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Kerr–Dold Vortex
In fluid dynamics, Kerr–Dold vortex is an exact solution of Navier–Stokes equations, which represents steady periodic vortices superposed on the stagnation point flow (or extensional flow). The solution was discovered by Oliver S. Kerr and John W. Dold in 1994. These steady solutions exist as a result of a balance between vortex stretching by the extensional flow and viscous diffusion, which are similar to Burgers vortex. These vortices were observed experimentally in a four-roll mill apparatus by Lagnado and L. Gary Leal. Mathematical description The stagnation point flow, which is already an exact solution of the Navier–Stokes equation is given by \mathbf=(0,-Ay,Az), where A is the strain rate. To this flow, an additional periodic disturbance can be added such that the new velocity field can be written as :\mathbf=\begin0 \\-Ay \\ Az \end + \beginu(x,y) \\v(x,y) \\ 0 \end where the disturbance u(x,y) and v(x,y) are assumed to be periodic in the x direction with a fundam ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fluid Dynamics
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 moment (physics), moments on aircraft, determining the mass flow rate of petroleum through pipeline transport, pipelines, weather forecasting, predicting weather patterns, understanding nebulae in interstellar space, understanding large scale Geophysical fluid dynamics, geophysical flows involving oceans/atmosphere and Nuclear weapon design, 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 fl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Navier–Stokes Equations
The Navier–Stokes equations ( ) are partial differential equations which describe the motion of viscous fluid substances. They were named after French engineer and physicist Claude-Louis Navier and the Irish physicist and mathematician George Gabriel Stokes. They were developed over several decades of progressively building the theories, from 1822 (Navier) to 1842–1850 (Stokes). The Navier–Stokes equations mathematically express momentum balance for Newtonian fluids and make use of conservation of mass. They are sometimes accompanied by an equation of state relating pressure, temperature and density. They arise from applying Isaac Newton's second law to fluid motion, together with the assumption that the stress in the fluid is the sum of a diffusing viscous term (proportional to the gradient of velocity) and a pressure term—hence describing ''viscous flow''. The difference between them and the closely related Euler equations is that Navier–Stokes equat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stagnation Point Flow
In fluid dynamics, a stagnation point flow refers to a fluid flow in the Neighbourhood (mathematics), neighbourhood of a stagnation point (in two-dimensional flows) or a stagnation line (in three-dimensional flows) with which the stagnation point/line refers to a point/line where the velocity is zero in the inviscid approximation. The flow specifically considers a class of stagnation points known as saddle points wherein incoming streamlines gets deflected and directed outwards in a different direction; the streamline deflections are guided by separatrices. The flow in the neighborhood of the stagnation point or line can generally be described using potential flow theory, although viscous effects cannot be neglected if the stagnation point lies on a solid surface. Stagnation point flow without solid surfaces When two streams either of two-dimensional or axisymmetric nature impinge on each other, a stagnation plane is created, where the incoming streams are diverted tangentially out ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John W
John is a common English name and surname: * John (given name) * John (surname) John may also refer to: New Testament Works * Gospel of John, a title often shortened to John * First Epistle of John, often shortened to 1 John * Second Epistle of John, often shortened to 2 John * Third Epistle of John, often shortened to 3 John People * John the Baptist (died ), regarded as a prophet and the forerunner of Jesus Christ * John the Apostle (died ), one of the twelve apostles of Jesus Christ * John the Evangelist, assigned author of the Fourth Gospel, once identified with the Apostle * John of Patmos, also known as John the Divine or John the Revelator, the author of the Book of Revelation, once identified with the Apostle * John the Presbyter, a figure either identified with or distinguished from the Apostle, the Evangelist and John of Patmos Other people with the given name Religious figures * John, father of Andrew the Apostle and Saint Peter * Pope John (disambigu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vortex Stretching
In fluid dynamics, vortex stretching is the lengthening of vortices in three-dimensional fluid flow, associated with a corresponding increase of the component of vorticity in the stretching direction—due to the conservation of angular momentum. Vortex stretching is associated with a particular term in the vorticity equation. For example, vorticity transport in an incompressible inviscid flow is governed by : = \left(\vec \cdot \vec\right) \vec, where ''D/Dt'' is the material derivative. The source term on the right hand side is the vortex stretching term. It amplifies the vorticity \vec when the velocity is diverging in the direction parallel to \vec. A simple example of vortex stretching in a viscous flow is provided by the Burgers vortex. Vortex stretching is at the core of the description of the turbulence energy cascade from the large scales to the small scales in turbulence. In turbulence, fluid elements are, on average, more lengthened than squeezed. In the end, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Burgers Vortex
In fluid dynamics, the Burgers vortex or Burgers–Rott vortex is an exact solution to the Navier–Stokes equations governing viscous flow, named after Jan Burgers and Nicholas Rott. The Burgers vortex describes a stationary, self-similar flow. An inward, radial flow, tends to concentrate vorticity in a narrow column around the symmetry axis, while an axial stretching causes the vorticity to increase. At the same time, viscous diffusion tends to spread the vorticity. The stationary Burgers vortex arises when the three effects are in balance. The Burgers vortex, apart from serving as an illustration of the vortex stretching mechanism, may describe such flows as tornados, where the vorticity is provided by continuous convection-driven vortex stretching. Flow field The flow for the Burgers vortex is described in cylindrical (r,\theta,z) coordinates. Assuming axial symmetry (no \theta-dependence), the flow field associated with the axisymmetric stagnation point flow is considered: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Strain Rate
In mechanics and materials science, strain rate is the time derivative of strain of a material. Strain rate has dimension of inverse time and SI units of inverse second, s−1 (or its multiples). The strain rate at some point within the material measures the rate at which the distances of adjacent parcels of the material change with time in the neighborhood of that point. It comprises both the rate at which the material is expanding or shrinking (expansion rate), and also the rate at which it is being deformed by progressive shearing without changing its volume ( shear rate). It is zero if these distances do not change, as happens when all particles in some region are moving with the same velocity (same speed and direction) and/or rotating with the same angular velocity, as if that part of the medium were a rigid body. The strain rate is a concept of materials science and continuum mechanics that plays an essential role in the physics of fluids and deformable solids. In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vorticity
In continuum mechanics, vorticity is a pseudovector (or axial vector) field that describes the local spinning motion of a continuum near some point (the tendency of something to rotate), as would be seen by an observer located at that point and traveling along with the flow. It is an important quantity in the dynamical theory of fluids and provides a convenient framework for understanding a variety of complex flow phenomena, such as the formation and motion of vortex rings. Mathematically, the vorticity \boldsymbol is the curl of the flow velocity \mathbf v: :\boldsymbol \equiv \nabla \times \mathbf v\,, where \nabla is the nabla operator. Conceptually, \boldsymbol could be determined by marking parts of a continuum in a small neighborhood of the point in question, and watching their ''relative'' displacements as they move along the flow. The vorticity \boldsymbol would be twice the mean angular velocity vector of those particles relative to their center of mass, orie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cauchy Product
In mathematics, more specifically in mathematical analysis, the Cauchy product is the discrete convolution of two infinite series. It is named after the French mathematician Augustin-Louis Cauchy. Definitions The Cauchy product may apply to infinite series or power series. When people apply it to finite sequences or finite series, that can be seen merely as a particular case of a product of series with a finite number of non-zero coefficients (see discrete convolution). Convergence issues are discussed in the next section. Cauchy product of two infinite series Let \sum_^\infty a_i and \sum_^\infty b_j be two infinite series with complex terms. The Cauchy product of these two infinite series is defined by a discrete convolution as follows: :\left(\sum_^\infty a_i\right) \cdot \left(\sum_^\infty b_j\right) = \sum_^\infty c_k where c_k=\sum_^k a_l b_. Cauchy product of two power series Consider the following two power series :\sum_^\infty a_i x ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sullivan Vortex
In fluid dynamics, the Sullivan vortex is an exact solution of the Navier–Stokes equations describing a two-celled vortex in an axially strained flow, that was discovered by Roger D. Sullivan in 1959. At large radial distances, the Sullivan vortex resembles a Burgers vortex, however, it exhibits a two-cell structure near the center, creating a downdraft at the axis and an updraft at a finite radial location. Specifically, in the outer cell, the fluid spirals inward and upward and in the inner cell, the fluid spirals down at the axis and spirals upwards at the boundary with the outer cell. Due to its multi-celled structure, the vortex is used to model tornadoes and large-scale complex vortex structures in turbulent flows. Flow description Consider the velocity components (v_r,v_\theta,v_z) of an incompressible fluid in cylindrical coordinates in the form :v_r=- \alpha r + \frac f(\eta), :v_z=2\alpha z\left -f'(\eta)\right :v_\theta=\frac\frac, where \eta =\alpha r^2/(2\nu) and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flow Regimes
Flow may refer to: Science and technology * Flow (fluid), Fluid flow, the motion of a gas or liquid * Flow (geomorphology), a type of mass wasting or slope movement in geomorphology * Flow (mathematics), a group action of the real numbers on a set * Flow (psychology), a mental state of being fully immersed and focused * Flow, a spacecraft of NASA's GRAIL program Computing * Flow network, graph-theoretic version of a mathematical flow * Dataflow, a broad concept in computer systems with many different meanings * Microsoft Flow (renamed to Power Automate in 2019), a workflow toolkit in Microsoft Dynamics * Neos Flow, a free and open source web application framework written in PHP * webMethods Flow, a graphical programming language * FLOW (programming language), an educational programming language from the 1970s * Flow (web browser), a web browser with a proprietary rendering engine * Flow (Google), a generative AI video creation tool Arts, entertainment and media * Flow (journal), ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
