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This monograph presents cutting-edge research on dispersive wave
modelling, and the numerical methods used to simulate the
propagation and generation of long surface water waves. Including
both an overview of existing dispersive models, as well as recent
breakthroughs, the authors maintain an ideal balance between theory
and applications. From modelling tsunami waves to smaller scale
coastal processes, this book will be an indispensable resource for
those looking to be brought up-to-date in this active area of
scientific research. Beginning with an introduction to various
dispersive long wave models on the flat space, the authors
establish a foundation on which readers can confidently approach
more advanced mathematical models and numerical techniques. The
first two chapters of the book cover modelling and numerical
simulation over globally flat spaces, including adaptive moving
grid methods along with the operator splitting approach, which was
historically proposed at the Institute of Computational
Technologies at Novosibirsk. Later chapters build on this to
explore high-end mathematical modelling of the fluid flow over
deformed and rotating spheres using the operator splitting
approach. The appendices that follow further elaborate by providing
valuable insight into long wave models based on the potential flow
assumption, and modified intermediate weakly nonlinear weakly
dispersive equations. Dispersive Shallow Water Waves will be a
valuable resource for researchers studying theoretical or applied
oceanography, nonlinear waves as well as those more broadly
interested in free surface flow dynamics.
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