Smoke introduced into the boundary layer of a cone rotating in a stream highlights the transition from laminar to turbulent flow. On the left side of the picture, the boundary layer is uniform and steady, i.e. laminar, until environmental disturbances cause the formation of spiral vortices. These vortices remain stable until further growing disturbances cause them to develop a lacy structure, which soon breaks down into fully turbulent flow. Understanding the underlying physics of these disturbances and their growth is part of the field of stability and transition in fluid mechanics. (Photo credit: R. Kobayashi, Y. Kohama, and M. Kurosawa; taken from Van Dyke’s An Album of Fluid Motion)
Tag: transition
Smoke Transition
Smoke issuing from a round jet undergoes transition from laminar to turbulent flow. As the smoke moves past the unmoving ambient air, the friction between these two layers creates shear and triggers a Kelvin-Helmholtz instability, recognizable by the formation and roll up of vortices along the edges of the jet. Those vortices then roll together in pairs, detach, and devolve into a generally turbulent flow. Because turbulence is far more efficient at mixing than a laminar flow is, the smoke seems to disappear.
Toroidal Vortex
When instabilities exist in laminar flow, they do not always lead immediately to turbulence. In this video, a viscous fluid fills the space between two concentric cylinders. As the inner cylinder rotates, a linear velocity profile (as viewed from above) forms; this is known as Taylor-Couette flow. If any tiny perturbations are added to that linear profile–say there is a nick in the surface of one of the cylinders–the flow will develop an instability. In this type of flow, an exchange of stabilities will occur. Rather than transitioning to turbulence, the fluid develops a stable secondary flow–the toroidal vortex highlighted by the dye in the video. If the rotation rate is increased further other instabilities will develop.
Osborne Reynolds and Transition
How and when flow through a pipe becomes turbulent has been a conundrum for fluid mechanicians since the days of Osbourne Reynolds (~1870s):
Typically, the laminar-to-turbulence transition is studied mathematically by linearizing the Navier-Stokes equations, the governing equations of fluid dynamics, then perturbing the system. These perturbations will gradually disappear in laminar flow, but if the flow is turbulent, they’ll grow and produce chaotic motion. The transition, then, is the critical point between these two.
However, for pipe flows, this linearized approach shows that the perturbations decay for all Reynolds numbers, even though this doesn’t happen in actual experiments. In the real world, as the Reynolds number increases, small, turbulent puffs begin to split and interact, and their lifetimes increase. Eventually, these puffs carry enough turbulence to transition the flow entirely. # (submitted by David T)
Reynolds on Transition
For although only the disciplined motion is recognized in military tactics, troops have another manner of motion when anything disturbs their order. And this is precisely how it is with water: it will move in a perfectly direct disciplined manner under some circumstances, while under others it becomes a mass of eddies and cross streams, which may be well likened to the motion of a whirling, struggling mob where each individual particle is obstructing the others. The larger the army, and the more rapid the evolutions, the greater the chance of disorder; so with fluid, the larger the channel, and the greater the velocity, the more chance of eddies.
Godspeed, Discovery!
The space shuttle, despite three decades of service, remains a triumph of engineering. Although it is nominally a space vehicle, fluid dynamics are vital throughout its operation. From the combustion in the engine to the overexpansion of the exhaust gases; from the turbulent plume of the shuttle’s wake to the life support and waste management systems on orbit, fluid mechanics cannot be escaped. Countless simulations and experiments have helped determine the forces, temperatures, and flight profiles for the vehicle during ascent and re-entry. Experiments have flown as payloads and hundreds of astronauts have “performed experiments in fluid mechanics” in microgravity. Since STS-114, flow transition experiments have even been mounted on the orbiter wing. The effort and love put into making these machines fly is staggering, but all things end. Godspeed to Discovery and her crew on this, her final mission!
Instability in a Jet
This photo shows the development of a flow instability in an axisymmetric jet. On the left, the jet is smooth and fully laminar, but, by the center of the photo, disturbances in the jet have grown large enough to distort the laminar profile. The jet is then in transition; by the right side of the frame, it has reached a turbulent state, as evidenced by the increased mixing (which causes the smoke to disperse more quickly) and intermittency of the flow. #
Wavy Vortices
Shown above is the flow between two concentric cylinders (Taylor-Couette flow). In the laminar regime, the velocity profile between the two cylinders is linear. As the rate of rotation of the inner cylinder increases, the flow develops toroidal vortices known as Taylor vortices, seen in the video above after 9 seconds or so. This is a fluid instability exhibited by transitional flow. Increasing the rotational rate further can result in wavy Taylor vortex flow. At high enough speeds, the flow will become completely turbulent.
Three Flows in One
These plumes of smoke demonstrate the three types of fluid flow: laminar, transitional, and turbulent. At the bottom of the photo, the plumes are smooth and orderly, as is typical for laminar flow. At the top, the smoke’s movement is chaotic and intermittent, full of turbulent eddies. Between these two stages, the flow is in transition; there is still some semblance of order to it, but disturbances in the plume are getting amplified and breaking down into turbulence.
Photo credit: J. Russo
