Physical simulation of resonant wave run-up on a beach
Nonlinear wave run-up on the beach caused by a harmonic wave maker located at some distance from the shore line is studied experimentally. It is revealed that under certain wave excitation frequencies, a significant increase in run-up amplification is observed. It is found that this amplification is due to the excitation of resonant mode in the region between the shoreline and wave maker. Frequency and magnitude of the maximum amplification are in good correlation with the numerical calculation results represented in the paper (Stefanakis et al., 2011). These effects are very important for understanding the nature of rogue waves in the coastal zone.
Analytical theory of tsunami wave generation by submarine landslides is extended to the case of narrow bays and channels of different geometry, in the shallow-water theory framework. New analytical solutions are obtained. For a number of bottom configurations, the wave field can be found explicitly in the form of the Duhamel integral. It is described by three waves: one forced wave propagating together with the landslide and two free waves propagating in opposite directions. The cases for bays with triangular (V-shaped bay), parabolic (U-shaped bay), and rectangular cross-sections are discussed in detail. The dynamics of the offshore-propagating wave in linearly inclined bays of different cross-section are also studied asymptotically for the resonant moving landslide. Different cases of landslides of increasing and decreasing volume are considered. It is shown that even if the landslide is moving under fully resonant conditions, the amplitude of the propagating tsunami wave may still be bounded, depending on the type of the landslide.
Run-up of long waves on a beach consisting of three pieces of constant but different slopes is studied. Linear shallow-water theory is used for incoming impulse evolution, and nonlinear corrections are obtained for the run-up stage. It is demonstrated that bottom profile influences the run-up characteristics and can lead to resonance effects: increase of wave height, particle velocity, and number of oscillations. Simple parameterization of tsunami source through an earthquake magnitude is used to calculate the run-up height versus earthquake magnitude. It is shown that resonance effects lead to the sufficient increase of run-up heights for the weakest earthquakes, and a tsunami wave does not break on chosen bottom relief if the earthquake magnitude does not exceed 7.8.
We present an exact analytical solution of the nonlinear shallow water theory for wave run-up in inclined channels of arbitrary cross-section, which generalizes previous studies on wave run-up for a plane beach and channels of parabolic cross-section. The solution is found using a hodograph-type transform, which extends the well-known Carrier–Greenspan transform for wave run-up on a plane beach. As a result, the nonlinear shallow water equations are reduced to a single one-dimensional linear wave equation for an auxiliary function and all physical variables can be expressed in terms of this function by purely algebraic formulas. In the special case of a U-shaped channel this equation coincides with a spherically symmetric wave equation in space, whose dimension is defined by the channel cross-section and can be fractional. As an example, the run-up of a sinusoidal wave on a beach is considered for channels of several different cross-sections and the influence of the cross-section on wave run-up characteristics is studied
A method based on the spectral analysis of thermowave oscillations formed under the effect of radiation of lasers operated in a periodic pulsed mode is developed for investigating the state of the interface of multilayered systems. The method is based on high sensitivity of the shape of the oscillating component of the pyrometric signal to adhesion characteristics of the phase interface. The shape of the signal is quantitatively estimated using the correlation coefficient (for a film–interface system) and the transfer function (for multilayered specimens).