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Triple-deck Theory
Triple deck theory is a theory that describes a three-layered boundary-layer structure when sufficiently large disturbances are present in the boundary layer. This theory is able to successfully explain the phenomenon of boundary layer separation, but it has found applications in many other flow setups as well, including the scaling of the lower-branch instability ( T-S) of the Blasius flow, etc. James Lighthill, Lev Landau and others were the first to realize that to explain boundary layer separation, different scales other than the classical boundary-layer scales need to be introduced. These scales were first introduced independently by James Lighthill and E. A. Müller in 1953. The triple-layer structure itself was independently discovered by Keith Stewartson (1969) and V. Y. Neiland (1969) and by A. F. Messiter (1970). Stewartson and Messiter considered the separated flow near the trailing edge of a flat plate, whereas Neiland studied the case of a shock impinging on a boundary ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Flow Separation
In fluid dynamics, flow separation or boundary layer separation is the detachment of a boundary layer from a surface into a wake. A boundary layer exists whenever there is relative movement between a fluid and a solid surface with viscous forces present in the layer of fluid close to the surface. The flow can be externally, around a body, or internally, in an enclosed passage. Boundary layers can be either laminar or turbulent. A reasonable assessment of whether the boundary layer will be laminar or turbulent can be made by calculating the Reynolds number of the local flow conditions. Separation occurs in flow that is slowing down, with pressure increasing, after passing the thickest part of a streamline body or passing through a widening passage, for example. Flowing against an increasing pressure is known as flowing in an adverse pressure gradient. The boundary layer separates when it has travelled far enough in an adverse pressure gradient that the speed of the bounda ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Tollmien–Schlichting Wave
In fluid dynamics, a Tollmien–Schlichting wave (often abbreviated T-S wave) is a streamwise unstable wave which arises in a bounded shear flow (such as boundary layer and channel flow). It is one of the more common methods by which a laminar bounded shear flow transitions to turbulence. The waves are initiated when some disturbance (sound, for example) interacts with leading edge roughness in a process known as receptivity. These waves are slowly amplified as they move downstream until they may eventually grow large enough that nonlinearities take over and the flow transitions to turbulence. These waves, originally discovered by Ludwig Prandtl, were further studied by two of his former students, Walter Tollmien and Hermann Schlichting after whom the phenomenon is named. Also, the T-S wave is defined as the most unstable eigen-mode of Orr–Sommerfeld equations. Physical mechanism In order for a boundary layer to be absolutely unstable (have an inviscid instability), it must sat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Blasius Boundary Layer
In physics and fluid mechanics, a Blasius boundary layer (named after Paul Richard Heinrich Blasius) describes the steady two-dimensional laminar boundary layer that forms on a semi-infinite plate which is held parallel to a constant unidirectional flow. Falkner and Skan later generalized Blasius' solution to wedge flow (Falkner–Skan boundary layer), i.e. flows in which the plate is not parallel to the flow. Prandtl's boundary layer equations Using scaling arguments, Ludwig Prandtl argued that about half of the terms in the Navier-Stokes equations are negligible in boundary layer flows (except in a small region near the leading edge of the plate). This leads to a reduced set of equations known as the Boundary layer#Boundary layer equations, boundary layer equations. For steady incompressible flow with constant viscosity and density, these read: * Mass Continuity: \dfrac + \dfrac = 0 * x-Momentum: u \dfrac + v \dfrac = - \dfrac \dfrac + \dfrac * y-Momentum: 0 = - \dfrac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
James Lighthill
Sir Michael James Lighthill (23 January 1924 – 17 July 1998) was a British applied mathematician, known for his pioneering work in the field of aeroacoustics and for writing the Lighthill report in 1973, which pessimistically stated that "In no part of the field (of AI) have the discoveries made so far produced the major impact that was then promised", contributing to the gloomy climate of AI winter. Education and early life James Lighthill was born to Ernest Balzar Lichtenberg and Marjorie Holmes: an Alsatian mining engineer who changed his name to Lighthill in 1917, and the daughter of an engineer. The family lived in Paris until 1927, when the father retired and returned to live in England. As a young man, James Lighthill was known as Michael Lighthill. Lighthill was educated at Winchester College, and graduated with a Bachelor of Arts degree from the University of Cambridge where he was an undergraduate student of Trinity College, Cambridge in 1943. Career and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Lev Landau
Lev Davidovich Landau (; 22 January 1908 – 1 April 1968) was a Soviet physicist who made fundamental contributions to many areas of theoretical physics. He was considered as one of the last scientists who were universally well-versed and made seminal contributions to all branches of physics. He is credited with laying the foundations of twentieth century condensed matter physics, and is also considered arguably the greatest Soviet theoretical physicist. His accomplishments include the independent co-discovery of the density matrix method in quantum mechanics (alongside John von Neumann), the quantum mechanical theory of diamagnetism, the theory of superfluidity, the theory of second-order phase transitions, invention of order parameter technique, the Ginzburg–Landau theory of superconductivity, the theory of Fermi liquids, the explanation of Landau damping in plasma physics, the Landau pole in quantum electrodynamics, the two-component theory of neutrinos, and Landau's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Keith Stewartson
Keith Stewartson (20 September 1925 – 7 May 1983) was an English mathematician and fellow of the Royal Society. Early life The youngest of three children, Stewartson was born to an English baker in 1925. He was raised in Billingham, County Durham, where he attended Stockton Secondary School, and went to St Catharine's College, Cambridge in 1942. He won the Drury Prize in 1943 for his work in the Mathematical Tripos. Career After graduation, with the Second World War still on-going, Stewartson began employment with the Ministry of Aircraft Production. During his time there he studied compressible fluid flow problems. After the war he returned to Cambridge and received the Mayhew Prize in 1946. He resumed research under the guidance of Leslie Howarth on boundary layer theory. His research led to his first publication, "Correlated incompressible and compressible boundary layers", which was published by the Royal Society in 1949. He received his doctorate the same year and b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Mathematika
''Mathematika'' is a peer-reviewed mathematics journal that publishes both pure and applied mathematical articles. The journal was founded by Harold Davenport in the 1950s. The journal is published by the London Mathematical Society, on behalf of the journal's owner University College London. Indexing and abstracting According to the ''Journal Citation Reports'', the journal has a 2023 impact factor of 0.8. The journal is indexed in the following bibliographic databases: * MathSciNet * Science Citation Index Expanded * Web of Science * Zentralblatt MATH zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Information Infrastru ... References {{reflist London Mathematical Society Mathematics education in the United Kingdom Mathematics journals Academic journals established in 1954 Quarterly journals Wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Reynolds Number
In fluid dynamics, the Reynolds number () is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between Inertia, inertial and viscous forces. At low Reynolds numbers, flows tend to be dominated by laminar flow, laminar (sheet-like) flow, while at high Reynolds numbers, flows tend to be turbulence, turbulent. The turbulence results from differences in the fluid's speed and direction, which may sometimes intersect or even move counter to the overall direction of the flow (Eddy (fluid dynamics), eddy currents). These eddy currents begin to churn the flow, using up energy in the process, which for liquids increases the chances of cavitation. The Reynolds number has wide applications, ranging from liquid flow in a pipe to the passage of air over an aircraft wing. It is used to predict the transition from laminar–turbulent transition, laminar to turbulent flow and is used in the scaling of similar but different-sized fl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Ludwig Prandtl
Ludwig Prandtl (4 February 1875 – 15 August 1953) was a German Fluid mechanics, fluid dynamicist, physicist and aerospace scientist. He was a pioneer in the development of rigorous systematic mathematical analyses which he used for underlying the science of aerodynamics, which have come to form the basis of the applied science of aeronautical engineering. In the 1920s, he developed the mathematical basis for the fundamental principles of Subsonic flight, subsonic aerodynamics in particular; and in general up to and including transonic velocities. His studies identified the boundary layer, thin-Airfoil, airfoils, and Lifting-line theory, lifting-line theories. The Prandtl number was named after him. Early years Prandtl was born in Freising, near Munich, on 4 February 1875. His mother suffered from a lengthy illness and, as a result, Ludwig spent more time with his father, a professor of engineering. His father also encouraged him to observe nature and think about his observati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Stream Function
In fluid dynamics, two types of stream function (or streamfunction) are defined: * The two-dimensional (or Lagrange) stream function, introduced by Joseph Louis Lagrange in 1781, is defined for incompressible flow, incompressible (divergence-free), two-dimensional fluid flow, flows. * The Stokes stream function, named after George Gabriel Stokes, is defined for incompressible, three-dimensional flows with axisymmetry. The properties of stream functions make them useful for analyzing and graphically illustrating flows. The remainder of this article describes the two-dimensional stream function. Two-dimensional stream function Assumptions The two-dimensional stream function is based on the following assumptions: * The flow field can be described as two-dimensional plane flow, with velocity vector : \quad \mathbf = \begin u (x,y,t) \\ v (x,y,t) \\ 0 \end. * The velocity satisfies the continuity equation for incompressible flow: : \quad \nabla \cdot \mathbf = 0. * The domain h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Cauchy Principal Value
In mathematics, the Cauchy principal value, named after Augustin-Louis Cauchy, is a method for assigning values to certain improper integrals which would otherwise be undefined. In this method, a singularity on an integral interval is avoided by limiting the integral interval to the non singular domain. Formulation Depending on the type of singularity in the integrand , the Cauchy principal value is defined according to the following rules: In some cases it is necessary to deal simultaneously with singularities both at a finite number and at infinity. This is usually done by a limit of the form \lim_\, \lim_ \,\left ,\int_^ f(x)\,\mathrmx \,~ + ~ \int_^ f(x)\,\mathrmx \,\right In those cases where the integral may be split into two independent, finite limits, \lim_ \, \left, \,\int_a^ f(x)\,\mathrmx \,\\; < \;\infty and then the function is integrable in the ordinary sense. Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Hilbert Transform
In mathematics and signal processing, the Hilbert transform is a specific singular integral that takes a function, of a real variable and produces another function of a real variable . The Hilbert transform is given by the Cauchy principal value of the convolution with the function 1/(\pi t) (see ). The Hilbert transform has a particularly simple representation in the frequency domain: It imparts a phase shift of ±90° (/2 radians) to every frequency component of a function, the sign of the shift depending on the sign of the frequency (see ). The Hilbert transform is important in signal processing, where it is a component of the Analytic signal, analytic representation of a real-valued signal . The Hilbert transform was first introduced by David Hilbert in this setting, to solve a special case of the Riemann–Hilbert problem for analytic functions. Definition The Hilbert transform of can be thought of as the convolution of with the function , known as the Cauchy ker ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
