2-year postdoctoral position examining the wave-turbulent behaviour of gravity-capillary water waves.

I investigated the behaviour of quasi-resonant triad (k_1+k_2+k_3=0, \omega_1+\omega_2+\omega_3 =/= 0) solutions to the Charney-Hasegawa-Mima equation using numerical methods in Mathematica in combination with analytical methods. The CHM equation may be used to describe atmospheric Rossby waves, or waves and turbulence in a plasma. The equation contains a quadratic nonlinearity, meaning wavenumbers can interact as triads.By expressing the system in terms of Fourier modes, a set of coupled equations can be obtained which describe the interaction of each wave component in a quasi-resonant triad. I derived the conserved quantites for this system and was able to demonstrate that, for a given choice of amplitude scaling parameter and interaction strength, a stationary point of the system is guaranteed. I also explored limits in which one of the triad amplitudes was much smaller than the others.For this project, I solved the coupled ODE set using Mathematica, and applied analytical and asymptotic methods. I gave a presentation and wrote a short thesis.

I performed wave hindcasts using the third-generation wave model SWAN (Simulating Waves Nearshore) for different input parameters and compared with buoy records from the Winter of 2013/2014. This Winter was notable for its high number of powerful storms, leading to very large waves off the Atlantic Coast of Ireland.Using SWAN and wind fields provided by ECMWF, I performed hindcasts with various different choices of input parameters, such as timestep, bottom friction dissipation model, and parametrisations of wave triad/quartet interaction. I compared these hindcasts with wave buoy measurements, and performed statistical analyses to determine the best choice of input parameters for a given location.I delivered two presentations, designed an academic poster, and wrote a scientific report for this internship.