|
Rossby-gravity Waves
Rossby-gravity waves are equatorially trapped waves (much like Kelvin waves), meaning that they rapidly decay as their distance increases away from the equator (so long as the Brunt–Vaisala frequency does not remain constant). These waves have the same trapping scale as Kelvin waves, more commonly known as the equatorial Rossby deformation radius.Gill, Adrian E., 1982: ''Atmosphere-Ocean Dynamics,'' International Geophysics Series, Volume 30, Academic Press, 662 pp. They always carry energy eastward, but their 'crests' and 'troughs' may propagate westward if their periods are long enough. Derivation The eastward speed of propagation of these waves can be derived for an inviscid slowly moving layer of fluid of uniform depth H.Zhang, Dalin, 2008: Personal Communication, “Waves in Rotating, Homogeneous Fluids,” University of Maryland, College Park. Because the Coriolis parameter (''f'' = 2Ω sin(''θ'') where Ω is the angular velocity of the earth, 7.2921&nb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kelvin Waves
A Kelvin wave is a wave in the ocean or atmosphere that balances the Earth's Coriolis force against a topographic boundary such as a coastline, or a waveguide such as the equator. A feature of a Kelvin wave is that it is non-dispersive, i.e., the phase speed of the wave crests is equal to the group speed of the wave energy for all frequencies. This means that it retains its shape as it moves in the alongshore direction over time. A Kelvin wave ( fluid dynamics) is also a long scale perturbation mode of a vortex in superfluid dynamics; in terms of the meteorological or oceanographical derivation, one may assume that the meridional velocity component vanishes (i.e. there is no flow in the north–south direction, thus making the momentum and continuity equations much simpler). This wave is named after the discoverer, Lord Kelvin (1879). Coastal Kelvin wave In a stratified ocean of mean depth ''H'', perturbed by some amount ''η'', free waves propagate along coastal boundaries ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rossby Radius Of Deformation
In atmospheric dynamics and physical oceanography, the Rossby radius of deformation is the length scale at which rotational effects become as important as buoyancy or gravity wave effects in the evolution of the flow about some disturbance. For a barotropic ocean: L_R \equiv \frac, where \,g is the gravitational acceleration, \,D is the water depth, and \,f is the Coriolis parameter. For ''f'' = 1×10−4 s−1 appropriate to 45° latitude, g = 9.81 m/s^2 and ''D'' = 4 km, ''LR'' ≈ 2000 km; using the same latitude and gravity but changing D to 40 m; ''LR'' ≈ 200 km. The ''n''th baroclinic Rossby radius is: : L_ \equiv \frac, where \,N is the Brunt–Väisälä frequency, \,H is the scale height, and ''n'' = 1, 2, .... In Earth's atmosphere, the ratio ''N''/''f''0 is typically of order 100, so the Rossby radius is about 100 times the vertical scale height, ''H''. For a vertical scale associated with the height of the tropopause, ''L''''R'', 1 & ... [...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 point ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Angular Velocity
In physics, angular velocity or rotational velocity ( or ), also known as angular frequency vector,(UP1) is a pseudovector representation of how fast the angular position or orientation of an object changes with time (i.e. how quickly an object rotates or revolves relative to a point or axis). The magnitude of the pseudovector represents the ''angular speed'', the rate at which the object rotates or revolves, and its direction is normal to the instantaneous plane of rotation or angular displacement. The orientation of angular velocity is conventionally specified by the right-hand rule.(EM1) There are two types of angular velocity. * Orbital angular velocity refers to how fast a point object revolves about a fixed origin, i.e. the time rate of change of its angular position relative to the origin. * Spin angular velocity refers to how fast a rigid body rotates with respect to its center of rotation and is independent of the choice of origin, in contrast to orbital angular ve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
Primitive Equations
The primitive equations are a set of nonlinear partial differential equations that are used to approximate global atmospheric flow and are used in most atmospheric models. They consist of three main sets of balance equations: # A ''continuity equation'': Representing the conservation of mass. # ''Conservation of momentum'': Consisting of a form of the Navier–Stokes equations that describe hydrodynamical flow on the surface of a sphere under the assumption that vertical motion is much smaller than horizontal motion (hydrostasis) and that the fluid layer depth is small compared to the radius of the sphere # A '' thermal energy equation'': Relating the overall temperature of the system to heat sources and sinks The primitive equations may be linearized to yield Laplace's tidal equations, an eigenvalue problem from which the analytical solution to the latitudinal structure of the flow may be determined. In general, nearly all forms of the primitive equations relate the five var ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frequency Relation
Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is equal to one event per second. The period is the interval of time between events, so the period is the reciprocal of the frequency. For example, if a heart beats at a frequency of 120 times a minute (2 hertz), the period, —the interval at which the beats repeat—is half a second (60 seconds divided by 120 beats). Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio signals (sound), radio waves, and light. Definitions and units For cyclical phenomena such as oscillations, waves, or for examples of simple harmonic motion, the term ''frequency'' is defined as the number of cycles or vibrations per unit of time. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rossby Wave
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] |
Equatorial Rossby Wave
Equatorial Rossby waves, often called planetary waves, are very long, low frequency water waves found near the equator and are derived using the equatorial beta plane approximation. Mathematics Using the equatorial beta plane approximation, f = \beta y, where ''β'' is the variation of the Coriolis parameter with latitude, \beta = \frac. With this approximation, the primitive equations become the following: * the continuity equation (accounting for the effects of horizontal convergence and divergence and written with geopotential height): ::\frac + c^2 \left ( \frac + \frac \right ) = 0 * the U-momentum equation (zonal component): ::\frac - v \beta y = -\frac * the V-momentum equation (meridional component): ::\frac + u \beta y = -\frac.Holton, James R., 2004: ''An Introduction to Dynamic Meteorology.'' Elsevier Academic Press, Burlington, MA, pp. 394–400. In order to fully linearize the primitive equations, one must assume the following solution: :: \beginu, v, \v ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physical Oceanography
Physical oceanography is the study of physical conditions and physical processes within the ocean, especially the motions and physical properties of ocean waters. Physical oceanography is one of several sub-domains into which oceanography is divided. Others include biological, chemical and geological oceanography. Physical oceanography may be subdivided into ''descriptive'' and ''dynamical'' physical oceanography. Descriptive physical oceanography seeks to research the ocean through observations and complex numerical models, which describe the fluid motions as precisely as possible. Dynamical physical oceanography focuses primarily upon the processes that govern the motion of fluids with emphasis upon theoretical research and numerical models. These are part of the large field of Geophysical Fluid Dynamics (GFD) that is shared together with meteorology. GFD is a sub field of Fluid dynamics describing flows occurring on spatial and temporal scales that are greatly influenced ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
