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Tsunami Amplification Phenomena

On September 30, 2013

PhD Thesis by Thémistoklis STEFANAKIS (CMLA)

This thesis is divided in four main parts. In the first part I will present our work on long wave run-up and some resonant amplification phenomena. With the use of numerical simulations for the nonlinear shallow water equations, we show that in the case of monochromatic waves normally incident on a plane beach, resonant run-up amplification occurs when the incoming wavelength is 5.2 times larger the beach length [Stefanakis et al., 2011]. This is consistent with the laboratory experiments of Ezersky et al. [2013], who further distinguished the resonant run-up frequencies from the natural frequencies of the wavemaker. We also show that this resonant run-up amplification can be observed for several wave profiles such as bichromatic, polychromatic and cnoidal. However, resonant run-up amplification is not restricted to infinitely sloping beaches. We varied the bathymetric profile, and we saw that resonance is present in the case of piecewise linear and real bathymetries.

In the second part I will present a new analytical solution to study the propagation of tsunamis from a finite strip source over constant depth using linear shallow-water wave theory [Kanoglu et al., 2013]. The solution, which is based on separation of variables and a double Fourier transform in space, is exact, easy to implement and allows the study of realistic waveforms such as N-waves. We show the existence of focusing points for N-wave type initial displacements, where unexpectedly large wave amplitudes may be observed. N-wave focusing is found analytically by both linear dispersive and linear non-dispersive theories and is a possible explanation for run-up amplification beyond what is assumed by widely used scaling relationships.

In the third part I will explore the effect of localized bathymetric features on long wave generation. The generation of waves in a fluid domain of uniform depth by uplift or subsidence of a portion of the flat bottom boundary has been elegantly studied by Hammack [1972] for idealized motions. However, even when the final displacement is known from seismic analysis, the deforming seafloor includes relief features such as mounts and trenches. We investigate analytically the effect of bathymetry on the surface wave generation, by solving the forced linear shallow water equation. Our model for bathymetry consists of a cylindrical sill on a flat bottom, to help understand the effect of seamounts on tsunami generation. We derive the same solution by applying both the Laplace and the Fourier transforms in time. We find that as the sill height increases, partial wave trapping reduces the wave height in the far field, while amplifying it above the sill.

Finally, in the last part I will try to explore whether small islands can protect nearby coasts from tsunamis as it is widely believed by local communities. Recent findings for the 2010 Mentawai Islands tsunami show amplified run-up on coastal areas behind small islands [Hill et al., 2012], compared with the run-up on adjacent locations, not influenced by the presence of the islands. We will investigate the conditions for this run-up amplification by numerically solving the nonlinear shallow water equations. Our bathymetric setup consists of a conical island sitting on a flat bed in front of a plane beach and we send normally incident single waves. The experimental setup is governed by five physical parameters. The objective is twofold: Find the maximum run-up amplification with the least number of simulations. Given that our input space is five-dimensional and a normal grid approach would be prohibitively computationally expensive, we present a recently developed active experimental design strategy, based on Gaussian Processes, which significantly reduces the computational cost. After running two hundred simulations, we find that in none of the cases considered the island did offer protection to the coastal area behind it. On the contrary, we have measured run-up amplification on the beach behind it compared to a lateral location on the beach, not directly affected by the presence of the island, which reached a maximum factor of 1.7. Thus, small islands in the vicinity of the mainland will act as amplifiers of long wave severity at the region directly behind them and not as natural barriers as it was commonly believed so far.

Type :
Recent Ph.D and HDR defenses
Place(s) :
Cachan Campus

Jurys Board

  • Nicolas VAYATIS, CMLA, ENS Cachan
  • Frédéric DIAS, School of Mathematical Sciences, University College Dublin, Ireland 


  • Paolo SAMMARCO, Dipartimento di Ingegneria Civile e Ingegneria Informatica, Università Tor Vergata, Italy
  • Esteban G. TABAK, Courant Institute of Mathematical Sciences, New York Univ., USA


  • Christian KHARIF, Ecole Centrale de Marseille & IRPHE, France
  • Costas E. SYNOLAKIS,  Department of Civil and Environmental Engineering, University of Southern California, USA
  • Serge GUILLAS, Department of Statistical Science, University College London, UK
  • Edward A. COX, School of Mathematical Sciences, University College Dublin, Ireland

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