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Lamb–Oseen Vortex
In fluid dynamics, the Lamb–Oseen vortex models a line vortex that decays due to viscosity. This vortex is named after Horace Lamb and Carl Wilhelm Oseen. Mathematical description Oseen looked for a solution for the Navier–Stokes equations in cylindrical coordinates (r,\theta,z) with velocity components (v_r,v_\theta,v_z) of the form :v_r=0, \quad v_\theta=\fracg(r,t), \quad v_z=0. where \Gamma is the circulation of the vortex core. Navier-Stokes equations lead to :\frac = \nu\left(\frac - \frac \frac\right) which, subject to the conditions that it is regular at r=0 and becomes unity as r\rightarrow\infty, leads to :g(r,t) = 1-\mathrm^, where \nu is the kinematic viscosity of the fluid. At t=0, we have a potential vortex with concentrated vorticity at the z axis; and this vorticity diffuses away as time passes. The only non-zero vorticity component is in the z direction, given by :\omega_z(r,t) = \frac \mathrm^. The pressure field simply ensures the vortex rotate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fluid Dynamics
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. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pressure
Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and even by industry. Further, both spellings are often used ''within'' a particular industry or country. Industries in British English-speaking countries typically use the "gauge" spelling. is the pressure relative to the ambient pressure. Various units are used to express pressure. Some of these derive from a unit of force divided by a unit of area; the SI unit of pressure, the pascal (Pa), for example, is one newton per square metre (N/m2); similarly, the pound-force per square inch (psi) is the traditional unit of pressure in the imperial and U.S. customary systems. Pressure may also be expressed in terms of standard atmospheric pressure; the atmosphere (atm) is equal to this pressure, and the torr is defined as of this. Manometric u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kaufmann (Scully) Vortex
The Kaufmann vortex, also known as the Scully model, is a mathematical model for a vortex taking account of viscosity.Mahendra J. Bhagwat and J. Gordon LeishmanGeneralized Viscous Vortex Model for Application to Free-Vortex Wake and Aeroacoustic Calculations, University of Maryland It uses an algebraic velocity profile. This vortex is not a solution of the Navier–Stokes equations. Kaufmann and Scully's model for the velocity in the Θ direction is: :V_\Theta\ (r) = \frac \frac The model was suggested by W. Kaufmann in 1962, and later by Scully and Sullivan in 1972 at the Massachusetts Institute of Technology.Scully, M. P., and Sullivan, J. P., “Helicopter Rotor Wake Geometry and Airloads and Development of Laser Doppler Velocimeter for Use in Helicopter Rotor Wakes,” Massachusetts Institute of Technology Aerophysics Laboratory Technical Report 183, MIT DSR No. 73032, August 1972 See also * Rankine vortex – a simpler, but more crude, approximation for a vortex. * Lamb–O ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rankine Vortex
The Rankine vortex is a simple mathematical model of a vortex in a Viscosity, viscous fluid. It is named after its discoverer, William John Macquorn Rankine. The vortices observed in nature are usually modelled with an Potential flow#Examples of two-dimensional flows#Line vortex, irrotational (potential or free) vortex. However, in potential vortex, the velocity becomes infinite at the vortex center. In reality, very close to the origin, the motion resembles a solid body rotation. The Rankine vortex model assumes a solid-body rotation inside a cylinder of radius a and a potential vortex outside the cylinder. The radius a is referred to as the vortex-core radius. The velocity components (v_r,v_\theta,v_z) of the Rankine vortex, expressed in terms of the cylindrical-coordinate system (r,\theta,z) are given by :v_r=0,\quad v_\theta(r) = \frac\begin r/a^2 & r \le a, \\ 1/ r & r > a \end, \quad v_z = 0 where \Gamma is the Circulation (fluid dynamics), circulation strength of the Rank ... [...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. At the same time, viscous diffusion tends to spread the vorticity. The stationary Burgers vortex arises when the two effects 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: :v_r= -\alpha r, :v_z=2\alpha z, :v_\theta=\fracg(r), where \alpha>0 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stagnation Point Flow
In fluid dynamics, stagnation point flow represents the flow of a fluid in the immediate neighborhood of a stagnation point (or a stagnation line) with which the stagnation point (or the line) is identified for a potential flow or inviscid flow. The flow specifically considers a class of stagnation points known as saddle points where the 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 orthogonally, a stagnation plane is created, where the incoming streams are diverted tangentially outwards; thus on the stagnation plane, the velocity component normal to t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Self-similar Solution
In the study of partial differential equations, particularly in fluid dynamics, a self-similar solution is a form of solution which is similar to itself if the independent and dependent variables are appropriately scaled. Self-similar solutions appear whenever the problem lacks a characteristic length or time scale (for example, the Blasius boundary layer of an infinite plate, but not of a finite-length plate). These include, for example, the Blasius boundary layer or the Sedov–Taylor shell. Concept A powerful tool in physics is the concept of dimensional analysis and scaling laws. By examining the physical effects present in a system, we may estimate their size and hence which, for example, might be neglected. In some cases, the system may not have a fixed natural length or time scale, while the solution depends on space or time. It is then necessary to construct a scale using space or time and the other dimensional quantities present—such as the viscosity \nu. These constru ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Centripetal
A centripetal force (from Latin ''centrum'', "center" and ''petere'', "to seek") is a force that makes a body follow a curved trajectory, path. Its direction is always orthogonality, orthogonal to the motion of the body and towards the fixed point of the instantaneous osculating circle, center of curvature of the path. Isaac Newton described it as "a force by which bodies are drawn or impelled, or in any way tend, towards a point as to a centre". In Newtonian mechanics, gravity provides the centripetal force causing astronomical orbits. One common example involving centripetal force is the case in which a body moves with uniform speed along a circular path. The centripetal force is directed at right angles to the motion and also along the radius towards the centre of the circular path. The mathematical description was derived in 1659 by the Dutch physicist Christiaan Huygens. Formula The magnitude of the centripetal force on an object of mass ''m'' moving at Speed#Tangenti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circumference
In geometry, the circumference (from Latin ''circumferens'', meaning "carrying around") is the perimeter of a circle or ellipse. That is, the circumference would be the arc length of the circle, as if it were opened up and straightened out to a line segment. More generally, the perimeter is the curve length around any closed figure. Circumference may also refer to the circle itself, that is, the locus corresponding to the edge of a disk. The is the circumference, or length, of any one of its great circles. Circle The circumference of a circle is the distance around it, but if, as in many elementary treatments, distance is defined in terms of straight lines, this cannot be used as a definition. Under these circumstances, the circumference of a circle may be defined as the limit of the perimeters of inscribed regular polygons as the number of sides increases without bound. The term circumference is used when measuring physical objects, as well as when considering abstract g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vorticity
In continuum mechanics, vorticity is a pseudovector 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 \vec is the curl of the flow velocity \vec: :\vec \equiv \nabla \times \vec\,, where \nabla is the nabla operator. Conceptually, \vec 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 \vec would be twice the mean angular velocity vector of those particles relative to their center of mass, oriented according to the right-hand rule. In a two-dimensional fl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vortex
In fluid dynamics, a vortex ( : vortices or vortexes) is a region in a fluid in which the flow revolves around an axis line, which may be straight or curved. Vortices form in stirred fluids, and may be observed in smoke rings, whirlpools in the wake of a boat, and the winds surrounding a tropical cyclone, tornado or dust devil. Vortices are a major component of turbulent flow. The distribution of velocity, vorticity (the curl of the flow velocity), as well as the concept of circulation are used to characterise vortices. In most vortices, the fluid flow velocity is greatest next to its axis and decreases in inverse proportion to the distance from the axis. In the absence of external forces, viscous friction within the fluid tends to organise the flow into a collection of irrotational vortices, possibly superimposed to larger-scale flows, including larger-scale vortices. Once formed, vortices can move, stretch, twist, and interact in complex ways. A moving vortex carries s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kinematic Viscosity
The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the internal frictional force between adjacent layers of fluid that are in relative motion. For instance, when a viscous fluid is forced through a tube, it flows more quickly near the tube's axis than near its walls. Experiments show that some stress (such as a pressure difference between the two ends of the tube) is needed to sustain the flow. This is because a force is required to overcome the friction between the layers of the fluid which are in relative motion. For a tube with a constant rate of flow, the strength of the compensating force is proportional to the fluid's viscosity. In general, viscosity depends on a fluid's state, such as its temperature, pressure, and rate of deformation. However, the dependence on some of these properties is n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
