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Roughness Length
Roughness length (z_0) is a parameter of some vertical wind profile equations that model the horizontal mean wind speed near the ground. In the log wind profile, it is equivalent to the height at which the wind speed theoretically becomes zero in the absence of wind-slowing obstacles and under neutral conditions. In reality, the wind at this height no longer follows a mathematical logarithm. It is so named because it is typically related to the height of terrain roughness elements (i.e. protrusions from and/or depressions into the surface). For instance, forests tend to have much larger roughness lengths than tundra. The roughness length does not exactly correspond to any physical length. However, it can be considered as a length-scale representation of the roughness of the surface. Mathematical foundation The roughness length z_0 appears in the expression for the mean wind speed u_z near the ground derived using the Monin–Obukhov similarity theory:American Meteorological Societ ...
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General Log Wind Profile (large Text)
A general officer is an officer of high rank in the armies, and in some nations' air forces, space forces, and marines or naval infantry. In some usages the term "general officer" refers to a rank above colonel."general, adj. and n.". OED Online. March 2021. Oxford University Press. https://www.oed.com/view/Entry/77489?rskey=dCKrg4&result=1 (accessed May 11, 2021) The term ''general'' is used in two ways: as the generic title for all grades of general officer and as a specific rank. It originates in the 16th century, as a shortening of ''captain general'', which rank was taken from Middle French ''capitaine général''. The adjective ''general'' had been affixed to officer designations since the late medieval period to indicate relative superiority or an extended jurisdiction. Today, the title of ''general'' is known in some countries as a four-star rank. However, different countries use different systems of stars or other insignia for senior ranks. It has a NATO rank scal ...
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Anemometer
In meteorology, an anemometer () is a device that measures wind speed and direction. It is a common instrument used in weather stations. The earliest known description of an anemometer was by Italian architect and author Leon Battista Alberti (1404–1472) in 1450. History The anemometer has changed little since its development in the 15th century. Alberti is said to have invented it around 1450. In the ensuing centuries numerous others, including Robert Hooke (1635–1703), developed their own versions, with some mistakenly credited as its inventor. In 1846, John Thomas Romney Robinson (1792–1882) improved the design by using four hemispherical cups and mechanical wheels. In 1926, Canadian meteorologist John Patterson (1872–1956) developed a three-cup anemometer, which was improved by Brevoort and Joiner in 1935. In 1991, Derek Weston added the ability to measure wind direction. In 1994, Andreas Pflitsch developed the sonic anemometer. Velocity anemometers Cup anemomet ...
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Atmospheric Dispersion Modeling
Atmospheric dispersion modeling is the mathematical simulation of how air pollutants disperse in the ambient atmosphere. It is performed with computer programs that include algorithms to solve the mathematical equations that govern the pollutant dispersion. The dispersion models are used to estimate the downwind ambient concentration of air pollutants or toxins emitted from sources such as industrial plants, vehicular traffic or accidental chemical releases. They can also be used to predict future concentrations under specific scenarios (i.e. changes in emission sources). Therefore, they are the dominant type of model used in air quality policy making. They are most useful for pollutants that are dispersed over large distances and that may react in the atmosphere. For pollutants that have a very high spatio-temporal variability (i.e. have very steep distance to source decay such as black carbon) and for epidemiological studies statistical land-use regression models are also used. ...
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Wind Profile Power Law
The wind profile power law is a relationship between the wind speeds at one height, and those at another. Definition The wind profile power law relationship is :\frac = \bigg(\frac \bigg)^\alpha where u is the wind speed (in metres per second) at height z (in metres), and u_r is the known wind speed at a reference height z_r. The exponent (\alpha) is an empirically derived coefficient that varies dependent upon the stability of the atmosphere. For neutral stability conditions, \alpha is approximately 1/7, or 0.143. In order to estimate the wind speed at a certain height ''z'', the relationship would be rearranged to :u = u_r\bigg(\frac \bigg)^\alpha The value of 1/7 for α is commonly assumed to be constant in wind resource assessments, because the differences between the two levels are not usually so great as to introduce substantial errors into the estimates (usually < 50 m). However, when a constant exponent is used, it does not account for the roughness of the surface, t ...
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Hydraulic Roughness
Hydraulic roughness is the measure of the amount of frictional resistance water experiences when passing over land and channel features. One roughness coefficient is '' Manning's n-value''. Manning’s n is used extensively around the world to predict the degree of roughness in channels. Flow velocity is strongly dependent on the resistance to flow. An increase in this n value will cause a decrease in the velocity of water flowing across a surface. Manning's n The value of Manning’s n is affected by many variables. Factors like suspended load, sediment grain size, presence of bedrock or boulders in the stream channel, variations in channel width and depth, and overall sinuosity of the stream channel can all affect Manning’s n value. Biological factors have the greatest overall effect on Manning’s n; bank stabilization by vegetation, height of grass and brush across a floodplain, and stumps and logs creating natural dams are the main observable influences. Biological I ...
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Coefficient Of Friction
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction: *Dry friction is a force that opposes the relative lateral motion of two solid surfaces in contact. Dry friction is subdivided into ''static friction'' ("stiction") between non-moving surfaces, and ''kinetic friction'' between moving surfaces. With the exception of atomic or molecular friction, dry friction generally arises from the interaction of surface features, known as asperities (see Figure 1). *Fluid friction describes the friction between layers of a viscous fluid that are moving relative to each other. *Lubricated friction is a case of fluid friction where a lubricant fluid separates two solid surfaces. *Skin friction is a component of drag, the force resisting the motion of a fluid across the surface of a body. *Internal friction is the force resisting motion between the elements making up a s ...
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Fetch (geography)
In oceanography wind fetch, also known as fetch length or simply fetch, is the length of water over which a given wind has blown without obstruction. Fetch is used in geography and meteorology and its effects are usually associated with sea state and when it reaches shore it is the main factor that creates storm surge which leads to coastal erosion and flooding. It also plays a large part in longshore drift. Fetch length, along with the wind speed (wind strength), and duration, determines the size (sea state) of waves produced. If the wind direction is constant, the longer the fetch and the greater the wind speed, the more wind energy is transferred to the water surface and the larger the resulting sea state will be.''November's fury'' by Michael Schumaker University of Minnesota Press Sea state will increase over time until local energy dissipation balances energy transfer to the water from the wind and a fully developed sea results. See also * Gale * Sea state * Ocean surface ...
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Law Of The Wall
In fluid dynamics, the law of the wall (also known as the logarithmic law of the wall) states that the average velocity of a turbulent flow at a certain point is proportional to the logarithm of the distance from that point to the "wall", or the boundary of the fluid region. This law of the wall was first published in 1930 by Hungarian-American mathematician, aerospace engineer, and physicist Theodore von Kármán. It is only technically applicable to parts of the flow that are close to the wall (<20% of the height of the flow), though it is a good approximation for the entire velocity profile of natural streams.


General logarithmic formulation

The logarithmic law of the wall is a solution for the mean velocity parallel to the wall, and is valid for flows at high

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Turbulence
In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to a laminar flow, which occurs when a fluid flows in parallel layers, with no disruption between those layers. Turbulence is commonly observed in everyday phenomena such as surf, fast flowing rivers, billowing storm clouds, or smoke from a chimney, and most fluid flows occurring in nature or created in engineering applications are turbulent. Turbulence is caused by excessive kinetic energy in parts of a fluid flow, which overcomes the damping effect of the fluid's viscosity. For this reason turbulence is commonly realized in low viscosity fluids. In general terms, in turbulent flow, unsteady vortices appear of many sizes which interact with each other, consequently drag due to friction effects increases. This increases the energy needed to pump fluid through a pipe. The onset of turbulence can be predicted by the dimensionless Rey ...
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Parameter
A parameter (), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when identifying the system, or when evaluating its performance, status, condition, etc. ''Parameter'' has more specific meanings within various disciplines, including mathematics, computer programming, engineering, statistics, logic, linguistics, and electronic musical composition. In addition to its technical uses, there are also extended uses, especially in non-scientific contexts, where it is used to mean defining characteristics or boundaries, as in the phrases 'test parameters' or 'game play parameters'. Modelization When a system is modeled by equations, the values that describe the system are called ''parameters''. For example, in mechanics, the masses, the dimensions and shapes (for solid bodies), the densities and the viscosities ...
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Von Kármán Constant
In fluid dynamics, the von Kármán constant (or Kármán's constant), named for Theodore von Kármán, is a dimensionless constant involved in the logarithmic law describing the distribution of the longitudinal velocity in the wall-normal direction of a turbulent fluid flow near a boundary with a no-slip condition. The equation for such boundary layer flow profiles is: :u=\frac\ln\frac, where ''u'' is the mean flow velocity at height ''z'' above the boundary. The roughness height (also known as roughness length) ''z0'' is where u appears to go to zero. Further ''κ'' is the von Kármán constant being typically 0.41, and u_\star is the friction velocity which depends on the shear stress ''τw'' at the boundary of the flow: :u_\star = \sqrt, with ''ρ'' the fluid density. The Kármán constant is often used in turbulence modeling, for instance in boundary-layer meteorology to calculate fluxes of momentum, heat and moisture from the atmosphere to the land surface. It is consider ...
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