Influence of bottom topography on the propagation of linear shallow water waves: an exact approach based on the invariant imbedding method

Abstract. In contrast to deep water waves, shallow water waves are influenced by bottom topography, which has consequences for the propagation of wave energy as well as for the energy and momentum exchange between the waves and the mean flow. The ERA-Interim reanalysis is used to assess the fraction of wave energy associated with shallow water waves in coastal regions in Europe. We show maps of the distribution of this fraction as well as time series statistics from 8 selected stations. There is a strong seasonal dependence and high values are typically associated with winter storms, indicating that shallow water wave effects can occasionally be important even in the deeper parts of the shelf seas otherwise dominated by deep water waves.

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Interaction of Shallow-Water Waves and Bottom Topography

Dynamical Problems in Continuum Physics - The IMA Volumes in Mathematics and Its Applications ◽

10.1007/978-1-4612-1058-0_6 ◽

1987 ◽

pp. 131-176 ◽

Cited By ~ 7

Author(s):

B. Boczar-Karakiewicz ◽

J. L. Bona ◽

D. L. Cohen

Keyword(s):

Shallow Water ◽

Water Waves ◽

Bottom Topography ◽

Shallow Water Waves

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The “shallow-waterness” of the wave climate in European coastal regions

Ocean Science ◽

10.5194/os-13-589-2017 ◽

2017 ◽

Vol 13 (4) ◽

pp. 589-597

Author(s):

Kai Håkon Christensen ◽

Ana Carrasco ◽

Jean-Raymond Bidlot ◽

Øyvind Breivik

Keyword(s):

Shallow Water ◽

Deep Water ◽

Wave Energy ◽

Water Waves ◽

Bottom Topography ◽

Mean Flow ◽

Momentum Exchange ◽

Shallow Water Waves ◽

Coastal Regions ◽

Deep Water Waves

Abstract. In contrast to deep water waves, shallow water waves are influenced by bottom topography, which has consequences for the propagation of wave energy as well as for the energy and momentum exchange between the waves and the mean flow. The ERA-Interim reanalysis is used to assess the fraction of wave energy associated with shallow water waves in coastal regions in Europe. We show maps of the distribution of this fraction as well as time series statistics from eight selected stations. There is a strong seasonal dependence and high values are typically associated with winter storms, indicating that shallow water wave effects can occasionally be important even in the deeper parts of the shelf seas otherwise dominated by deep water waves.

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Generalized Form of the Invariant Imbedding Method and Its Application to the Study of Back-Scattering in Shallow-Water Acoustics

Journal of Marine Science and Engineering ◽

10.3390/jmse9091033 ◽

2021 ◽

Vol 9 (9) ◽

pp. 1033

Author(s):

Mikhail Kazak ◽

Konstantin Koshel ◽

Pavel Petrov

Keyword(s):

Shallow Water ◽

Acoustic Waves ◽

Boundary Value ◽

Coupled Systems ◽

Problem Solution ◽

Invariant Imbedding ◽

Coupled Equations ◽

Back Scattering ◽

Invariant Imbedding Method ◽

Imbedding Method

A generalized form of the matrix-invariant imbedding method was developed to solve boundary-value problems for coupled systems of Helmholtz-type equations. Within this approach, a boundary-value problem solution can be obtained by solving evolutionary first-order imbedding equations for a matrix-valued function. The proposed method is applied to the solution of coupled equations for mode amplitudes describing the propagation of acoustic waves in a range-dependent shallow-water waveguide. The back-scattering of modes by bathymetry features is investigated, and the coefficients of the modal expansion of the wave reflected by an inhomogeneity in the bottom relief are computed. It is demonstrated that back-scattering is strongly connected with the modal interactions and that the back-scattered field consists of modes with numbers different from the number of the incident mode.

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