Abstract : The goal of this mini-symposium is to provide a forum for presenting and discussing recent advances in mathematical and numerical modelling of fluid motion. The phenomena under consideration range from small oscillations of fluid droplets to large ocean waves. Topics of interest cover nonlinear waves and solitons in fluids, surface and internal ocean waves, atmospheric flows, as well as fluid dynamics methods for fatigue fracture analysis. In this mini-symposium a holistic approach to fluid dynamics is sought where the problem is studied by modern mathematical methods requiring advanced tools in functional analysis, geometry, PDEs, soliton theory and numerical modeling.
[03903] Paradigm and Long-Time Evolution of Localized Solutions of Wave Systems: Consistency vs Integrability
Format : Talk at Waseda University
Author(s) :
Michail Todorov (Technical University of Sofia)
Abstract : Boussinesq’s equation was the first model for the propagation of surface waves over shallow inviscid fluid layer. He proved that the balance between the steepening effect of the nonlinearity and the flattening effect of the dispersion maintains the shape of the wave - so termed ‘Boussinesq Paradigm.’ Apart from the significance for the shallow water flows, this paradigm is very important for understanding the particle-like behavior of nonlinear localized waves. As it should have been expected, most of the physical systems are not fully integrable (even in one spatial dimension) and only a numerical approach can lead to unearthing the pertinent physical mechanisms of the interactions. A different approach to removing the incorrectness is by changing the spatial fourth derivative to a mixed fourth derivative, which resulted into an equation know nowadays as the Regularized Long Wave Equation or Benjamin–Bona–Mahony equation - known as the ‘Linear Impedance Relation’. The latter has produced innumerable instances of unphysical results.
[05180] Modelling of tsunami generated by submarine volcanic eruptions in statified oceans.
Format : Talk at Waseda University
Author(s) :
Manish kanojia (Trinity College Dublin)
Abstract :
We present a novel mathematical model for the generation of tsunamis by submarine volcanic eruptions in stratified oceans. Unlike current models, our model accounts for the complex stratification of the ocean, providing a more accurate representation of the tsunami generation process.
[05211] Physics-informed neural network for computating steady periodic water waves
Format : Online Talk on Zoom
Author(s) :
Lin Chen (Tongji University)
Ben Li (Tongji University)
Chenyi Luo (ETH Zurich)
Abstract : We investigate full-field recovery and computation of rotational flow under nonlinear periodic water waves using physics-informed neural networks (PINNs). Flow characteristics beneath water waves are of interest in various disciplines, e.g., for hydraulic loading analysis. In ocean or water tunnel tests, wave heights, flow velocity, and pressure data are often collected at specific points. It is not feasible to measure the flow with very high spatial resolution, particularly for water waves with a wavelength of over 100 m in practice. Therefore, we develop PINNs for flow recovery taking multiple types of measurement data into account and with the Euler equation governing rotational flow embedded. High-fidelity datasets are obtained using the numerical continuation method which is able to solve nonlinear waves with limiting wave height. Different PINN architectures are proposed and compared based on the numerically computed datasets. Influences of the wave height, vorticity, the volume of datasets, and hyperparameters are discussed in detail.
[01814] Pressure distribution on seawalls due to wave effects
Format : Talk at Waseda University
Author(s) :
Paul Suman (Indian Institute of Engineering Science and Technology, Shibpur)
Aparna Dey Ghosh (Indian Institute of Engineering Science and Technology, Shibpur)
Biswajit Basu (Trnity College Dublin)
Abstract : A numerical approach to obtain wave forces on seawalls is proposed using Bernoulli’s equation. The nonlinear formulation computes horizontal and vertical velocities, and pressure distribution along the depth, without any restriction on wave height. Forces are obtained on the seawall for nonbreaking travelling waves. The wave force increases for waves of longer time periods. The existing guidelines are found to overestimate the wave forces as compared to the forces obtained from the proposed nonlinear formulation.
[02962] Internal waves, Coriolis force and undercurrents
Format : Talk at Waseda University
Author(s) :
Rossen I. Ivanov (Technological University Dublin)
David J. Henry (University College Cork)
Abstract : We study the linear and nonlinear differential equations modelling the interacting surface and internal waves of two fluid layers with different densities over a flat bed. Other effects such as underlying currents and Coriolis force are also included. We use the Hamiltonian formulation for the nonlinear governing equations that is adequate for structure-preserving perturbations, at the linear and at the nonlinear level.
Specific weakly nonlinear long-wave regimes are structure-enhancing and the dynamics is described by integrable Hamiltonian equations. Consequently, integrable models and their soliton solutions will be presented.
[05173] On three dimensional models of equatorial ocean flows
Format : Talk at Waseda University
Author(s) :
BISWAJIT BASU (Trinity College Dublin)
Abstract : A recently developed three dimensional model of equatorial ocean flow is presented in this paper. The model is
inspired by the work of Constantin and Johnson and provides some explicit solution of velocity fields. The effect of
density variation is discussed alongwith the influence of undercurrent. Some additional insights are provided based on conservation of potential vorticity.
[03835] Eddy viscosities and ageostrophic wind-speed profiles
Format : Online Talk on Zoom
Author(s) :
Tony Lyons (South East Technological University)
Abstract : Wind speed profiles in the Ekman layer are used to deduce corresponding variable eddy coefficients. These eddy coefficients are parameterized in terms of a deflection angle, the geostrophic wind speed, and the transfer rate of horizontal momentum in the vertical direction. The classical Ekman flow has deflection angle $45^\circ$, while incorporating variable eddy coefficients changes this deflection angle. This deviation of deflection angle is used to estimate the depth of the Ekman layer.
