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Hydrodynamic Stability
In fluid dynamics, hydrodynamic stability is the field of study, 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 Hermann von Helmholtz, Helmholtz, William Thomson, 1st Baron Kelvin, Kelvin, John Strutt, 3rd Baron Rayleigh, Rayleigh and Osborne Reynolds, Reynolds during the nineteenth century. These foundations have given many useful tools to study hydrodynamic stability. These include Reynolds number, the Euler equations (fluid dynamics), 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 ... [...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 The following terms are used to describe leaf morphology in the description and taxonomy of plants. Leaves may be simple (that is, the leaf blade or 'lamina' is undivided) or compound (that is, the leaf blade is divided into two or more leaflets .... Proper nouns: * Laminar Research, a Columbia, South Carolina, software company * Icaro Laminar, an Italian hang gl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mode Of A Linear Field
Mode ( 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'' (book series), a quartet of novels by Piers Anthony * Modern Organization for Dance Evolvement, known as MODE, a 1970s modern dance organisation in New York * ''Mode'', a defunct Indonesian women's magazine 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kelvin Helmholz Wave Clouds
The kelvin (symbol: K) is the base unit for temperature in the International System of Units (SI). The Kelvin scale is an absolute temperature scale that starts at the lowest possible temperature (absolute zero), taken to be 0 K. By definition, the Celsius scale (symbol °C) and the Kelvin scale have the exact same magnitude; that is, a rise of 1 K is equal to a rise of 1 °C and vice versa, and any temperature in degrees Celsius can be converted to kelvin by adding 273.15. The 19th century British scientist Lord Kelvin first developed and proposed the scale. It was often called the "absolute Celsius" scale in the early 20th century. The kelvin was formally added to the International System of Units in 1954, defining 273.16 K to be the triple point of water. The Celsius, Fahrenheit, and Rankine scales were redefined in terms of the Kelvin scale using this definition. The 2019 revision of the SI now defines the kelvin in terms of energy by setting the Bol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bifurcation Theory
Bifurcation theory is the Mathematics, 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 mathematics, 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 differential equation, ordinary, Delay differential equation, delay or Partial differential equation, 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. Bifurcation types It is useful to divide bifurcations into two principal classes: * Local bif ... [...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] |
Incompressible Flow
In fluid mechanics, or more generally continuum mechanics, incompressible flow is a flow in which the material density does not vary over time. Equivalently, the divergence of an incompressible flow velocity is zero. Under certain conditions, the flow of compressible fluids can be modelled as incompressible flow to a good approximation. 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. Mathematically, this constraint implies that the material derivative (discussed below) of the density must vanish to ensure incompressible flow. Before introducing this constraint, we must apply the conservation of mass to generate the necessary relations. The mass is calculated by a volume integral of the density, \rho : : = . The conservation of mass requires that the time derivative of the mass inside a control volume be equal to the mass flux, J, acro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Operator (mathematics)
In mathematics, an operator is generally a Map (mathematics), mapping or function (mathematics), function that acts on elements of a space (mathematics), 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 of a function, domain is a set of functions or other structured objects. Also, the domain of an operator is often difficult to characterize explicitly (for example in the case of an integral operator), and may be extended so as to act on 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 from \mathbb^n to \mathbb^n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Steady Flow
In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases. It has several subdisciplines, including (the study of air and other gases in motion) and (the study of water and other 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, understanding large scale geophysical flows involving oceans/atmosphere 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 f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partial Differential Equations
In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives. The function is often thought of as an "unknown" that solves the equation, similar to how is thought of as an unknown number solving, e.g., an algebraic equation like . However, it is usually impossible to write down explicit formulae 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 existence an ... [...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 Crystal structure, 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 rubber elasticity, 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 Prop ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plasma Physics
Plasma () is a state of matter characterized by the presence of a significant portion of charged particles in any combination of ions or electrons. It is the most abundant form of ordinary matter in the universe, mostly in stars (including the Sun), but also dominating the rarefied intracluster medium and intergalactic medium. Plasma can be artificially generated, for example, by heating a neutral gas or subjecting it to a strong electromagnetic field. The presence of charged particles makes plasma electrically conductive, with the dynamics of individual particles and macroscopic plasma motion governed by collective electromagnetic fields and very sensitive to externally applied fields. The response of plasma to electromagnetic fields is used in many modern devices and technologies, such as plasma televisions or plasma etching. Depending on temperature and density, a certain number of neutral particles may also be present, in which case plasma is called partially ioni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magnetohydrodynamics
In physics and engineering, magnetohydrodynamics (MHD; also called magneto-fluid dynamics or hydromagnetics) is a model of electrically conducting fluids that treats all interpenetrating particle species together as a single Continuum mechanics, continuous medium. It is primarily concerned with the low-frequency, large-scale, magnetic behavior in Plasma (physics), plasmas and liquid metals and has applications in multiple fields including space physics, geophysics, astrophysics, and engineering. 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. History The MHD description of electrically conducting fluids was first developed by Hannes Alfvén in a 1942 paper published in Nature (journal), ''Nature'' titled "Existence of Electromagnetic–Hydrodynamic Waves" which outlined his discovery ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
