Some of my ongoing work in collaboration with the University of Michigan and Los Alamos National Laboratory aims to understand how a fluid instability well known for dissipating airplane wakes and generating the patterns we see regularly in jet contrails is also responsible for clumping in circumstellar environments. Let's take a look at how contrails and circumstellar material might be related.
The top image in the figure shown below probably looks familiar - I captured this beautiful contrail with my phone while out on a walk (flight patterns at LAX and typical mid-afternoon atmospheric conditions in LA make the western view from Caltech ideal for spotting contrails). The vortices shed into the wake of the aircraft generate a counter-rotating vortex pair. The rotation in the vortices causes the pair to descend toward the surface of the earth, so in the reference frame of the pair, the contrail experiences an upward-pointing headwind. As the vortex pair propagates, fluid is ejected downstream (behind it, or upwards in this case), resulting in a thin sheet-like wake of condensed gas. Dynamics related to the initial formation of the vortex pair results in an initially thicker wake, which marks the origin of the pair. The action of the Crow instability causes the growth of perturbations along the vortices comprising the pair, which pushes the vortex cores together at regular locations where vortex reconnection triggers the reorganization of the vortex pair into a descending line of vortex rings. Eventually, these rings dissipate, but the gas they transported remains visible as the clumps.
Now let's consider a famous circumstellar environment, that which surrounds Supernova 1987A. As a result of dynamics that are thought to have occurred some twenty to forty thousand years in advance of the supernova, a torus of gaseous material encircled the dying star and was subject to its solar wind. If shear from the wind stimulated the formation of a counter-rotating vortex pair within the torus, like the one in airplane wakes but wrapped into a circle owing to the cylindrical nature of the system, we would expect to see some the same features in the supernova remnant as in contrails. The image on the bottom left of the figure below shows new data from the James Webb Space Telescope (Link to Article), revealing an unprecedented visualization of the material surrounding the supernova remnant that includes a thin sheet of gas spanning the space between a thick (bright) edge and an array of clumps, the number of which matches the prediction from Crow instability theory (Link to Article). Significant evidence therefore supports the hypothesis that dynamics in circumstellar environments including, but not limited to, that surrounding the progenitor of Supernova 1987A are akin to those in airplane wakes!
The image in the lower right of the figure below is the same contrail from earlier after applying a cylindrical coordinate transformation (i.e., wrapping it into a circle) such that the direction of the headwind now mirrors the radial outflow of the solar wind. I find the similarities between this contrail and the supernova remnant truly remarkable. The next time you see a contrail in the sky, perhaps you too will be amazed by and convinced of the connection between aircraft wakes and circumstellar environments.
Vivienne, Eddie, and Danica, three Pasadena-area high schoolers, spent part of their summers with me on campus at Caltech through the Summer Research Connection Program. I challenged them not only to learn an enormous amount of fluid mechanics, but also to put their skills to use in designing experiments to test their very own hypotheses regarding the behavior of vortices. Their work ethic, ability to grasp advanced concepts, and intellectual curiosity absolutely blew me away! Check out their end-of-summer presentation here: Link to Presentation
Axel spent the summer with the Shepherd Research Group developing a platform for generating circular vortex pairs and using it to study the Crow instability. This instability is famous in aeronautics for dissipating airplane wakes, and its dynamics can often be viewed in real time in jet contrails. Axel's significant contributions to this project show how the instability also affects interacting vortex rings.