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Richardson Number
The Richardson number (Ri) is named after Lewis Fry Richardson (1881–1953). It is the dimensionless number that expresses the ratio of the buoyancy term to the flow velocity, flow shear (fluid), shear term: : \mathrm = \frac = \frac \frac where g is gravitational acceleration, gravity, \rho is density, u is a representative flow speed, and z is depth. The Richardson number, or one of several variants, is of practical importance in weather forecasting and in investigating density and turbidity currents in oceans, lakes, and reservoirs. When considering flows in which density differences are small (the Boussinesq approximation (buoyancy), Boussinesq approximation), it is common to use the Boussinesq approximation (buoyancy)#Advantages, reduced gravity ''g' '' and the relevant parameter is the densimetric Richardson number : \mathrm = \frac which is used frequently when considering atmospheric or oceanic flows. If the Richardson number is much less than unity, buoyancy is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lewis Fry Richardson
Lewis Fry Richardson, Fellow of the Royal Society, FRS (11 October 1881 – 30 September 1953) was an English mathematician, physicist, meteorologist, psychologist, and Pacifism, pacifist who pioneered modern mathematical techniques of weather forecasting, and the application of similar techniques to studying the causes of wars and how to prevent them. He is also noted for his pioneering work on fractals and a method for solving a system of linear equations known as modified Richardson iteration. Early life Lewis Fry Richardson was the youngest of seven children born to Catherine Fry (1838–1919) and David Richardson (1835–1913). They were a prosperous Quaker family, David Richardson operating a successful tanning and leather-manufacturing business. At age 12 he was sent to a Quaker boarding school, Bootham School in York, where he received an education in science, which stimulated an active interest in natural history. In 1898 he went on to Durham College of Science (a coll ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
RWTH Aachen University
RWTH Aachen University (), in German ''Rheinisch-Westfälische Technische Hochschule Aachen'', is a German public research university located in Aachen, North Rhine-Westphalia, Germany. With more than 47,000 students enrolled in 144 study programs, it is the second largest technical university in Germany. RWTH Aachen in 2019 emerged from the final of the third federal and state excellence strategy. The university will be funded as a university of excellence for the next seven years. RWTH Aachen was already part of the federal and state excellence initiative in 2007 and 2012. Since 2007, RWTH Aachen has been continuously funded by the Deutsche Forschungsgemeinschaft, DFG and the German Council of Science and Humanities as one of eleven (previously nine) German German Universities Excellence Initiative, Universities of Excellence for its future concept ''RWTH 2020: Meeting Global Challenges'' and the follow-up concept ''The Integrated Interdisciplinary University of Science and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complex Number
In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the form a + bi, where and are real numbers. Because no real number satisfies the above equation, was called an imaginary number by René Descartes. For the complex number is called the , and is called the . The set of complex numbers is denoted by either of the symbols \mathbb C or . Despite the historical nomenclature, "imaginary" complex numbers have a mathematical existence as firm as that of the real numbers, and they are fundamental tools in the scientific description of the natural world. Complex numbers allow solutions to all polynomial equations, even those that have no solutions in real numbers. More precisely, the fundamental theorem of algebra asserts that every non-constant polynomial equation with real or complex coefficie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brunt–Väisälä Frequency
In atmospheric dynamics, oceanography, asteroseismology and geophysics, the Brunt–Väisälä frequency, or buoyancy frequency, is a measure of the stability of a fluid to vertical displacements such as those caused by convection. More precisely it is the frequency at which a vertically displaced parcel will oscillate within a statically stable environment. It is named after David Brunt and Vilho Väisälä. It can be used as a measure of atmospheric stratification. Derivation for a general fluid Consider a parcel of water or gas that has density \rho_0. This parcel is in an environment of other water or gas particles where the density of the environment is a function of height: \rho = \rho (z). If the parcel is displaced by a small vertical increment z', ''and it maintains its original density so that its volume does not change,'' it will be subject to an extra gravitational force against its surroundings of: \rho_0 \frac = - g \left rho (z)-\rho (z+z')\right/math> where g is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kelvin–Helmholtz Instability
The Kelvin–Helmholtz instability (after Lord Kelvin and Hermann von Helmholtz) is a fluid instability that occurs when there is shear velocity, velocity shear in a single continuum mechanics, continuous fluid or a velocity difference across the interface between two fluids. Kelvin-Helmholtz instabilities are visible in the atmospheres of planets and moons, such as in List of cloud types, cloud formations on Earth or the Great Red Spot#Great Red Spot, Red Spot on Jupiter, and the Stellar atmosphere, atmospheres of the Sun and other stars. Theory overview and mathematical concepts Fluid dynamics predicts the onset of instability and transition to turbulent flow within fluids of different density, densities moving at different speeds. If surface tension is ignored, two fluids in parallel motion with different velocities and densities yield an interface that is unstable to short-wavelength perturbations for all speeds. However, surface tension is able to stabilize the short w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Taylor–Goldstein Equation
The Taylor–Goldstein equation is an ordinary differential equation used in the fields of geophysical fluid dynamics, and more generally in fluid dynamics, in presence of quasi- 2D flows. It describes the dynamics of the Kelvin–Helmholtz instability, subject to buoyancy forces (e.g. gravity), for stably stratified fluids in the dissipation-less limit. Or, more generally, the dynamics of internal waves in the presence of a (continuous) density stratification and shear flow. The Taylor–Goldstein equation is derived from the 2D Euler equations, using the Boussinesq approximation. The equation is named after G.I. Taylor and S. Goldstein, who derived the equation independently from each other in 1931. The third independent derivation, also in 1931, was made by B. Haurwitz. Formulation The equation is derived by solving a linearized version of the Navier–Stokes equation, in presence of gravity g and a mean density gradient (with gradient-length L_\rho), for the perturbati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oceanography
Oceanography (), also known as oceanology, sea science, ocean science, and marine science, is the scientific study of the ocean, including its physics, chemistry, biology, and geology. It is an Earth science, which covers a wide range of topics, including ocean currents, waves, and geophysical fluid dynamics; fluxes of various chemical substances and physical properties within the ocean and across its boundaries; ecosystem dynamics; and plate tectonics and seabed geology. Oceanographers draw upon a wide range of disciplines to deepen their understanding of the world’s oceans, incorporating insights from astronomy, biology, chemistry, geography, geology, hydrology, meteorology and physics. History Early history Humans first acquired knowledge of the waves and currents of the seas and oceans in pre-historic times. Observations on tides were recorded by Aristotle and Strabo in 384–322 BC. Early exploration of the oceans was primarily for cartography and mainly ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
No-slip Condition
In fluid dynamics, the no-slip condition is a Boundary conditions in fluid dynamics, boundary condition which enforces that at a solid boundary, a viscous fluid attains zero bulk velocity. This boundary condition was first proposed by Osborne Reynolds, who observed this behaviour while performing his influential pipe flow experiments. The form of this boundary condition is an example of a Dirichlet boundary condition. In the majority of fluid flows relevant to fluids engineering, the no-slip condition is generally utilised at solid boundaries. This condition often fails for systems which exhibit non-newtonian fluid, non-Newtonian behaviour. Fluids which this condition fails includes common food-stuffs which contain a high fat content, such as mayonnaise or melted cheese. Physical justification The no-slip condition is an empirical assumption that has been useful in modelling many macroscopic experiments. It was one of three alternatives that were the subject of contention in the 19 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Difference
A finite difference is a mathematical expression of the form . Finite differences (or the associated difference quotients) are often used as approximations of derivatives, such as in numerical differentiation. The difference operator, commonly denoted \Delta, is the operator (mathematics), operator that maps a function to the function \Delta[f] defined by \Delta[f](x) = f(x+1)-f(x). A difference equation is a functional equation that involves the finite difference operator in the same way as a differential equation involves derivatives. There are many similarities between difference equations and differential equations. Certain Recurrence relation#Relationship to difference equations narrowly defined, recurrence relations can be written as difference equations by replacing iteration notation with finite differences. In numerical analysis, finite differences are widely used for #Relation with derivatives, approximating derivatives, and the term "finite difference" is often used a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Representations Of The Atmospheric Boundary Layer In Global Climate Models
Representations of the atmospheric boundary layer in global climate models play a role in simulations of past, present, and future climates. Representing the planetary boundary layer, atmospheric boundary layer (ABL) within Global circulation model, global climate models (GCMs) are difficult due to differences in surface type, scale mismatch between physical processes affecting the ABL and scales at which GCMs are run, and difficulties in measuring different physical processes within the ABL. Various parameterization techniques described below attempt to address the difficulty in ABL representations within GCMs. What is the ABL? The ABL is the lowest part of the Earth's troposphere, loosely about the altitude zone 0 km to 1.5 km. The ABL is the only part of the troposphere directly affected by daily cycled contact with the Earth's surface, so the ABL is directly affected by forcings originating at the surface. Such forcings include: heat flux, moisture flux, convecti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reynolds-averaged Navier–Stokes Equations
The Reynolds-averaged Navier–Stokes equations (RANS equations) are time-averaged equations of motion for fluid flow. The idea behind the equations is Reynolds decomposition, whereby an instantaneous quantity is decomposed into its time-averaged and fluctuating quantities, an idea first proposed by Osborne Reynolds. The RANS equations are primarily used to describe turbulent flows. These equations can be used with approximations based on knowledge of the properties of flow turbulence to give approximate time-averaged solutions to the Navier–Stokes equations. For a stationary flow of an incompressible Newtonian fluid, these equations can be written in Einstein notation in Cartesian coordinates as: \rho\bar_j \frac = \rho \bar_i + \frac \left - \bar\delta_ + \mu \left( \frac + \frac \right) - \rho \overline \right The left hand side of this equation represents the change in mean momentum of a fluid element owing to the unsteadiness in the mean flow and the convection by the m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
