Extended mild-slope equations for compressible fluids
Emiliano Renzi
C. Cecioni
G. Bellotti
Paolo Sammarco
F. Dias
2134/18142
https://repository.lboro.ac.uk/articles/conference_contribution/Extended_mild-slope_equations_for_compressible_fluids/9376175
In this paper we derive new forms of the mildslope
equation (MSE) for water waves in a
weakly compressible fluid on a slowly varying
bathymetry, with surface and bottom disturbances.
The MSE is a powerful tool to model the
refraction-diffraction dynamics of water waves
propagating on a variable bathymetry [1]. Traditionally,
mild-slope models are derived by assuming
that the wave steepness is small, the fluid
is inviscid and incompressible and the motion
is irrotational. Furthermore, no disturbances
are normally considered both on the free surface
and at the bottom of the fluid domain [2]. In
this paper we shall find new expressions of the
MSE by relaxing the incompressibility hypothesis
and considering both surface and bottom disturbances.
We shall name the set of new formulae
as the extended acoustic-gravity mild-slope
equations (EAG-MSE). Such a system of equations
can be implemented in numerical models
for the early detection of coastal flooding based
on the hydro-acoustic precursors of surface gravity
waves (see [3]–[5]).
2015-07-03 11:06:10
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Mathematical Sciences not elsewhere classified