FYFD

Tag: vortex line

  • Tornadogenesis

    Tornadogenesis

    Tornadogenesis–the formation of tornadoes–remains a topic of active research as there is relatively little direct experimental data, owing to the difficulty of prediction as well as measurement. Initially, a variation of wind speed at different altitudes in the atmosphere causes shearing, which can lead to the formation of a horizontal column of rotating air–a vortex line similar to a roll cloud. Beneath a developing storm, the updraft of warm local air can pull this vortex line upwards, creating vertical rotation in the cloud, thereby birthing a supercell.  Supercells do not always spawn tornadoes, and the exact causes that result in tornadic or nontornadic supercells are not fully understood.  However, the formation of tornadoes within the supercell seems dependent on the downdraft of cool air within the storm as well as stretching of the vortex line, which increases its rate of rotation. For more information, check out this explanatory video and some of the talks by Paul Markowski. (Thanks to mindscrib, aggieastronaut and others for their submissions related to this topic! Photo credits: P. Markowski and D. Zaras)

  • Smokestack Plumes

    Smokestack Plumes

    On a cold and windy day, the plume from a smokestack sometimes sinks downstream of the stack instead of immediately rising (Figure 1). This isn’t an effect of temperature–after all, the exhaust should be warm compared to the ambient, which would make it rise. It’s actually caused by vorticity.

    Figure 2: Simple geometry (side view)

    In Figure 2, we see a simplified geometry. The wind is blowing from right to left, and its velocity varies with height due to the atmospheric boundary layer. Mathematically, vorticity is the curl of the velocity vector, and because we have a velocity gradient, there is positive (counterclockwise) vorticity generated.

    Figure 3: Vortex lines (top view)

    According to Helmholtz, we can imagine this vorticity as a bunch of infinite vortex lines convecting toward the smokestack, shown in Figure 3. Those vortex lines pile up against the windward side of the smokestack–Helmholtz says that vortex lines can’t end in a fluid–and get stretched out in the wake of the stack. If we could stand upstream of the smokestack and look at the caught vortex line, we would see a downward velocity immediately behind the smokestack and an upward velocity to either side of the stack. It’s this downward velocity that pulls the smokestack’s plume downward.

    Figure 4: Vortex wrapped around stack

    Now Helmholtz’s theories actually apply to inviscid flows and the real world has viscosity in it–slight though its effects might be–and that’s why this effect will fade. The vortex lines can’t sit against the smokestack forever; viscosity dissipates them.