Vortex filaments are one-dimensional regions of concentrated vorticity in an ideal fluid. These are important models of localised vortex structures that often emerge as distinctive features in a variety of physical phenomena. Vortex filaments can be used to describe various physical phenomena, such as the flow of superfluids, and to model filamentary structures that arise in geological and climatological systems and magnetohydrodynamics\footnote{\eg tornado's and slender plasma-filled tubes in the solar corona}. The oldest and simplest mathematical model of the dynamics of an Eulerian vortex filament is the vortex filament equation derived by Luigi Sante Da Rios in 1906. It computes the velocity field at a point along a curved filament by taking into account only the the local effects of it's own vorticity. Da Rios studied the influence that the localised vorticity has on the behaviour of the vortex with a velocity proportional to it's local curvature. The set of basic assumptions that leads to the this law of motion is nowadays commonly referred to as the \LIA. Da Rios was the first person to come up with this idea but was by no means the only one. Da Rios came up with …show more content…
The evolution in time of a curve, a unit circle for example, consists of translating the circle in the time direction. This translation does not change the shape of this curve and this quality is why the vortex filament equation is sometimes referred to as the 'smoke ring evolution'. Vortex rings are a good party trick with interesting behaviours, especially when interacting two of them to produce more appealing curves than the simple circle. Extensive study has been made of evolution of vortex filaments both numerically and in the context of explaining the onset of
walking across them. The lines and pulleys and some parts of the waves are example of
Water spouts have happen in the Pacific oceans in Huntington Beach where an intense funnel-shaped cloud vortex happens over a body of water. This vortex is a non-supercell form tornado over water.(water spouts definition). During a water spouts you can see dark clouds over the ocean.
3. I. Boldea and S.A. Nasar, Linear Motion and Electromagnetic Systems. John Wiley & Sons Inc., 1995.
The development of the Chaos began with a computer and mathematic problems of random data that can calculate and predict patterns that repeat themselves. For example, it picks up the pattern of a person’s heart beat and the pattern of snowflakes hitting the ground. Researchers have found that the patterns may be viewed as “unstable”, “random” and “disorderly” they tend to mimic zig-zags, lightning bolts or electrical currents. This theory has not only been used by physicist, but has also been used by astronomers, mathematicians, biologists, and computer scientists. The Chaos Theory can be applied to predict air turbulence, weather and other underlying parts of nature that is not easily understood (Fiero, p.
As evening approached, several thunderstorms began to take on the characteristics of a supercell thunderstorm. Supercells, which are intense, broadly rotating thunderstorms, are the most v...
1. According to the USA Today Tornado Information website, a tornado is a "violently rotating column of air in contact with the ground and pendant from a thunderstorm." Therefore, thunderstorms are the first step in the creation of a tornado.
When a river flows downstream it frequently encounters obstacles and changes in the river channel that form “rapids, particularly turbulent water with a rough surface. Rapids also form where the channel abruptly narrows or its gradient changes, suddenly accelerating the water.”(Marshak, 2009) These changes in the dynamics of the river flow create the rapids that modern day thrill seekers look for.
Introduction to Aerodynamics Aerodynamics is the study of the motion of fluids in the gas state and bodies in motion relative to the fluid/air. In other words, the study of aerodynamics is the study of fluid dynamics specifically relating to air or the gas state of matter. When an object travels through fluid/air there are two types of flow characteristics that happen, laminar and turbulent. Laminar flow is a smooth, steady flow over a smooth surface and it has little disturbance. Intuition would lead to the belief that this type of air flow would be desirable.
This begins the formation of a supercell. Finally, the spinning tube is stretch causing the supercell to act as it is a vacuum. Instead of the vacuum sucking up dirt, it is sucking up air. After this the air acts to balance the pressure which forms a
Tornado Facts: What You Need to Know About the Spinning Air of Destruction Most people know what a tornado is, but not all of them know what a tornado really is. There is more to it than just a swirling mass of wind that only scares the bejeezus out of you or leaves destruction on its wake. What is a tornado? Also known as twisters, cyclone and funnel, a tornado is a tube of air that touches both the ground and clouds and spins rapidly.
The history of Continuum Mechanics is traced from the early work of the Hellenic period up to the present century. This history is based upon early work in statics, deformable solids, dynamics, fluid mechanics and aerodynamics. The unifying theory of continuum mechanics came in the 1900s combined with the advances in thermodynamics and rheology. Truesdell was the major force in developing this unifying theory. This history has tried to summarize the major contributions to the development of continuum mechanics, but so many contributed to the field that many have been overlooked and only the individuals who made major contributions are listed.
On a more scientific note I am interested in mechanics of fluids. This interest was enforced last year when I had the opportunity to attend a lecture on fluid mechanics at P&G. At the conference I greatly expanded my knowledge regarding the physical aspect of fluids and their properties. In last year's AS course we have met a topic in this field. I will be applying ideas and knowledge gathered from last year for this investigation.
"vile vortexes," that are places around the world with similar dimensions, where ship and other vessels
Abstractions from nature are one the important element in mathematics. Mathematics is a universal subject that has connections to many different areas including nature. [IMAGE] [IMAGE] Bibliography: 1. http://users.powernet.co.uk/bearsoft/Maths.html 2. http://weblife.bangor.ac.uk/cyfrif/eng/resources/spirals.htm 3.