Propagation characteristics of subaerial landslide-generated impulse waves

Abstract

Subaerial landslide-generated impulse waves were investigated in a rectangular prismatic channel based on the Froude similarity criterion. Landslides were modeled with a deformable granular material, and were controlled by a landslide generator. Four dominant parameters, namely, the slide Froude number F, the relative landslide thickness S, the relative landslide length L and the landslide impact angle α, were determined using dimensional analysis. According to the experimental results, the initial flow regime of impulse waves was subdivided into separated and unseparated, and the length of the impulse wave generation zone was provided by empirical equations. Moreover, the wave types were classified as Stokes-like waves, cnoidal-like waves and solitary-like waves. On this basis, a relationship between the dominant parameters and wave types was developed. Furthermore, by taking the propagation characteristics of an impulse wave, such as its amplitude, wave height and period, into consideration, an equation for the free surface was presented for estimating the Stokes-like waves. These semi-theoretical free surfaces were in good agreement with the experimental data.

Appendices

Appendix A. Empirical formulas

The empirical formulas reported in the literature for calculating the maximum wave amplitudes are described in this section.

From Fritz et al. [2],

$$\frac{{\xi_{m} }}{h} = 0.25\left( {\frac{{v_{s} }}{{\sqrt {gh} }}} \right)^{1.4} \left( {\frac{s}{h}} \right)^{0.8} .$$

(37)

From Heller and Hager [17],

$$\frac{{\xi_{\text{m} } }}{h} = \frac{4}{9}\left[ {\left( {\frac{{v_{s} }}{{\sqrt {gh} }}} \right)\left( {\frac{s}{h}} \right)^{0.5} \left( {\frac{{m_{s} }}{{\rho_{w} bh^{2} }}} \right)^{0.25} \left( {\cos \frac{6\alpha }{7}} \right)^{0.5} } \right]^{0.8}$$

(38)

where b is the landslide width, m_s is the landslide mass.

Appendix B. Experimental data

The governing parameters in this study such as the slide Froude number F, the relative landslide thickness S, the relative landslide length L and the landslide impact angle α, are shown in Table 3. Moreover, the initial flow regime of impulse waves, wave types, the ratio of the maximum wave height to water depth H_m/h, the ratio of the maximum wave amplitude to water depth ξ_m/h, the length of the impulse wave generation zone Δx_g and the ratios of the maximum wave height to water depth (i.e. H₁₁/h, H₂₁/h, H₃₁/h, H₄₁/h and H₅₁/h) at each DWG for the first wave are also listed in Table 3 for each case.