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Baroclinic Instabilities In The Ocean
A baroclinic instability is a fluid dynamical instability of fundamental importance in the atmosphere and ocean. It can lead to the formation of transient mesoscale eddies, with a horizontal scale of 10-100 km. In contrast, flows on the largest scale in the ocean are described as ocean currents, the largest scale eddies are mostly created by shearing of two ocean currents and static mesoscale eddies are formed by the flow around an obstacle (as seen in the animation on eddy (fluid dynamics). Mesoscale eddies are circular currents with swirling motion and account for approximately 90% of the ocean's total kinetic energy. Therefore, they are key in mixing and transport of for example heat, salt and nutrients. In a baroclinic medium, the density depends on both the temperature and pressure. The effect of the temperature on the density allows lines of equal density (isopycnals) and lines of equal pressure (isobars) to intersect. This is in contrast to a barotropic fluid, in which ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Baroclinity
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 ba ... [...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] |
Taylor–Proudman Theorem
In fluid mechanics, the Taylor–Proudman theorem (after Geoffrey Ingram Taylor and Joseph Proudman) states that when a solid body is moved slowly within a fluid that is steadily rotated with a high angular velocity \Omega, the fluid velocity will be uniform along any line parallel to the axis of rotation. \Omega must be large compared to the movement of the solid body in order to make the Coriolis force large compared to the acceleration terms. Derivation The Navier–Stokes equations for steady flow, with zero viscosity and a body force corresponding to the Coriolis force, are : \rho(\cdot\nabla)=-\nabla p, where is the fluid velocity, \rho is the fluid density, and p the pressure. If we assume that F=\nabla\Phi=-2\rho\mathbf\Omega\times is a scalar potential and the advective term on the left may be neglected (reasonable if the Rossby number is much less than unity) and that the flow is incompressible (density is constant), the equations become: : 2\rho\mathbf\Omega\times=-\n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rossby Number
The Rossby number (Ro), named for Carl-Gustav Arvid Rossby, is a dimensionless number used in describing fluid flow. The Rossby number is the ratio of inertial force to Coriolis force, terms , \mathbf \cdot \nabla \mathbf, \sim U^2 / L and \Omega \times \mathbf \sim U\Omega in the Navier–Stokes equations respectively. It is commonly used in geophysical phenomena in the oceans and atmosphere, where it characterizes the importance of Coriolis accelerations arising from planetary rotation. It is also known as the Kibel number. The Rossby number (Ro, not Ro) is defined as : \text = \frac, where ''U'' and ''L'' are respectively characteristic velocity and length scales of the phenomenon, and f = 2\Omega \sin \phi is the Coriolis frequency, with \Omega being the angular frequency of planetary rotation, and \phi the latitude. A small Rossby number signifies a system strongly affected by Coriolis forces, and a large Rossby number signifies a system in which inertial and centrifugal f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gravity
In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the strong interaction, 1036 times weaker than the electromagnetic force and 1029 times weaker than the weak interaction. As a result, it has no significant influence at the level of subatomic particles. However, gravity is the most significant interaction between objects at the macroscopic scale, and it determines the motion of planets, stars, galaxies, and even light. On Earth, gravity gives weight to physical objects, and the Moon's gravity is responsible for sublunar tides in the oceans (the corresponding antipodal tide is caused by the inertia of the Earth and Moon orbiting one another). Gravity also has many important biological functions, helping to guide the growth of plants through the process of gravitropism and influencing the circ ... [...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
North Carolina State University (NC State) is a public land-grant research university in Raleigh, North Carolina. Founded in 1887 and part of the University of North Carolina system, it is the largest university in the Carolinas. The universit ... . Accessed 1 ...
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Scale Analysis (mathematics)
Scale analysis (or order-of-magnitude analysis) is a powerful tool used in the mathematical sciences for the simplification of equations with many terms. First the approximate magnitude of individual terms in the equations is determined. Then some negligibly small terms may be ignored. Example: vertical momentum in synoptic-scale meteorology Consider for example the momentum equation of the Navier–Stokes equations in the vertical coordinate direction of the atmosphere where ''R'' is Earth radius, Ω is frequency of rotation of the Earth, ''g'' is gravitational acceleration, φ is latitude, ρ is density of air and ν is kinematic viscosity of air (we can neglect turbulence in free atmosphere). In synoptic scale we can expect horizontal velocities about ''U'' = 101 m.s−1 and vertical about ''W'' = 10−2 m.s−1. Horizontal scale is ''L'' = 106 m and vertical scale is ''H'' = 104 m. Typical time scale is ''T'' = ''L''/''U'' = 105 s. Pressure diffe ... [...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] |
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] |
Gravitational Acceleration
In physics, gravitational acceleration is the acceleration of an object in free fall within a vacuum (and thus without experiencing drag). This is the steady gain in speed caused exclusively by the force of gravitational attraction. All bodies accelerate in vacuum at the same rate, regardless of the masses or compositions of the bodies; the measurement and analysis of these rates is known as gravimetry. At a fixed point on the surface, the magnitude of Earth's gravity results from combined effect of gravitation and the centrifugal force from Earth's rotation. At different points on Earth's surface, the free fall acceleration ranges from , depending on altitude, latitude, and longitude. A conventional standard value is defined exactly as . Locations of significant variation from this value are known as gravity anomalies. This does not take into account other effects, such as buoyancy or drag. Relation to the Universal Law Newton's law of universal gravitation states that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zonal And Meridional Flow
Zonal and meridional flow are directions and regions of fluid flow on a globe. Zonal flow follows a pattern along latitudinal lines, latitudinal circles or in the west–east direction. Meridional flow follows a pattern from north to south, or from south to north, along the Earth's longitude lines, longitudinal circles (meridian) or in the north–south direction. These terms are often used in the atmospheric and earth sciences to describe global phenomena, such as "meridional wind", or "zonal average temperature". In the context of physics, zonal flow connotes a tendency of flux to conform to a pattern parallel to the equator of a sphere. In meteorological term regarding atmospheric circulation, zonal flow brings a temperature contrast along the Earth's longitude. Extratropical cyclones in zonal flows tend to be weaker, moving faster and producing relatively little impact on local weather. Extratropical cyclones in meridional flows tend to be stronger and move slowe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Longitude
Longitude (, ) is a geographic coordinate that specifies the east–west position of a point on the surface of the Earth, or another celestial body. It is an angular measurement, usually expressed in degrees and denoted by the Greek letter lambda (λ). Meridians are semicircular lines running from pole to pole that connect points with the same longitude. The prime meridian defines 0° longitude; by convention the International Reference Meridian for the Earth passes near the Royal Observatory in Greenwich, England on the island of Great Britain. Positive longitudes are east of the prime meridian, and negative ones are west. Because of the Earth's rotation, there is a close connection between longitude and time measurement. Scientifically precise local time varies with longitude: a difference of 15° longitude corresponds to a one-hour difference in local time, due to the differing position in relation to the Sun. Comparing local time to an absolute measure of time allows ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
