Research

Anyone who swims in the ocean knows how waves can push you around even when they don't break. As the wave crest approaches, you get pulled towards the wave, rise up over the crest, get pushed forwards, and sink back down. It might seem like you're right back where you've started, but if you track the trajectory of an individual fluid particle, it would slowly drift in the direction of wave propagation (see video below). This effect is commonly referred to as the Stokes drift, and it transports more than just water. Anything that floats near the surface, be it plankton or marine litter, is constantly being pushed around by the motion of the waves, potentially travelling very far from their initial location.

In the original 1847 derivation, this drift mostly fell out of the math, and physical explanations for its existence tended to come post factum. In my first paper I answered the following questions:

1. Why, fundamentally, should irrotational surface waves induce a mean motion of water?
2. What sets its magnitude and direction?
3. How is this drift related to other physical quantities such as vorticity and energy density?

Any practical model of the wave-induced drift must account for the fact that the real ocean consists of many different waves which superimpose and interact. In almost all cases, it is assumed the total drift is just a sum of the individual drifts of each wave, with no interaction between different wave components. Using a combination of laboratory data, numerical simulations, and theoretical predictions, I show that this assumption can significantly underpredict the total drift when waves superimpose and steepen.

A plunging breaking wave is one of the most powerful and fasinating displays of fluid mechanics in nature. However, there is no satisfactory analytical solution that describes both their shape and dynamics. In this project I'm seeking analytical free-surface solutions which approximate the behavior in the barrel of breaking waves.