On the resonance hypothesis of storm surge and surf beat run-up
Resonance has recently been proposed as the fundamental underlying mechanism that shapes the amplification in coastal run-up for storm surges and surf beats, which are long-wavelength disturbances created by fluid velocity differences between the wave groups and the regions outside the wave group...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Copernicus Publications
2017-06-01
|
| Series: | Natural Hazards and Earth System Sciences |
| Online Access: | http://www.nat-hazards-earth-syst-sci.net/17/905/2017/nhess-17-905-2017.pdf |
| Summary: | Resonance has recently been proposed as the fundamental underlying mechanism
that shapes the amplification in coastal run-up for storm surges and surf
beats, which are long-wavelength disturbances created by fluid velocity
differences between the wave groups and the regions outside the wave groups.
It is without doubt that the resonance plays a role in run-up phenomena of
various kinds; however, we think that the extent to which it plays its role
has not been completely understood. For incident waves, which we assume to be
linear, the best approach to investigate the role played by the resonance
would be to calculate the normal modes by taking radiation damping into
account and then testing how those modes are excited by the incident waves.
Such modes diverge offshore, but they can still be used to calculate the
run-up. There are a small number of previous works that attempt to calculate
the resonant frequencies, but they do not relate the amplitudes of the normal
modes to those of the incident wave. This is because, by not including
radiation damping, they automatically induce a resonance that leads to
infinite amplitudes, thus preventing them from predicting the exact
contribution of the resonance to coastal run-up. In this study we consider
two different coastal geometries: an infinitely wide beach with a constant
slope connecting to a flat-bottomed deep ocean and a bay with sloping bottom,
again, connected to a deep ocean. For the fully 1-D problem we find
significant resonance if the bathymetric discontinuity is large.The
linearisation of the seaward boundary condition leads to slightly smaller
run-ups. For the 2-D ocean case the analysis shows that the wave confinement
is very effective when the bay is narrow. The bay aspect ratio is the
determining factor for the radiation damping. One reason why we include a
bathymetric discontinuity is to mimic some natural settings where bays and
gulfs may lead to abrupt depth gradients such as the Tokyo Bay. The other
reason is, as mentioned above, to test the role played by the depth
discontinuity for resonance. |
|---|---|
| ISSN: | 1561-8633 1684-9981 |