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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] |
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] |
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] |
Gravity Waves
In fluid dynamics, gravity waves are waves generated in a fluid medium or at the interface between two media when the force of gravity or buoyancy tries to restore equilibrium. An example of such an interface is that between the atmosphere and the ocean, which gives rise to wind waves. A gravity wave results when fluid is displaced from a position of equilibrium. The restoration of the fluid to equilibrium will produce a movement of the fluid back and forth, called a ''wave orbit''. Gravity waves on an air–sea interface of the ocean are called surface gravity waves (a type of surface wave), while gravity waves that are the body of the water (such as between parts of different densities) are called ''internal waves''. Wind-generated waves on the water surface are examples of gravity waves, as are tsunamis and ocean tides. The period of wind-generated gravity waves on the free surface of the Earth's ponds, lakes, seas and oceans are predominantly between 0.3 and 30 sec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Potential Vorticity
In fluid mechanics, potential vorticity (PV) is a quantity which is proportional to the dot product of vorticity and stratification. This quantity, following a parcel of air or water, can only be changed by diabatic or frictional processes. It is a useful concept for understanding the generation of vorticity in cyclogenesis (the birth and development of a cyclone), especially along the polar front, and in analyzing flow in the ocean. Potential vorticity (PV) is seen as one of the important theoretical successes of modern meteorology. It is a simplified approach for understanding fluid motions in a rotating system such as the Earth's atmosphere and ocean. Its development traces back to the circulation theorem by Bjerknes in 1898, which is a specialized form of Kelvin's circulation theorem. Starting from Hoskins et al., 1985, PV has been more commonly used in operational weather diagnosis such as tracing dynamics of air parcels and inverting for the full flow field. Even after deta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Buoyancy
Buoyancy (), or upthrust, is an upward force exerted by a fluid that opposes the weight of a partially or fully immersed object. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus the pressure at the bottom of a column of fluid is greater than at the top of the column. Similarly, the pressure at the bottom of an object submerged in a fluid is greater than at the top of the object. The pressure difference results in a net upward force on the object. The magnitude of the force is proportional to the pressure difference, and (as explained by Archimedes' principle) is equivalent to the weight of the fluid that would otherwise occupy the submerged volume of the object, i.e. the displaced fluid. For this reason, an object whose average density is greater than that of the fluid in which it is submerged tends to sink. If the object is less dense than the liquid, the force can keep the object afloat. This can occur only in a no ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tropics
The tropics are the regions of Earth surrounding the Equator. They are defined in latitude by the Tropic of Cancer in the Northern Hemisphere at N and the Tropic of Capricorn in the Southern Hemisphere at S. The tropics are also referred to as the tropical zone and the torrid zone (see geographical zone). In terms of climate, the tropics receive sunlight that is more direct than the rest of Earth and are generally hotter and wetter as they aren't affected as much by the solar seasons. The word "tropical" sometimes refers to this sort of climate in the zone rather than to the geographical zone itself. The tropical zone includes deserts and snow-capped mountains, which are not tropical in the climatic sense. The tropics are distinguished from the other climatic and biomatic regions of Earth, which are the middle latitudes and the polar regions on either side of the equatorial zone. The tropics constitute 40% of Earth's surface area and contain 36% of Earth's landmass. , the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geostrophic
A geostrophic current is an oceanic current in which the pressure gradient force is balanced by the Coriolis effect. The direction of geostrophic flow is parallel to the isobars, with the high pressure to the right of the flow in the Northern Hemisphere, and the high pressure to the left in the Southern Hemisphere. This concept is familiar from weather maps, whose isobars show the direction of geostrophic winds. Geostrophic flow may be either barotropic or baroclinic. A geostrophic current may also be thought of as a rotating shallow water wave with a frequency of zero. The principle of ''geostrophy'' or ''geostrophic balance'' is useful to oceanographers because it allows them to infer ocean currents from measurements of the sea surface height (by combined satellite altimetry and gravimetry) or from vertical profiles of seawater density taken by ships or autonomous buoys. The major currents of the world's oceans, such as the Gulf Stream, the Kuroshio Current, the Agulhas Curr ... [...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] |
Equatorial Waves
Equatorial waves are oceanic and atmospheric waves trapped close to the equator, meaning that they decay rapidly away from the equator, but can propagate in the longitudinal and vertical directions.Holton, James R., 2004: ''An Introduction to Dynamic Meteorology''. Elsevier Academic Press, Burlington, MA, pp. 394–400. Wave trapping is the result of the Earth's rotation and its spherical shape which combine to cause the magnitude of the Coriolis force to increase rapidly away from the equator. Equatorial waves are present in both the tropical atmosphere and ocean and play an important role in the evolution of many climate phenomena such as El Niño. Many physical processes may excite equatorial waves including, in the case of the atmosphere, diabatic heat release associated with cloud formation, and in the case of the ocean, anomalous changes in the strength or direction of the trade winds. Equatorial waves may be separated into a series of subclasses depending on their fundame ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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