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Hydrodynamic Stability
In fluid dynamics, hydrodynamic stability is the field which analyses the stability and the onset of instability of fluid flows. The study of hydrodynamic stability aims to find out if a given flow is stable or unstable, and if so, how these instabilities will cause the development of turbulence.See Drazin (2002), ''Introduction to hydrodynamic stability'' The foundations of hydrodynamic stability, both theoretical and experimental, were laid most notably by Helmholtz, Kelvin, Rayleigh and Reynolds during the nineteenth century. These foundations have given many useful tools to study hydrodynamic stability. These include Reynolds number, the Euler equations, and the Navier–Stokes equations. When studying flow stability it is useful to understand more simplistic systems, e.g. incompressible and inviscid fluids which can then be developed further onto more complex flows. Since the 1980s, more computational methods are being used to model and analyse the more complex flows. Stable ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Laminar And Turbulent Flows
Laminar means "flat". Laminar may refer to: Terms in science and engineering: *Laminar electronics or organic electronics, a branch of material sciences dealing with electrically conductive polymers and small molecules * Laminar armour or "banded mail", armour made from horizontal overlapping rows or bands of solid armour plates * Laminar flame speed, a property of a combustible mixture * Laminar flow, a fluid flowing in parallel layers with no disruption between the layers * Laminar organization, the way certain tissues are arranged in layers *Laminar set family, a mathematical structure. *A common leaf shape. Proper nouns: * Laminar Research, a Columbia, South Carolina, software company * Icaro Laminar, an Italian hang glider design * Pazmany Laminar, a personal light aircraft designed by Ladislao Pazmany See also * Lamina (other) Lamina may refer to: Science and technology * Planar lamina, a two-dimensional planar closed surface with mass and density, in mathemati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mode Of A Linear Field
Mode ( la, modus meaning "manner, tune, measure, due measure, rhythm, melody") may refer to: Arts and entertainment * '' MO''D''E (magazine)'', a defunct U.S. women's fashion magazine * ''Mode'' magazine, a fictional fashion magazine which is the setting for the ABC series ''Ugly Betty'' * ''Mode'' (video game), a 1996 video game * Mode Records, a record label * Mode Media, a defunct digital media company * ''Mode'' series, a quartet of novels by Piers Anthony * Modern Organization for Dance Evolvement, known as MODE, a 1970s modern dance organisation in New York Music * Mode (music), a system of musical tonality involving a type of scale coupled with a set of characteristic melodic behaviors ** Modus (medieval music) *** Gregorian mode, a system of modes used in Gregorian chant (as opposed to ancient Greek modes or Byzantine octoechos) * "Mode", a song by PRhyme from the 2015 soundtrack '' Southpaw: Music from and Inspired by the Motion Picture'' Computing * Data types ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kelvin Helmholz Wave Clouds
The kelvin, symbol K, is the primary unit of temperature in the International System of Units (SI), used alongside its prefixed forms and the degree Celsius. It is named after the Belfast-born and University of Glasgow-based engineer and physicist William Thomson, 1st Baron Kelvin (1824–1907). The Kelvin scale is an absolute thermodynamic temperature scale, meaning it uses absolute zero as its null (zero) point. Historically, the Kelvin scale was developed by shifting the starting point of the much-older Celsius scale down from the melting point of water to absolute zero, and its increments still closely approximate the historic definition of a degree Celsius, but since 2019 the scale has been defined by fixing the Boltzmann constant to be exactly . Hence, one kelvin is equal to a change in the thermodynamic temperature that results in a change of thermal energy by . The temperature in degree Celsius is now defined as the temperature in kelvins minus 273.15, meaning ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bifurcation Theory
Bifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family of curves, such as the integral curves of a family of vector fields, and the solutions of a family of differential equations. Most commonly applied to the mathematical study of dynamical systems, a bifurcation occurs when a small smooth change made to the parameter values (the bifurcation parameters) of a system causes a sudden 'qualitative' or topological change in its behavior. Bifurcations occur in both continuous systems (described by ordinary, delay or partial differential equations) and discrete systems (described by maps). The name "bifurcation" was first introduced by Henri Poincaré in 1885 in the first paper in mathematics showing such a behavior. Henri Poincaré also later named various types of stationary points and classified them . Bifurcation types It is useful to divide bifurcations into two principal classes: * Local bifurcations, which can b ... [...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 bounding surface formed by the fluid flowing along the surface. The fluid's interaction with the wall induces a 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, 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 viscous forces distort the surrounding non-viscous flow. In the Earth's atmosphere, the atmospheric boun ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Incompressible Flow
In fluid mechanics or more generally continuum mechanics, incompressible flow ( isochoric flow) refers to a flow in which the material density is constant within a fluid parcel—an infinitesimal volume that moves with the flow velocity. An equivalent statement that implies incompressibility is that the divergence of the flow velocity is zero (see the derivation below, which illustrates why these conditions are equivalent). Incompressible flow does not imply that the fluid itself is incompressible. It is shown in the derivation below that (under the right conditions) even compressible fluids can – to a good approximation – be modelled as an incompressible flow. Incompressible flow implies that the density remains constant within a parcel of fluid that moves with the flow velocity. Derivation The fundamental requirement for incompressible flow is that the density, \rho , is constant within a small element volume, ''dV'', which moves at the flow velocity u. Mathematic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Operator (mathematics)
In mathematics, an operator is generally a mapping or function that acts on elements of a space to produce elements of another space (possibly and sometimes required to be the same space). There is no general definition of an ''operator'', but the term is often used in place of ''function'' when the domain is a set of functions or other structured objects. Also, the domain of an operator is often difficult to be explicitly characterized (for example in the case of an integral operator), and may be extended to related objects (an operator that acts on functions may act also on differential equations whose solutions are functions that satisfy the equation). See Operator (physics) for other examples. The most basic operators are linear maps, which act on vector spaces. Linear operators refer to linear maps whose domain and range are the same space, for example \R^n to \R^n. Such operators often preserve properties, such as continuity. For example, differentiation and indef ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Steady Flow
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) and hydrodynamics (the study of liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and modelling fission weapon detonation. Fluid dynamics offers a systematic structure—which underlies these practical disciplines—that embraces empirical and semi-empirical laws derived from flow measurement and used to solve practical problems. The solution to a fluid dynamics problem typically involves the calculation of various properties of the fluid, such as flow velocity, pressure, density, and temperature, as functions of space and time. Be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partial Differential Equations
In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similarly to how is thought of as an unknown number to be solved for in an algebraic equation like . However, it is usually impossible to write down explicit formulas for solutions of partial differential equations. There is, correspondingly, a vast amount of modern mathematical and scientific research on methods to numerically approximate solutions of certain partial differential equations using computers. Partial differential equations also occupy a large sector of pure mathematical research, in which the usual questions are, broadly speaking, on the identification of general qualitative features of solutions of various partial differential equations, such as existence, uniqueness, regularity, and stability. Among the many open questions are the e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elasticity (physics)
In physics and materials science, elasticity is the ability of a body to resist a distorting influence and to return to its original size and shape when that influence or force is removed. Solid objects will deform when adequate loads are applied to them; if the material is elastic, the object will return to its initial shape and size after removal. This is in contrast to ''plasticity'', in which the object fails to do so and instead remains in its deformed state. The physical reasons for elastic behavior can be quite different for different materials. In metals, the atomic lattice changes size and shape when forces are applied (energy is added to the system). When forces are removed, the lattice goes back to the original lower energy state. For rubbers and other polymers, elasticity is caused by the stretching of polymer chains when forces are applied. Hooke's law states that the force required to deform elastic objects should be directly proportional to the distance of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plasma Physics
Plasma ()πλάσμα , Henry George Liddell, Robert Scott, ''A Greek English Lexicon'', on Perseus is one of the . It contains a significant portion of charged particles – s and/or s. The presence of these charged particles is what primarily sets plasma apart from the other fundamental states of matter. It is the most abundant form of |
Magnetohydrodynamics
Magnetohydrodynamics (MHD; also called magneto-fluid dynamics or hydromagnetics) is the study of the magnetic properties and behaviour of electrically conducting fluids. Examples of such magnetofluids include plasmas, liquid metals, salt water, and electrolytes. The word ''magnetohydrodynamics'' is derived from ' meaning magnetic field, ' meaning water, and ' meaning movement. The field of MHD was initiated by Hannes Alfvén, for which he received the Nobel Prize in Physics in 1970. The fundamental concept behind MHD is that magnetic fields can induce currents in a moving conductive fluid, which in turn polarizes the fluid and reciprocally changes the magnetic field itself. The set of equations that describe MHD are a combination of the Navier–Stokes equations of fluid dynamics and Maxwell’s equations of electromagnetism. These differential equations must be solved simultaneously, either analytically or numerically. History The first record ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
