An Introduction to Vortices and Vorticity - vortex.pdf
Prof. A.H. Techet
Department of Ocean Engineering
Massachusetts Institute of Technology
Cambridge, MA 02139
To better understand the fluid forcing produced by fish when they are swimming it is necessary to first discuss the basic concept of a vortex and vorticity. A vortex arises when flow encircles a central point. Examples of where vortices occur in nature include: whirlpools, tornados, ocean eddies, blood flow through heart valves, and flow swirling behind rocks in a river current. Vortices appear in engineering fluid applications as well: flow around offshore platforms, tip-vortices from aircraft wings, helical vortices in propeller wakes and helicopter rotors. In general, vortices can form when flow passes any object with a non-streamlined shape or a sharp corner, and separates from the body.
As will be shown in class, a swimming fish actively manipulates the surrounding fluid to produce a jet-like wake comprised of alternately signed vortices. This is in contrast to the wake behind a stationary bluff body in uniform inflow, which produces a drag wake. In both cases, the flow separates from the body and rolls up to form vortices shed alternately from one side of the body then the next. The vortices shed from one side of the body have opposite direction of rotation from those shed from the other side. In the case of the stationary bluff body, the vortices rotate such that the tangential velocity of each vortex along the centerline of the body points upstream. For the swimming fish, the tangential velocity of the vortices along the centerline of the wake is oriented aft of the fish, or downstream. The bluff body wake, such as a cylinder, is referred to as a classic vonKármán vortex street and the fish wake is often referred to as a reverse Kármán street. Figure 1 illustrates the vortex shedding configuration for a swimming fish and a stationary cylinder.
Figure 1: Differences in the wake formation behind a swimming fish and a stationary cylinder. The fish forms a jet like wake and the cylinder a classic drag wake. ...