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Weak Temperature Gradient Approximation
In atmospheric science, the weak temperature gradient approximation (WTG) is a theoretical framework used to simplify the equations governing tropical atmospheric dynamics and circulation. The WTG approximation assumes that free tropospheric temperature in the tropics has negligible horizontal (and temporal) gradients compared to its vertical gradient. The assumption of horizontal homogeneity of temperature follows from observations of free tropospheric temperature in the tropical regions as well as early work on the simplified equations governing tropical circulation. It is understood to occur as a result of the weak Coriolis force in the tropics. In a multitude of theoretical, modelling and observational studies, the WTG has been applied to study synoptic- and mesoscale phenomena in the tropics. Physical explanation Free tropospheric temperature refers to the temperature in the upper layers of the troposphere where the influence from the surface and the boundary layer is n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Atmospheric Science
Atmospheric science is the study of the Atmosphere of Earth, Earth's atmosphere and its various inner-working physical processes. Meteorology includes atmospheric chemistry and atmospheric physics with a major focus on weather forecasting. Climatology is the study of atmospheric conditions over timescales longer than those of weather, weather, focusing on average climate conditions and their climate variability and change, variability over time. Aeronomy is the study of the upper layers of the atmosphere, where dissociation (chemistry), dissociation and ionization are important. Atmospheric science has been extended to the field of planetary science and the study of the atmospheres of the planets and natural satellites of the Solar System. Experimental instruments used in atmospheric science include satellites, rocketsondes, radiosondes, weather balloons, radars, and lasers. The term aerology (from Ancient Greek, Greek ἀήρ, ''aēr'', "air"; and -λογία, ''-logy, -logia'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gravity Wave
In fluid dynamics, gravity waves are waves 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, ocean tides, and the wakes of surface vessels. The period of wind-generated gravity waves on the free surface of the Earth's ponds, lakes, seas and oceans are predominantl ... [...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. Definition and theory 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Froude Number
In continuum mechanics, the Froude number (, after William Froude, ) is a dimensionless number defined as the ratio of the flow inertia to the external force field (the latter in many applications simply due to gravity). The Froude number is based on the speed–length ratio which he defined as: \mathrm = \frac where is the local flow velocity (in m/s), is the local gravity field (in m/s2), and is a characteristic length (in m). The Froude number has some analogy with the Mach number. In theoretical fluid dynamics the Froude number is not frequently considered since usually the equations are considered in the high Froude limit of negligible external field, leading to homogeneous equations that preserve the mathematical aspects. For example, homogeneous Euler equations are conservation equations. However, in naval architecture the Froude number is a significant figure used to determine the resistance of a partially submerged object moving through water. Origins In open c ... [...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 poi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Navier–Stokes Equations
The Navier–Stokes equations ( ) are partial differential equations which describe the motion of viscous fluid substances. They were named after French engineer and physicist Claude-Louis Navier and the Irish physicist and mathematician George Gabriel Stokes. They were developed over several decades of progressively building the theories, from 1822 (Navier) to 1842–1850 (Stokes). The Navier–Stokes equations mathematically express momentum balance for Newtonian fluids and make use of conservation of mass. They are sometimes accompanied by an equation of state relating pressure, temperature and density. They arise from applying Isaac Newton's second law to fluid motion, together with the assumption that the stress in the fluid is the sum of a diffusing viscous term (proportional to the gradient of velocity) and a pressure term—hence describing ''viscous flow''. The difference between them and the closely related Euler equations is that Navier–Stokes equat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 Primitive equations, 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 viscosity, 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Virtual Temperature
In atmospheric thermodynamics, the virtual temperature (T_v) of a moist air parcel is the temperature at which a theoretical dry air parcel would have a total pressure and density equal to the moist parcel of air. The virtual temperature of unsaturated moist air is always greater than the absolute air temperature, however, as the existence of suspended cloud droplets reduces the virtual temperature. The virtual temperature effect is also known as the vapor buoyancy effect. It has been described to increase Earth's thermal emission by warming the tropical atmosphere. Introduction Description In atmospheric thermodynamic processes, it is often useful to assume air parcels behave approximately adiabatically, and approximately ideally. The specific gas constant for the standardized mass of one kilogram of a particular gas is variable, and described mathematically as :R_x = \frac, where R^* is the molar gas constant, and M_x is the apparent molar mass of gas x in kilograms per mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Buoyancy
Buoyancy (), or upthrust, is the force exerted by a fluid opposing the weight of a partially or fully immersed object (which may be also be a parcel of fluid). 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 Displacement (fluid), displaced fluid. For this reason, an object with average density greater than the surrounding fluid tends to sink because its weight is greater than the weight of the fluid it displaces. If the objec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Troposphere
The troposphere is the lowest layer of the atmosphere of Earth. It contains 80% of the total mass of the Atmosphere, planetary atmosphere and 99% of the total mass of water vapor and aerosols, and is where most weather phenomena occur. From the planetary surface of the Earth, the average height of the troposphere is in the tropics; in the middle latitudes; and in the high latitudes of the polar regions in winter; thus the average height of the troposphere is . The term ''troposphere'' derives from the Greek words ''tropos'' (rotating) and ''sphere, sphaira'' (sphere) indicating that rotational turbulence mixes the layers of air and so determines the structure and the phenomena of the troposphere. The rotational friction of the troposphere against the planetary surface affects the flow of the air, and so forms the planetary boundary layer (PBL) that varies in height from hundreds of meters up to . The measures of the PBL vary according to the latitude, the landform, and the t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boundary Layer
In physics and fluid mechanics, a boundary layer is the thin layer of fluid in the immediate vicinity of a Boundary (thermodynamic), bounding surface formed by the fluid flowing along the surface. The fluid's interaction with the wall induces a No-slip condition, no-slip boundary condition (zero velocity at the wall). The flow velocity then monotonically increases above the surface until it returns to the bulk flow velocity. The thin layer consisting of fluid whose velocity has not yet returned to the bulk flow velocity is called the velocity boundary layer. The air next to a human is heated, resulting in gravity-induced convective airflow, which results in both a velocity and thermal boundary layer. A breeze disrupts the boundary layer, and hair and clothing protect it, making the human feel cooler or warmer. On an aircraft wing, the velocity boundary layer is the part of the flow close to the wing, where viscosity, viscous forces distort the surrounding non-viscous flow. In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Temperature
Temperature is a physical quantity that quantitatively expresses the attribute of hotness or coldness. Temperature is measurement, measured with a thermometer. It reflects the average kinetic energy of the vibrating and colliding atoms making up a substance. Thermometers are calibrated in various temperature scales that historically have relied on various reference points and thermometric substances for definition. The most common scales are the Celsius scale with the unit symbol °C (formerly called ''centigrade''), the Fahrenheit scale (°F), and the Kelvin scale (K), with the third being used predominantly for scientific purposes. The kelvin is one of the seven base units in the International System of Units (SI). Absolute zero, i.e., zero kelvin or −273.15 °C, is the lowest point in the thermodynamic temperature scale. Experimentally, it can be approached very closely but not actually reached, as recognized in the third law of thermodynamics. It would be impossible ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
