Abstract
The process of tsunami generation by dynamic bottom deformations is treated as a hydrodynamical problem of an incompressible liquid. Two basic approximations are presented, which are used in describing gravitational waves on water—the theory of long waves and the potential theory. Within the framework of linear potential theory of an incompressible liquid in a basin of fixed depth, the general analytical solution is constructed for the two-dimensional (2D) and three-dimensional (3D) problems of tsunami generation by bottom deformations of small amplitudes. The solution of the 3D problem is constructed in both Cartesian and cylindrical coordinates. For a series of model bottom deformation laws (piston, membrane and running displacements, bottom oscillations and alternating-sign displacement) physical regularities are revealed that relate the amplitude, energy, and direction of tsunami wave emission to peculiarities of the bottom deformation at the source. In some cases, the theoretical regularities, obtained within potential theory, are compared with dependences following from the linear theory of long waves and, also, with the results of laboratory experiments. The practical problem of calculating the initial elevation on a water surface at a tsunami source is considered within the framework of the assumption of instantaneity of bottom deformation. Exact analytic solutions of this problem are presented for flat horizontal and inclined bottoms. Within the framework of the linear theory of long waves on account of the Earth’s rotation, investigation is performed of horizontal motions of the water layer accompanying tsunami generation by an earthquake in a homogeneous and stratified ocean. The displacement of water by coseismic bottom deformations is shown to serve as the cause of formation not only of tsunami waves, but also of long-lived “traces” of the tsunamigenic earthquake in the ocean—of potential and eddy residual hydrodynamical fields. The field of residual horizontal displacements of water particles is calculated and analyzed for the 2011 Tohoku-Oki earthquake.
Keywords
- Hydrodynamic description
- Gravity waves
- Long-wave theory
- Potential theory
- Fluid velocity potential
- Coseismic deformation
- Tsunami source
- Tsunami generation
- Initial elevation
- Ocean bottom displacement
- Laplace transformation
- Fourier transformation
- Analytical solution
- Phase dispersion
- Directional diagrams
- Residual hydrodynamic fields
- Coriolis force
- Geostrophic vortex
- Rossby radius of deformation
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Levin, B.W., Nosov, M.A. (2016). Hydrodynamic Processes at the Source of a Tsunami of Seismotectonic Origin: Incompressible Ocean. In: Physics of Tsunamis. Springer, Cham. https://doi.org/10.1007/978-3-319-24037-4_3
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