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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 fir ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geostrophic Motion
In atmospheric science, geostrophic flow () is the theoretical wind that would result from an exact balance between the Coriolis force and the pressure gradient force. This condition is called '' geostrophic equilibrium'' or ''geostrophic balance'' (also known as ''geostrophy''). The geostrophic wind is directed parallel to isobars (lines of constant pressure at a given height). This balance seldom holds exactly in nature. The true wind almost always differs from the geostrophic wind due to other forces such as friction from the ground. Thus, the actual wind would equal the geostrophic wind only if there were no friction (e.g. above the atmospheric boundary layer) and the isobars were perfectly straight. Despite this, much of the atmosphere outside the tropics is close to geostrophic flow much of the time and it is a valuable first approximation. Geostrophic flow in air or water is a zero-frequency inertial wave. Origin A useful heuristic is to imagine air starting from rest, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geopotential
Geopotential is the potential of the Earth's gravity field. For convenience it is often defined as the ''negative'' of the potential energy per unit mass, so that the gravity vector is obtained as the gradient of this potential, without the negation. In addition to the actual potential (the geopotential), a hypothetical normal potential and their difference, the disturbing potential, can also be defined. Concept For geophysical applications, gravity is distinguished from gravitation. Gravity is defined as the resultant force of gravitation and the centrifugal force caused by the Earth's rotation. Likewise, the respective scalar potentials can be added to form an effective potential called the geopotential, W. Global mean sea surface is close to one of the isosurfaces of the geopotential. This ''equipotential surface'', or surface of constant geopotential, is called the ''geoid''. How the gravitational force and the centrifugal force add up to a force orthogonal to the geoid is ill ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Q-Vectors
Q-vectors are used in atmospheric dynamics to understand physical processes such as vertical motion and frontogenesis. Q-vectors are not physical quantities that can be measured in the atmosphere but are derived from the quasi-geostrophic equations and can be used in the previous diagnostic situations. On meteorological charts, Q-vectors point toward upward motion and away from downward motion. Q-vectors are an alternative to the omega equation for diagnosing vertical motion in the quasi-geostrophic equations. Derivation First derived in 1978, Q-vector derivation can be simplified for the midlatitudes, using the midlatitude β-plane quasi-geostrophic prediction equations: # \frac - f_v_a - \beta y v_g = 0 (x component of quasi-geostrophic momentum equation) # \frac + f_u_a + \beta y u_g = 0 (y component of quasi-geostrophic momentum equation) # \frac - \frac \omega = \frac (quasi-geostrophic thermodynamic equation) And the thermal wind equations: f_ \frac = \frac \frac (x ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thermal Wind
The thermal wind is the vector difference between the geostrophic wind at upper altitudes minus that at lower altitudes in the atmosphere. It is the hypothetical vertical wind shear that would exist if the winds obey geostrophic balance in the horizontal, while pressure obeys hydrostatic balance in the vertical. The combination of these two force balances is called ''thermal wind balance'', a term generalizable also to more complicated horizontal flow balances such as gradient wind balance''.'' Since the geostrophic wind at a given pressure level flows along geopotential height contours on a map, and the geopotential thickness of a pressure layer is proportional to virtual temperature, it follows that the thermal wind flows along thickness or temperature contours. For instance, the thermal wind associated with pole-to-equator temperature gradients is the primary physical explanation for the jet stream in the upper half of the troposphere, which is the atmospheric layer extendin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Beta-plane Approximation
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] |
Ageostrophy
Ageostrophy or (ageostrophic flow) is the difference between the ''actual'' wind or current and the geostrophic wind or geostrophic current. Since geostrophy is an exact balance between the Coriolis force and the pressure gradient force, ageostrophic flow reflects an imbalance, and thus is often implicated in disturbances, vertical motions (important for weather), and rapid changes with time. Ageostrophic flow reflects the existence of all the other terms in the momentum equation neglected in that idealization, including friction and material acceleration Dv/Dt, which includes the centrifugal force in curved flow. See also *geostrophic *geostrophic wind In atmospheric science, geostrophic flow () is the theoretical wind that would result from an exact balance between the Coriolis force and the pressure gradient force. This condition is called '' geostrophic equilibrium'' or ''geostrophic balanc ... References External linksMeteo 422 – Lecture 17 – The Omega Equation Al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Material Derivative
In continuum mechanics, the material derivative describes the time rate of change of some physical quantity (like heat or momentum) of a material element that is subjected to a space-and-time-dependent macroscopic velocity field. The material derivative can serve as a link between Eulerian and Lagrangian descriptions of continuum deformation. For example, in fluid dynamics, the velocity field is the flow velocity, and the quantity of interest might be the temperature of the fluid. In which case, the material derivative then describes the temperature change of a certain fluid parcel with time, as it flows along its pathline (trajectory). Other names There are many other names for the material derivative, including: *advective derivative *convective derivative *derivative following the motion *hydrodynamic derivative *Lagrangian derivative *particle derivative *substantial derivative *substantive derivative *Stokes derivative *total derivative, although the material derivative ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Laplacian
In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a scalar function on Euclidean space. It is usually denoted by the symbols \nabla\cdot\nabla, \nabla^2 (where \nabla is the nabla operator), or \Delta. In a Cartesian coordinate system, the Laplacian is given by the sum of second partial derivatives of the function with respect to each independent variable. In other coordinate systems, such as cylindrical and spherical coordinates, the Laplacian also has a useful form. Informally, the Laplacian of a function at a point measures by how much the average value of over small spheres or balls centered at deviates from . The Laplace operator is named after the French mathematician Pierre-Simon de Laplace (1749–1827), who first applied the operator to the study of celestial mechanics: the Laplacian of the gravitational potential due to a given mass density distribution is a constant multiple of that densit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geostrophic Wind
In atmospheric science, geostrophic flow () is the theoretical wind that would result from an exact balance between the Coriolis force and the pressure gradient force. This condition is called '' geostrophic equilibrium'' or ''geostrophic balance'' (also known as ''geostrophy''). The geostrophic wind is directed parallel to isobars (lines of constant pressure at a given height). This balance seldom holds exactly in nature. The true wind almost always differs from the geostrophic wind due to other forces such as friction from the ground. Thus, the actual wind would equal the geostrophic wind only if there were no friction (e.g. above the atmospheric boundary layer) and the isobars were perfectly straight. Despite this, much of the atmosphere outside the tropics is close to geostrophic flow much of the time and it is a valuable first approximation. Geostrophic flow in air or water is a zero-frequency inertial wave. Origin A useful heuristic is to imagine air starting from rest, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coriolis Force
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 appe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jule Charney
Jule Gregory Charney (January 1, 1917 – June 16, 1981) was an American meteorologist who played an important role in developing numerical weather prediction and increasing understanding of the general circulation of the atmosphere by devising a series of increasingly sophisticated mathematical models of the atmosphere. His work was the driving force behind many national and international weather initiatives and programs. Considered the father of modern dynamical meteorology, Charney is credited with having "guided the postwar evolution of modern meteorology more than any other living figure." Charney's work also influenced that of his close colleague Edward Lorenz, who explored the limitations of predictability and was a pioneer of the field of chaos theory. Biography Charney was born in San Francisco, California, on January 1, 1917, to Russian immigrants Ely Charney and Stella Littman, tailors in the garment industry. Charney spent most of his early life in California. Afte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Order Of Magnitude
An order of magnitude is an approximation of the logarithm of a value relative to some contextually understood reference value, usually 10, interpreted as the base of the logarithm and the representative of values of magnitude one. Logarithmic distributions are common in nature and considering the order of magnitude of values sampled from such a distribution can be more intuitive. When the reference value is 10, the order of magnitude can be understood as the number of digits in the base-10 representation of the value. Similarly, if the reference value is one of some powers of 2, since computers store data in a binary format, the magnitude can be understood in terms of the amount of computer memory needed to store that value. Differences in order of magnitude can be measured on a base-10 logarithmic scale in “decades” (i.e., factors of ten). Examples of numbers of different magnitudes can be found at Orders of magnitude (numbers). Definition Generally, the order of magnitude ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
