2026-08-13 –, Room 4
Interfacial water waves are governed by complex Euler equations, that satisfy non-trivial nonlinear travelling and standing wave solutions. Analyzing these solutions and their stability is important for understanding oceanic dynamics, from coastal impacts to mysteries like rogue waves. To streamline this, we introduce InterfacialWaves.jl, a Julia package that enables researchers to easily generate nonlinear wave equilibriums and analyze their stability to decode the secrets of breaking and rogue waves
InterfacialWaves.jl
InterfacialWaves.jl solves primarily for boundary-value and initial-value problems in travelling and standing interfacial wave equations.
Key Capabilities
The package enables users to numerically calculate waves to a very high accuracy. Features include:
* Wave Calculations:
* Stokes waves (travelling waves)
* Gravity-Capillary waves (travelling as well as standing waves)
* Viscous Gravity-Capillary waves (travelling waves)
* Standing Wave Solutions: Functions to calculate nonlinear, non-trivial standing wave solutions in wall-bounded containers (in both cartesian and axisymmetric settings). For example the video here demonstrates axisymmetric capillary standing waves .
* Linear Stability Analysis: Available for both travelling and standing waves across arbitrary modes.
* Symbolic-Numeric Interface: Allows solving initial-value problems for standing waves by programming standard perturbative methods.
Documentation
The package documentation is expected to be comprehensive description that covers:
* Basics and preliminaries of nonlinear interfacial waves.
* Examples showing the usage of methods exported by the package.
* Descriptions of the important API.
Dependencies
The package is built upon several well-known, publicly available Julia packages, such as:
OrdinaryDiffEq.jl, NonlinearSolve.jl, FFTW.jl, ApproxFun.jl, BifurcationKit.jl, Symbolics.jl, and ForwardDiff.jl.
Talk Overview
This talk is structured to showcase the package's abilities in simulating nonlinear interfacial waves, complete with validations against the known physics of interfacial waves.
I am a PhD student at IIT Bombay. My research interests are fluid dynamics, numerical methods and complex systems. My PhD work involves studying interfacial waves. I have been one of the major (maybe not that major ! ) contributors to Catalyst.jl. I have also contributed in small proportions to MethodOfLines.jl , DataDrivenDiffEq.jl and Symbolics.jl (very small contributions).