Physics of Tsunamis

Fundamental information on the physics and geography of tsunami waves is presented. Examples are given of known historical events, illustrating the character of tsunami manifestation on coasts. Quantitative characteristics are introduced that describe tsunami strength: magnitude and intensity. Physical principles of the operation of tsunami warning systems are described. Information is provided on tsunami catalogs and electronic databases. The seaquake phenomenon is defined and a synthesized description is given. Information is presented on the main hydroacoustic effects, related to underwater earthquakes: the T-phase, low-frequency elastic oscillations, and cavitation.

Modern ideas are presented concerning the source of an earthquake and the seismotectonic source of a tsunami. The main physical processes taking place at a tsunami source are described. Estimation is performed of the role of secondary effects: of displacements of the bottom, occurring in its own plane, of the Coriolis force, of density stratification of the water. The Okada formulae are presented and the technique is exposed for calculating coseismic ocean bottom deformations caused by an underwater earthquake. The dependence of the properties of coseismic ocean bottom deformation at the tsunami source upon the earthquake magnitude and depth is analyzed applying the Okada formulae in the case of a rectangular fault. Formulae are presented that relate the maximum values of the ocean bottom deformation amplitude, the displaced volume, and the initial elevation energy to the moment magnitude of the earthquake. From the slip distribution, adopted from the SRCMOD database, the vector fields of coseismic ocean bottom deformations were calculated applying the Okada formulae for the sources of 75 underwater earthquakes that occurred during the period between 1923 and 2013. It was shown that horizontal deformation components of an inclined bottom, as a rule, provide an additional and noticeable contribution to the displaced water volume and to the potential energy of the initial elevation (the tsunami energy). The relationships were analyzed between the ocean bottom deformation amplitude, the displaced volume and the tsunami energy, and the moment magnitude of the earthquake; the respective regression dependences were plotted. The part of the earthquake energy transferred to the tsunami waves was shown to increase with its moment magnitude, but even in the case of catastrophic earthquakes it does not exceed 0.1 %. From HTDB/WLD and GHTD/NGDC data the peculiarities were investigated of the space–time distribution of tsunamis.

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.

The necessity is substantiated for taking into account the compressibility of water in describing behavior of water column in tsunami source. Within the framework of linear potential theory of a compressible liquid in a basin of fixed depth, the general analytical solution is constructed for 2D and quasi-3D (cylindrical symmetry) problems of the generation of acoustic-gravity waves by bottom deformations of small amplitudes. Manifestations of compressibility of the water column in the problem of tsunami generation are studied, making use of the example of model bottom deformation laws (piston, membrane, and running displacements). The main difference between the behavior of a compressible water column as compared to an incompressible model medium is shown to consist in the formation of elastic oscillations exhibiting significant amplitudes and a discrete spectrum. Characteristic features of the dynamics of acoustic-gravity waves in a basin of variable depth are described. Records of ocean bottom pressure gauges and seismometers are used for analyzing manifestations of the 2003 Tokachi-Oki and the 2011 Tohoku-Oki tsunamigenic earthquakes. The mechanism is considered of tsunami formation, related to nonlinear energy transfer from “high-frequency” forced or elastic oscillations of the water column to “low-frequency” gravitational waves.

The physics is described of tsunami formation by sources of nonseismic origin: landslides, volcanic eruptions, meteorological causes, and cosmic bodies falling into the ocean. Short descriptions are given of certain remarkable historical events (with the exception of cosmogenic tsunamis). Approaches to the mathematical description of tsunami generation by these sources are expounded. Basic regularities, relating parameters of a source and of the tsunami wave generated by it are presented.

Traditional ideas of tsunami propagation in the open ocean are dealt with. The significance is estimated of manifestations of phase and amplitude dispersions. Classical problems are considered, concerning variation of the amplitude of a long wave in a basin with gently varying depth (the Green’s law) and the reflection of a wave from a step and from a rectangular obstacle. Formulae of the ray method are presented in Cartesian and spherical coordinate systems. Phenomena of long-wave refraction and capture by underwater ridges and the shelf are described. Estimation is performed of linear (viscous) and nonlinear (turbulent) dissipation of the energy of long waves. The effect of a wave amplitude being reduced by scattering on bottom irregularities is considered. Approaches to the numerical simulation of tsunami wave propagation are described. Conventionally applied equations of nonlinear long-wave theory, taking into account the Coriolis force and bottom friction, are presented both in Cartesian and spherical coordinate systems. The technique for formulating initial and boundary conditions in the tsunami propagation problem is described. Brief information is given on certain tsunami models (codes), that are actively applied, at present. Features of transoceanic wave propagation are considered, taking advantage of the December 26, 2004 tsunami as an example. The main results, due to investigation of the issues of a tsunami run-up on the shore, are presented.

The traditional method for tsunami wave registration by coastal mareographs is described. The technique is described for measuring tsunami waves in the open ocean with the aid of bottom pressure sensors. The advantages of this technique are discussed. The technique for studying and documenting effects of tsunami influence on the coast are briefly expounded. The significance of searching for and identifying paleotsunami sediments is discussed. The application is described of satellite altimeters for registering tsunamis in the open ocean. Data are presented on tsunami manifestations in the Earth’s ionosphere.