Development of an in-house Boundary Integral Code for simulating surface waves

Due to the relatively low kinematic viscosity of water, most theoretical models for surface gravity and capillary gravity waves in the ocean, assume irrotationality (curl zero) as the Reynolds number for free waves in the wavelength range 0.1 mm - 10 cm (capillary and capillary-gravity waves) are quite high (10^5 and above). However, the interfacial momentum boundary layer which is generated in the air and water side of these waves, generates interesting and occasionally surprising phenomena which cannot be rationalized within the irrotational approximation. For example, in a bursting bubble at an air-water interface, the momentum boundary layer affects the jet which accompanies this bursting, quite non-trivially. This phenomena has been extensively studied recently. This boundary layer has also been recently studied in our group (to appear shortly in J. Fluid Mechanics, 2025)

Focusing of concentric free-surface waves

In our group, we already have in-house developed as well as expertise with open-source codes which can solve the full Navier-Stokes  equation with a free-surface, thereby fully resolving the aforementioned boundary layer. The purpose of this project is to develop an inhouse BI code which can solve the Laplace equation numerically with a free-surface to simulate irrotational waves. The aim is to compare the evolution of these waves with and without this boundary layer to understand its role.

Preliminary work on this has been initiated by an UG student. The MTech student will work closely with a PhD student in this project. Please choose only if you are reasonably strong in Physics & Maths and have interest in coding and CFD.