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Beta Plane
In geophysical fluid dynamics, an approximation whereby the Coriolis parameter, ''f'', is set to vary linearly in space is called a beta plane approximation. On a rotating sphere such as the Earth, ''f'' varies with the sine of latitude; in the so-called f-plane approximation, this variation is ignored, and a value of ''f'' appropriate for a particular latitude is used throughout the domain. This approximation can be visualized as a tangent plane touching the surface of the sphere at this latitude. A more accurate model is a linear Taylor series approximation to this variability about a given latitude \phi_0: f = f_0 + \beta y, where f_0 is the Coriolis parameter at \phi_0, \beta = (\mathrmf/\mathrmy), _ = 2\Omega\cos(\phi_0)/a is the Rossby parameter, y is the meridional distance from \phi_0, \Omega is the angular rotation rate of the Earth, and a is the Earth's radius. In analogy with the f-plane, this approximation is termed the beta plane, even though it no longer describes d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geophysical
Geophysics () is a subject of natural science concerned with the physical processes and physical properties of the Earth and its surrounding space environment, and the use of quantitative methods for their analysis. The term ''geophysics'' sometimes refers only to solid earth applications: Earth's shape; its gravitational and magnetic fields; its internal structure and composition; its dynamics and their surface expression in plate tectonics, the generation of magmas, volcanism and rock formation. However, modern geophysics organizations and pure scientists use a broader definition that includes the water cycle including snow and ice; fluid dynamics of the oceans and the atmosphere; electricity and magnetism in the ionosphere and magnetosphere and solar-terrestrial physics; and analogous problems associated with the Moon and other planets. Gutenberg, B., 1929, Lehrbuch der Geophysik. Leipzig. Berlin (Gebruder Borntraeger). Runcorn, S.K, (editor-in-chief), 1967, Internationa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fluid Dynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) and hydrodynamics (the study of liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and modelling fission weapon detonation. Fluid dynamics offers a systematic structure—which underlies these practical disciplines—that embraces empirical and semi-empirical laws derived from flow measurement and used to solve practical problems. The solution to a fluid dynamics problem typically involves the calculation of various properties of the fluid, such as flow velocity, pressure, density, and temperature, as functions of space and ti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coriolis Parameter
The Coriolis frequency ''ƒ'', also called the Coriolis parameter or Coriolis coefficient, is equal to twice the rotation rate ''Ω'' of the Earth multiplied by the sine of the latitude \varphi. :f = 2 \Omega \sin \varphi.\, The rotation rate of the Earth (''Ω'' = 7.2921 × 10−5 rad/s) can be calculated as 2''π'' / ''T'' radians per second, where ''T'' is the rotation period of the Earth which is one ''sidereal'' day (23 h 56 min 4.1 s). In the midlatitudes, the typical value for f is about 10−4 rad/s. Inertial oscillations on the surface of the earth have this frequency. These oscillations are the result of the Coriolis effect. Explanation Consider a body (for example a fixed volume of atmosphere) moving along at a given latitude \varphi at velocity v in the earth's rotating reference frame. In the local reference frame of the body, the vertical direction is parallel to the radial vector po ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
F-plane
In geophysical fluid dynamics, the ''f''-plane approximation is an approximation where the Coriolis parameter, denoted ''f'', is set to a constant value. This approximation is frequently used for the analysis of highly idealized tropical cyclones. Using a constant Coriolis parameter prevents the formation of beta gyres which are largely responsible for the North-westward direction of most tropical cyclones. Rossby waves also depend on variations in ''f'', and do not occur in the ''f''-plane approximation. In reality, the Coriolis parameter varies with latitude, and so the ''f''-plane approximation is not appropriate when considering flows over large length scales. The ''f''-plane approximation is also poor near the equator, where variations in ''f'' are on the same order of magnitude as ''f''. The beta plane approximation is an improvement on the ''f''-plane approximation which takes leading-order variations in ''f'' into account. References * * Isaac HeldRotating radiative-con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Taylor Series
In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor series are equal near this point. Taylor series are named after Brook Taylor, who introduced them in 1715. A Taylor series is also called a Maclaurin series, when 0 is the point where the derivatives are considered, after Colin Maclaurin, who made extensive use of this special case of Taylor series in the mid-18th century. The partial sum formed by the first terms of a Taylor series is a polynomial of degree that is called the th Taylor polynomial of the function. Taylor polynomials are approximations of a function, which become generally better as increases. Taylor's theorem gives quantitative estimates on the error introduced by the use of such approximations. If the Taylor series of a function is convergent, its sum is the limit of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rossby Parameter
The Rossby parameter (or simply beta \beta) is a number used in geophysics and meteorology which arises due to the meridional variation of the Coriolis force caused by the spherical shape of the Earth. It is important in the generation of Rossby waves. The Rossby parameter \beta is given by for Atmospheric Science Mesoscale Dynamics (MEA 713). North Carolina State University. Accessed 14 July 2007. : where is the , is the latitude, [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rossby Waves
Rossby waves, also known as planetary waves, are a type of inertial wave naturally occurring in rotating fluids. They were first identified by Sweden-born American meteorologist Carl-Gustaf Arvid Rossby. They are observed in the atmospheres and oceans of planets owing to the rotation of the planet. Atmospheric Rossby waves on Earth are giant meanders in high-altitude winds that have a major influence on weather. These waves are associated with pressure systems and the jet stream (especially around the polar vortices). Oceanic Rossby waves move along the thermocline: the boundary between the warm upper layer and the cold deeper part of the ocean. Rossby wave types Atmospheric waves Atmospheric Rossby waves result from the conservation of potential vorticity and are influenced by the Coriolis force and pressure gradient. The rotation causes fluids to turn to the right as they move in the northern hemisphere and to the left in the southern hemisphere. For example, a fluid that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coriolis Effect
In physics, the Coriolis force is an inertial or fictitious force that acts on objects in motion within a frame of reference that rotates with respect to an inertial frame. In a reference frame with clockwise rotation, the force acts to the left of the motion of the object. In one with anticlockwise (or counterclockwise) rotation, the force acts to the right. Deflection of an object due to the Coriolis force is called the Coriolis effect. Though recognized previously by others, the mathematical expression for the Coriolis force appeared in an 1835 paper by French scientist Gaspard-Gustave de Coriolis, in connection with the theory of water wheels. Early in the 20th century, the term ''Coriolis force'' began to be used in connection with meteorology. Newton's laws of motion describe the motion of an object in an inertial (non-accelerating) frame of reference. When Newton's laws are transformed to a rotating frame of reference, the Coriolis and centrifugal accelerations appea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coriolis Frequency
The Coriolis frequency ''ƒ'', also called the Coriolis parameter or Coriolis coefficient, is equal to twice the rotation rate ''Ω'' of the Earth multiplied by the sine of the latitude \varphi. :f = 2 \Omega \sin \varphi.\, The rotation rate of the Earth (''Ω'' = 7.2921 × 10−5 rad/s) can be calculated as 2''π'' / ''T'' radians per second, where ''T'' is the rotation period of the Earth which is one ''sidereal'' day (23 h 56 min 4.1 s). In the midlatitudes, the typical value for f is about 10−4 rad/s. Inertial oscillations on the surface of the earth have this frequency. These oscillations are the result of the Coriolis effect. Explanation Consider a body (for example a fixed volume of atmosphere) moving along at a given latitude \varphi at velocity v in the earth's rotating reference frame. In the local reference frame of the body, the vertical direction is parallel to the radial vector point ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Baroclinic Instability
In fluid dynamics, the baroclinity (often 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 flow is one in which the density depends on both temperature and pressure (the fully general case). A simpler case, barotropic flow, allows for density dependence only on pressure, so that the curl of the pressure-gradient force vanishes. Baroclinity is proportional to: :\nabla p \times \nabla \rho which is proportional to the sine of 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. In Earth's atmosphere, barotropic flow is a better approximation in the tropics, where density surfaces and pressure surfaces are both nearly level, whereas in higher latitudes the flow is more baroclinic. These midlatitude belts of high atmospheric b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quasi-geostrophic Equations
While geostrophic motion refers to the wind that would result from an exact balance between the Coriolis force and horizontal pressure-gradient forces, quasi-geostrophic (QG) motion refers to flows where the Coriolis force and pressure gradient forces are ''almost'' in balance, but with inertia also having an effect. Origin Atmospheric and oceanographic flows take place over horizontal length scales which are very large compared to their vertical length scale, and so they can be described using the shallow water equations. The Rossby number is a dimensionless number which characterises the strength of inertia compared to the strength of the Coriolis force. The quasi-geostrophic equations are approximations to the shallow water equations in the limit of small Rossby number, so that inertial forces are an order of magnitude smaller than the Coriolis and pressure forces. If the Rossby number is equal to zero then we recover geostrophic flow. The quasi-geostrophic equations were ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fluid Dynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) and hydrodynamics (the study of liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and modelling fission weapon detonation. Fluid dynamics offers a systematic structure—which underlies these practical disciplines—that embraces empirical and semi-empirical laws derived from flow measurement and used to solve practical problems. The solution to a fluid dynamics problem typically involves the calculation of various properties of the fluid, such as flow velocity, pressure, density, and temperature, as functions of space and ti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
