Nonlinear properties of laboratory wind waves at energy containing frequencies

Nonlinear properties of wind waves in a wind-wave tunnel are investigated by measuring the probability density distribution of surface elevation. The surface elevation distribution of raw records are found to have a positive skewness (K ₃=0.21 to 0.43) and a negative kurtosis (K ₄=–0.74 to –0.41) with magnitude depending of fetch and wind speed. The values of skewness are in qualitative agreement with a prediction of the weak interaction theory for a random wave field incorporating the effects of second harmonics (Tayfun, 1980), but the values of kurtosis are different in sign from the prediction.To examine the nonlinear properties of energy containing components, higher harmonic components are excluded from the wave records by using a kind of a band-pass filter. The surface elevation distributions of the filtered waves show a sharp decrease in skewness , but the distributions remain highly non-Gaussian with a large negative kurtosis almost independent of the fetch and wind speed . It is concluded that the negative kurtosis is due to the non-random character of the phase and amplitude among the energy containing components, and that nonlinear interactions occur amongst the energy containing frequencies.     

Magnitude scale for the Central American tsunamis

Based on the tsunami data in the Central American region, the regional characteristic of tsunami magnitude scales is discussed in relation to earthquake magnitudes during the period from 1900 to 1993. Tsunami magnitudes on the Imamura-Iida scale of the 1985 Mexico and 1992 Nicaragua tsunamis are determined to bem=2.5, judging from the tsunami height-distance diagram. The magnitude values of the Central American tsunamis are relatively small compared to earthquakes with similar size in other regions. However, there are a few large tsunamis generated by low-frequency earthquakes such as the 1992 Nicaragua earthquake. Inundation heights of these unusual tsunamis are about 10 times higher than those of normal tsunamis for the same earthquake magnitude (M _s =6.9–7.2). The Central American tsunamis having magnitudem>1 have been observed by the Japanese tide stations, but the effect of directivity toward Japan is very small compared to that of the South American tsunamis.     

Tsunami magnitudes in Taiwan, the Philippines and Indonesia

The regional characteristics of tsunami magnitudes in the SE Asia region are discussed in relation to earthquake magnitudes during the period from 1960 to 1994. Tsunami magnitudes on the Imamura-Iida scale are investigated by the author's method (Hatori 1979, 1986) using the data of inundation heights near the source area and tide-gauge records observed in Japan. The magnitude values of the Taiwan tsunamis showed relatively to be small. On the contrary, the magnitudes of tsunamis in the vicinities of the Philippines and Indonesia exceed more than 1–2 grade (tsunami heights: 2–5 times) compared to earthquakes with similar size on the circum-Pacific zone. The relation between tsunami magnitude, m, and earthquake magnitude, M _s, is expressed as m = 2.66 M _s– 17.5 for these regions. For example, the magnitudes for the 1976 Mindanao tsunami (M _s= 7.8, 3702 deaths) and the 1992 Flores tsunami (M _s= 7.5, 1713 deaths) were determined to be m = 3 and m = 2.5, respectively. The focal depth of tsunamigenic earthquakes is shallower thand< 36 km, and the detectively of tsunamis is small for deep earthquakes being d > 40 km. For future tsunamis, it is indispensable to take precautions against shallow earthquakes having the magnitudes M _s> 6.5.     

Experimental study on strong interaction between regular waves and wind waves—I

The interaction between mechanically generated regular waves and wind waves is experimentally investigated in a wind-wave tunnel. It is shown that the growth process of regular waves is divided into the four distinct stages as follows: (1) almost independent coexistence of wind waves and regular waves, (2) attenuation of wind waves with simultaneous growth of regular waves, (3) rapid growth of regular waves after disappearance of wind waves, and (4) transition of regular waves to wind waves after the wave breaking. At the second stage there is an apparent relation between the attenuation of wind waves and the growth of regular waves. This fact suggests that there is some strong nonlinear interactions which transfers energy effectively from wind waves to regular waves.     

Long-period waves in the vicinity of Onagawa Bay (I)

To investigate the response characteristics of a bay to tsunamis, field measurements of long-period waves have been carried out at Onagawa and Okachi Bays, both of which face the Pacific Ocean in northern Japan. In Onagawa Bay, the observed transfer function is in good agreement with the prediction based on the one-dimensional numerical model, in the period range larger than about 15 minutes. The response of shorter periods seems to be influenced by the two-dimensionality of the bay. The oscillations within Onagawa Harbor are also discussed with respect to the relative amplitude and phase at two stations inside the harbor and it is estimated that the reflection coefficient at the waterfront is about 0.7. In Okachi Bay, the oscillations in the period range larger than about 10 minutes could be explained by a Y-shaped model of the bay. The dominant oscillations offshore of these two-bays are found to be the mode with the motion predominantly in the direction normal to the shelf orientation, and the estimated power spectral density of incoming waves in deep water varies asf ^–2,f being the frequency. The waves of lateral modes, such as edge waves on the shelf, are small and of minor importance to generate bay oscillations of longer periods.