Ira Didenkulova

Runup of Tsunami Waves in U-Shaped Bays

The problem of tsunami wave shoaling and runup in U-shaped bays (such as fjords) and underwater canyons is studied in the framework of 1D shallow water theory with the use of an assumption of the uniform current on the cross-section. The wave shoaling in bays, when the depth varies smoothly along the channel axis, is studied with the use of asymptotic approach. In this case a weak reflection provides significant shoaling effects. The existence of traveling (progressive) waves, propagating in bays, when the water depth changes significantly along the channel axis, is studied within rigorous solutions of the shallow water theory. It is shown that traveling waves do exist for certain bay bathymetry configurations and may propagate over large distances without reflection. The tsunami runup in such bays is significantly larger than for a plane beach.

Rogue waves in nonlinear hyperbolic systems (shallow-water framework)*

The formation of rogue waves is studied in the framework of nonlinear hyperbolic systems with an application to nonlinear shallow-water waves. It is shown that the nonlinearity in the random Riemann (travelling) wave, which manifests in the steeping of the face-front of the wave, does not lead to extreme wave formation. At the same time, the strongly nonlinear Riemann wave cannot be described by the Gaussian statistics for all components of the wave field. It is shown that rogue waves can appear in nonlinear hyperbolic systems only in the result of nonlinear wave–wave or/and wave–bottom interaction. Two special cases of wave interaction with a vertical wall (interaction of two Riemann waves propagating in opposite directions) and wave transformation in the basin of variable depth are studied in detail. Open problems of the rogue wave occurrence in nonlinear hyperbolic systems are discussed.

Run-up of Long Waves on a Beach: The Influence of the Incident Wave Form

The influence of the incident wave form on the extreme (maximal) characteristics of a wave at a beach (run-up and draw-down heights, run-up and draw-down velocities, and the breaking parameter) is studied. It is suggested to use in the calculations the definition of wavelength at a level of 2/3 of the maximal height, which to a certain degree correlates with the definition of the significant wavelength accepted in oceanology. Such a definition allows us to unify the relations for extreme run-up characteristics so that the influence of the incident wave form becomes insignificant. The obtained universal relations can be used for the estimates of run-up characteristics when the exact information about the form of the incident wave is not available.

Nonlinear wave evolution and runup in an inclined channel of a parabolic cross-section

Nonlinear wave dynamics of long water waves is studied in an inclined channel of a parabolic cross-section. Such situation occurs when sea waves enter and propagate in a narrow bay or a fjord. Nonlinear shallow water equations can in this case be written in 1D form and solved analytically with the use of the hodograph transformation. This approach generalizes the well-known Carrier-Greenspan transformation for long wave runup on a plane beach. In the case of an inclined channel of a parabolic cross-section, it leads to the associated spherical symmetrical linear wave equation. As a result, the solution of the Cauchy problem can be expressed in terms of elementary functions and has a simple form (with respect to analysis) for any kind of initial conditions. Wave regimes associated with various localized initial conditions, corresponding to problems of evolution and runup of N-waves and wind set-down and set-up relaxation, are considered and analyzed. Special attention is paid to the wave breaking criterion...

New Trends in the Analytical Theory of Long Sea Wave Runup

A modern view on the analytical theory of the long sea wave runup on a plane beach is presented. This theory is based on rigorous solutions of nonlinear shallow-water equations. The dynamics of the moving shoreline is studied in detail. It is demonstrated that extreme characteristics of the runup process (runup and rundown amplitudes, extreme values of on- and off-shore velocities, and critical amplitude of the breaking wave) can be found using the solution of the linear shallow-water theory, meanwhile the description of the time series of the wave field requires the nonlinear theory. The key and novel results presented here are: i) parameterization of basic formulas for extreme runup characteristics for bell-shape waves, showing that they weakly depend on the initial wave shape, which is usually unknown in real sea conditions; ii) runup analysis of periodic asymmetric waves with a steep front, as such waves are penetrating inland over larger distances and with greater velocities than symmetric waves.

Catalogue of rogue waves reported in media in 2006–2010

The data of rogue wave accidents reported in mass media during 2006–2010 years are collected and analysed. The collection includes 106 events, which are classified by their validity as true (78) and possible (28) and by the location of their occurrence: we distinguish deep, shallow and coastal rogue waves, which occurred in deep/shallow waters or at the coast. The validity of the event has been estimated by the rogue wave height, which should be twice larger than the significant wave height (significant wave height has been taken from satellite data), and/or by the associated hazard. It is shown that rogue waves cause especially high damage in shallow waters and at the coast.

Analysis of Tide-Gauge Records of the 1883 Krakatau Tsunami

The 1883 Krakatau volcanic eruption has generated giant tsunami waves reached heights of 40 m above sea level. Sea level oscillations related with this event have been reported in the Indian, Atlantic and Pacific Oceans. Main goal of this study is to analyze all available tide-gauge records (35) of this event. They are digitized with time step 2 min and processed. First of all, the tidal components are calculated and eliminated from the records. Filtered tide-gauge records are used to re-determine the observed tsunami characteristics (positive and negative amplitudes, wave heights). The results of given analysis are compared with the results of the direct numerical simulation of the tsunami wave propagation in the framework of the linear shallow-water theory using the ETOPO2 bathymetry.

The 1956 Greek tsunami recorded at Yafo, Israel, and its numerical modeling

floating-type tidal gauge installed in the port of Yafo, Israel. The tsunami was triggered by an earthquake in the Aegean Sea on 9 July 1956. This paper presents a retrieval of tsunami waves from the record. At the first stage of the study an attempt had been undertaken to reproduce the 1956 tsunami assuming a coseismic nature of its generation source. Although these simulations resulted in tsunami waves with their amplitude close to that obtained from the record measured at Yafo, they did not contain significant spectral energy components with periods of � 15 min as appear in the spectra of 1956 tide-gauge records. When landslide movement, triggered by the main shock and/or by the largest aftershock, is suggested as a source of these tsunami waves, the spectra of the resulted marigram obtained in the proximity to Yafo contain harmonics with frequencies very close to those measured. This corroborates the landslide nature of the tsunamigenic source responsible for generation of higher-frequency (relative to the tidal waves) energy components. The peak periods determined via spectral analysis of the recent tide-gauge records (1 year and longer) in the absence of tsunami events vary from 50 to 60 min. Similar periods have been revealed in a special numerical study dealing with longwave propagation toward the coast of Israel, thus confirming that their origin is related to continental shelf resonance. These resonance periods differ significantly from those found for the 1956 tsunami.

Run-up of Solitary Waves on Slopes with Different Profiles

The problem of sea-wave run-up on a beach is discussed within the framework of exact solutions of a nonlinear theory of shallow water. Previously, the run-up of solitary waves with different forms (Gaussian and Lorentzian pulses, a soliton, special-form pulses) has already been considered in the literature within the framework of the same theory. Depending on the form of the incident wave, different formulas were obtained for the height of wave run-up on a beach. A new point of this study is the proof of the universality of the formula for the maximum height of run-up of a solitary wave on a beach for the corresponding physical choice of the determining parameters of the incident wave, so that the effect of difference in form is eliminated. As a result, an analytical formula suitable for applications, in particular, in problems related to tsunamis, has been proposed for the height of run-up of a solitary wave on a beach.

Tsunami runup in narrow bays: the case of Samoa 2009 tsunami

Abnormal tsunami amplification and runup in narrow bays is studied with respect to the Samoa tsunami of 29 September 2009. The data of the tide gauge in Pago Pago harbour are used to calculate wave runup in the city of Pago Pago (Tutuila, American Samoa) for two approximations of the bottom topography: a plane beach and a narrow bay. Theoretical estimates of tsunami runup are compared with field survey data for the 2009 Samoa tsunami. It is shown that both formulations result in equally good estimates of runup, having approximately the same difference with the field measurements. However, the narrow bay model presents more wave amplification and, consequently, runup, which is the main observation of the field survey. The differences in estimated shoreline velocity, travel time and wave breaking regime, calculated in the framework of these two approximations, are also discussed. It is concluded that wave runup in narrow bays should be calculated by the corresponding formulas, which should be taken into account by tsunami early warning systems.