Articles | Volume 20, issue 3
Nonlin. Processes Geophys., 20, 379–395, 2013

Special issue: Nonlinear dynamics of the coastal zone

Nonlin. Processes Geophys., 20, 379–395, 2013

Research article 13 Jun 2013

Research article | 13 Jun 2013

Simulating run-up on steep slopes with operational Boussinesq models; capabilities, spurious effects and instabilities

F. Løvholt1,2,3, P. Lynett4, and G. Pedersen1,3 F. Løvholt et al.
  • 1University of Oslo, Department of Mathematics, P.O. Box 1072, Blindern 0316, Oslo, Norway
  • 2Norwegian Geotechnical Institute, P.O. Box 3930, 0806 Ullevål Stadion, Oslo, Norway
  • 3International Centre for Geohazards, Norwegian Geotechnical Institute, P.O. Box 3930, 0806 Ullevål Stadion, Oslo, Norway
  • 4Sonny Astani Department of Civil and Environmental Engineering, University of Southern California, Los Angeles, USA

Abstract. Tsunamis induced by rock slides plunging into fjords constitute a severe threat to local coastal communities. The rock slide impact may give rise to highly non-linear waves in the near field, and because the wave lengths are relatively short, frequency dispersion comes into play. Fjord systems are rugged with steep slopes, and modeling non-linear dispersive waves in this environment with simultaneous run-up is demanding. We have run an operational Boussinesq-type TVD (total variation diminishing) model using different run-up formulations. Two different tests are considered, inundation on steep slopes and propagation in a trapezoidal channel. In addition, a set of Lagrangian models serves as reference models. Demanding test cases with solitary waves with amplitudes ranging from 0.1 to 0.5 were applied, and slopes were ranging from 10 to 50°. Different run-up formulations yielded clearly different accuracy and stability, and only some provided similar accuracy as the reference models. The test cases revealed that the model was prone to instabilities for large non-linearity and fine resolution. Some of the instabilities were linked with false breaking during the first positive inundation, which was not observed for the reference models. None of the models were able to handle the bore forming during drawdown, however. The instabilities are linked to short-crested undulations on the grid scale, and appear on fine resolution during inundation. As a consequence, convergence was not always obtained. It is reason to believe that the instability may be a general problem for Boussinesq models in fjords.