Video footage of Iceland’s Grimsvotn volcano erupting shows a massive turbulent plume of ash. The largest scales of the plume are of the order of hundreds, if not thousands of meters, and the eddies of the plume appear to move very slowly, especially far from the base. According to Kolmogorov, however, at the smallest scales of the flow (< 1 mm), the turbulent motions are isotropic. No one has been able to achieve Reynolds numbers high enough to fully prove or disprove Kolmogorov’s hypothesis, but natural events like volcanic eruptions produce some of the largest Reynolds numbers on earth. (See also: interview with videographer; via Gizmodo, jshoer)
Tag: turbulent flow
Combustion
Fluid dynamics are vital to combustion. Like here, many practical flames–such as those responsible for internal combustion in automobiles, jet engines, and rockets–are turbulent. The turbulence aids mixing of the fuel and oxidizer, resulting in more complete combustion and greater efficiency. #
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.
Volcanic Turbulence
One of the characteristics of turbulence is its large range of lengthscales. Consider the ash plume from this Japanese volcano. Some of the eddy structures are tens, if not hundreds, of meters in size, yet there is also coherence down to the scale of centimeters. In turbulence, energy cascades from these very large scales to scales small enough that viscosity can dissipate it. This is one of the great challenges in directly calculating or even simply modeling turbulence because no lengthscale can be ignore without affecting the accuracy of the results. #
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.
Effects of Viscosity
[original media no longer available]
Today’s video demonstrates the effect of viscosity, which measures a fluid’s resistance to deformation. On the left is a column of highly viscous fluid; the fluids become less viscous as one moves right. When a jet of dye is released into the highly viscous fluid, the jet is very slow to penetrate, whereas, in the rightmost column, the dye expands quickly into a turbulent jet. Between these extremes, we see a laminar dye jet entering the liquid. The mushroom-like shape the laminar jet takes is the result of the Rayleigh-Taylor instability, which occurs when a denser fluid is on top of a lighter fluid in a gravitational field.
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
