Branched Flow

The latest issue of physics today leads with an outstanding essay on the burgeoning field of “branched flow”. This new area of numerical physics brings together ideas from computation, visualization, fluid mechanics, complex systems all under the guise of classical ray tracing.

The authors introduce readers to the idea with the example of the Tsunami generated by the 2011 Tohoku Earthquake in Japan. The devastation was massive, and the height of the tsunami itself varied wildly from place to place. Modeling of the flow of water from NOAA satellites revealed that the tsunami was indeed branched flow, with large, distinct channels rather than a simple, collective expansion.

The main explanation for branches in fluid flow relates to the formation of caustics in phase space. Weak perturbations in the wave speed - generated either by fluctuations in refractive index or - in the case of the tsunami, water depth - that are larger than the wavelength set the stage for this complex behavior.

There’s also a fun, intuitive algorithm for creating flow branches in photoshop. As someone who has spent a lot of time with caustics and catastrophes in phase space, I wholly recommend the article.