2 and an atom of atomic oxygen, a continuing process called the ozone-oxygen cycle. This occurs in the ozone layer, the region from about 10 to 50 km (33,000 to 160,000 ft) above Earth's surface. About 90% of the ozone in our atmosphere is contained in the stratosphere. Ozone concentrations are greatest between about 20 and 40 km (66,000 and 130,000 ft), where they range from about 2 to 8 parts per million.
Tropopause
The boundary between the stratosphere and troposphere.
Troposphere
From the greek word "τρέπω" meaning to turn or change. The troposphere is the lowest layer of the atmosphere; it begins at the surface and extends to between 7 km (23,000 ft) at the poles and 17 km (56,000 ft) at the equator, with some variation due to weather factors. The troposphere has a great deal of vertical mixing because of solar heating at the area. This heating makes air masses less dense so they rise. When an air mass rises, the pressure upon it decreases so it expands, doing work against the opposing pressure of the surrounding air. To do work is to expend energy, so the temperature of the air mass decreases. As the temperature decreases, water vapor in the air mass may condense or solidify, releasing latent heat that further uplifts the air mass. This process determines the maximum rate of decline of temperature with height, called the adiabatic lapse rate. The troposphere contains roughly 80% of the total mass of the atmosphere. Fifty percent of the total mass of the atmosphere is located in the lower 5.6 km (18,000 ft) of the troposphere.

The average temperature of the atmosphere at the surface of Earth is 20 °C (68 °F; 293 K)

### Weather forecasting

One of the earliest scientific approaches to weather prediction occurred around 300 B.C.E., documented in Aristotle's work, "Meteorologica." The ancient Greeks invented the term meteorology, which means the study of atmospheric disturbances or meteors. Aristotle tried to explain the weather through the interaction of earth, fire, air, and water. His pupil Theophrastus really went to work and wrote the ultimate weather text The Book of Signs, which contained a collection of weather lore and forecast signs. Amazingly it served as the definitive weather book for 2,000 years! (What if they're still reading this 2,000 years from now?)
Weather Words

"There is a sound of abundance of rain."

—1 Kings

Theophrastus's weather lore included colors of the sky, rings and halos, and even sound. Hippocrates—also known as "the Father of Medicine"—was also very much involved with the weather. His work On Airs, Waters, and Places became a medical classic, linking good health with favorable weather conditions. The opening of his work begins with the advice that those who wish to investigate medicine must first begin with an understanding of seasons and weather.
Weather-Speak

Meteorology is the science of studying the atmosphere.

Weather forecasting advanced little from these ancient times to the Renaissance. Then beginning in the fifteenth century, Leonardo da Vinci designed an instrument for measuring humidity called a hygrometer. Later Galileo Galilei invented the thermometer and his student Evangelista Torricelli came up with the barometer for measuring air pressure. With these tools, people could monitor the atmosphere. Then Sir Isaac Newton derived the physics and mathematics that accurately described the atmosphere. Newton's work on motion remains The Book of Signs of modern meteorology. To this day, his principles form the foundation of all computer analyses and predictions.

Our brief exploration into forecasting pretty much follows the techniques and methods developed by early weather wizards. From the earliest of times, hunters, farmers, warriors, shepherds, and sailors learned the importance of being able to tell what the weather might be up to next. Ancient civilizations appealed to the gods of the sky. The Egyptians looked to Ra, the sun god. The Greeks sought out the all-powerful Zeus. Then there was Thor, the god of thunder and lightning in ancient Nordic times. Some societies, such as the Aztecs, used human sacrifice to satisfy the rain god, Tlaloc. Native American and Australian aborigines performed rain dances. Those who were able to predict the weather and seemed to influence its production were held in highest esteem. After all, they appeared to be very well connected.

### Cirrus Cloud

Cirrus is composed mainly of ice crystals and is usually white in colour. Ice crystals make the cloud look even brighter and more translucent. Against a blue sky, the white delicate filaments of cirrus are spotlessly clean and display a silk-like gloss. Cirrus is usually thin, wispy and scattered. There are patches of narrow bands with fibrous texture which look like feathers, hair, tenuous trail or ponytails. It is fascinating to see cirrus in a variety of shapes and sizes.

Cirrus is a kind of high-level cloud. Among all cloud genera, cirrus is the highest in the troposphere. The average height of cirrus is over 6,000 metres. It is so high in the upper air that when the sun has not risen above the horizon before dawn or has gone downhill after nightfall, sunlight can still shine on this detached, over-hanging and shadowless cloud. After scattering the sunlight, it produces an attractive red or orange hue, a very common sight on summer days.

"Bright white clouds floating on the azure sky. Like cotton fiber spreading on bluish green sea." - the most beautiful cloud is cirrus.

Since Cirrus is very high in the sky, even if it turns into water droplets, they tend to evaporate before reaching ground. This is the reason why rain is not detected on the ground and Cirrus is mainly associated with fine weather.

Do you know what kind of cloud will appear in the sky a couple of days before the arrival of bad weather or tropical cyclone? (Hint: This cloud is most probably present at a height more than 10 kilometres. It is among the highest clouds.) The answer is Cirrus. The rising air associated with tropical cyclones pushes moist air up to the height of 5 to 6 kilometres. Because of the low temperature there, water vapour condenses into small, clear crystals. A layer of glossy Cirrus forms which drifts out from the centre of the tropical cyclone because of divergence at that level. So, when the outer edge of a tropical cyclone reaches Hong Kong, we can see Cirrus high in the sky. People call it the “Mother of Typhoon”.