In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to a laminar flow, which occurs when a fluid flows in parallel layers, with no disruption between those layers.
In fluid dynamics, a vortex 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.
In continuum mechanics, the vorticity is a pseudovector field that describes the local spinning motion of a continuum near some point, as would be seen by an observer located at that point and traveling along with the flow.
The Ekman number (Ek) is a dimensionless number used in fluid dynamics to describe the ratio of viscous forces to Coriolis forces. It is frequently used in describing geophysical phenomena in the oceans and atmosphere in order to characterise the ratio of viscous forces to the Coriolis forces arising from planetary rotation. It is named after the Swedish oceanographer Vagn Walfrid Ekman.
In fluid dynamics, a Kármán vortex street is a repeating pattern of swirling vortices, caused by a process known as vortex shedding, which is responsible for the unsteady separation of flow of a fluid around blunt bodies. It is named after the engineer and fluid dynamicist Theodore von Kármán, and is responsible for such phenomena as the "singing" of suspended telephone or power lines and the vibration of a car antenna at certain speeds.
In fluid dynamics, Couette flow is the flow of a viscous fluid in the space between two surfaces, one of which is moving tangentially relative to the other. The configuration often takes the form of two parallel plates or the gap between two concentric cylinders. The flow is driven by virtue of viscous drag force acting on the fluid, but may additionally be motivated by an applied pressure gradient in the flow direction. The Couette configuration models certain practical problems, like flow in lightly loaded journal bearings, and is often employed in viscometry and to demonstrate approximations of reversibility. This type of flow is named in honor of Maurice Couette, a Professor of Physics at the French University of Angers in the late 19th century.
Stokes flow, also named creeping flow or creeping motion, is a type of fluid flow where advective inertial forces are small compared with viscous forces. The Reynolds number is low, i.e. . This is a typical situation in flows where the fluid velocities are very slow, the viscosities are very large, or the length-scales of the flow are very small. Creeping flow was first studied to understand lubrication. In nature this type of flow occurs in the swimming of microorganisms and sperm and the flow of lava. In technology, it occurs in paint, MEMS devices, and in the flow of viscous polymers generally.
In fluid dynamics, the Taylor–Couette flow consists of a viscous fluid confined in the gap between two rotating cylinders. For low angular velocities, measured by the Reynolds number Re, the flow is steady and purely azimuthal. This basic state is known as circular Couette flow, after Maurice Marie Alfred Couette, who used this experimental device as a means to measure viscosity. Sir Geoffrey Ingram Taylor investigated the stability of Couette flow in a ground-breaking paper. Taylor's paper became a cornerstone in the development of hydrodynamic stability theory and demonstrated that the no-slip condition, which was in dispute by the scientific community at the time, was the correct boundary condition for viscous flows at a solid boundary.
Inertial waves, also known as inertial oscillations, are a type of mechanical wave possible in rotating fluids. Unlike surface gravity waves commonly seen at the beach or in the bathtub, inertial waves flow through the interior of the fluid, not at the surface. Like any other kind of wave, an inertial wave is caused by a restoring force and characterized by its wavelength and frequency. Because the restoring force for inertial waves is the Coriolis force, their wavelengths and frequencies are related in a peculiar way. Inertial waves are transverse. Most commonly they are observed in atmospheres, oceans, lakes, and laboratory experiments. Rossby waves, geostrophic currents, and geostrophic winds are examples of inertial waves. Inertial waves are also likely to exist in the molten core of the rotating Earth.
The Spalart–Allmaras model is a one-equation model that solves a modelled transport equation for the kinematic eddy turbulent viscosity. The Spalart–Allmaras model was designed specifically for aerospace applications involving wall-bounded flows and has been shown to give good results for boundary layers subjected to adverse pressure gradients. It is also gaining popularity in turbomachinery applications.
In fluid dynamics, Görtler vortices are secondary flows that appear in a boundary layer flow along a concave wall. If the boundary layer is thin compared to the radius of curvature of the wall, the pressure remains constant across the boundary layer. On the other hand, if the boundary layer thickness is comparable to the radius of curvature, the centrifugal action creates a pressure variation across the boundary layer. This leads to the centrifugal instability of the boundary layer and consequent formation of Görtler vortices.
A Taylor column is a fluid dynamics phenomenon that occurs as a result of the Coriolis effect. It was named after Geoffrey Ingram Taylor. Rotating fluids that are perturbed by a solid body tend to form columns parallel to the axis of rotation called Taylor columns.
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. 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.
The Reynolds number is an important dimensionless quantity in fluid mechanics used to help predict flow patterns in different fluid flow situations. At low Reynolds numbers, flows tend to be dominated by laminar (sheet-like) flow, while at high Reynolds numbers 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. 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 to turbulent flow, and is used in the scaling of similar but different-sized flow situations, such as between an aircraft model in a wind tunnel and the full size version. The predictions of the onset of turbulence and the ability to calculate scaling effects can be used to help predict fluid behaviour on a larger scale, such as in local or global air or water movement and thereby the associated meteorological and climatological effects.
In fluid mechanics, dynamic similarity is the phenomenon that when there are two geometrically similar vessels with the same boundary conditions and the same Reynolds and Womersley numbers, then the fluid flows will be identical. This can be seen from inspection of the underlying Navier-Stokes equation, with geometrically similar bodies, equal Reynolds and Womersley Numbers the functions of velocity (u’,v’,w’) and pressure (P’) for any variation of flow.
Rossby Wave Instability (RWI) is a concept related to astrophysical discs. In non-self-gravitating discs, for example around newly forming stars, the instability can be triggered by an axisymmetric bump, at some radius , in the disc surface mass-density. It gives rise to exponentially growing non-axisymmetric perturbation [ , ] in the vicinity of consisting of anticyclonic vortices. These vortices are regions of high pressure and consequently act to trap dust particles which in turn can facilitate planetesimal growth in proto-planetary discs. The Rossby vortices in the discs around stars and black holes may cause the observed quasi-periodic modulations of the disc's thermal emission.
In fluid dynamics, the Craik–Leibovich (CL) vortex force describes a forcing of the mean flow through wave–current interaction, specifically between the Stokes drift velocity and the mean-flow vorticity. The CL vortex force is used to explain the generation of Langmuir circulations by an instability mechanism. The CL vortex-force mechanism was derived and studied by Sidney Leibovich and Alex D.D. Craik in the 1970s and 80s, in their studies of Langmuir circulations.
Von Kármán swirling flow is a flow created by a uniformly rotating infinitely long plane disk, named after Theodore von Kármán who solved the problem in 1921. This problem is used as a model for centrifugal fans or compressors. This flow is classified under the category of steady flows in which vorticity generated at a solid surface is prevented from diffusing far away by an opposing convection, the other examples being the Blasius boundary layer with suction, stagnation point flow etc.
In fluid dynamics, Stokes problem also known as Stokes second problem or sometimes referred to as Stokes boundary layer or Oscillating boundary layer is a problem of determining the flow created by an oscillating solid surface, named after Sir George Stokes. This is considered as one of the simplest unsteady problem that have exact solution for the Navier-Stokes equations. In turbulent flow, this is still named a Stokes boundary layer, but now one has to rely on experiments, numerical simulations or approximate methods in order to obtain useful information on the flow.
In fluid dynamics, Beltrami flows are flows in which the vorticity vector and the velocity vector are parallel to each other. In other words, Beltrami flow is a flow where Lamb vector is zero. It is named after the Italian mathematician Eugenio Beltrami due to his derivation of the Beltrami vector field, while initial developments in fluid dynamics were done by the Russian scientist Ippolit S. Gromeka in 1881.
