An analytical and numerical study of long wave run-up in U-shaped and V-shaped bays

Details

• Journal Title:
  Applied Mathematics and Computation
• Personal Author:
  Garayshin, V.V. ; Harris, Matthew W. ; Nicolsky, D.J. ; Pelinovsky, Efim N. ; Rybkin, A.V.
• NOAA Program & Office:
  OAR (Oceanic and Atmospheric Research) ; CIFAR (Cooperative Institute for Alaska Research)
• Description:
  By assuming the flow is uniform along the narrow long bays, the 2-D nonlinear shallow-water equations are reduced to a linear semi-axis variable-coefficient 1-D wave equation via the generalized Carrier–Greenspan transformation. The run-up of long waves in constantly sloping U-shaped and V-shaped bays is studied both analytically and numerically within the framework of the 1-D nonlinear shallow-water theory. An analytic solution, in the form of a double integral, to the resulting linear wave equation is obtained by utilizing the Hankel transform, and consequently the solution to the tsunami run-up problem is developed by applying the inverse generalized Carrier–Greenspan transform. The presented solution is a generalization of the solutions found by Carrier et al. (2003) and Didenkulova and Pelinovsky (2011) for the case of a plane beach and a parabolic bay, respectively. The shoreline dynamics in U-shaped and V-shaped bays are computed via a double integral through standard integration techniques.
• Keywords:
  Bays Waves
• Source:
  Applied Mathematics and Computation, 279: 187-197
• DOI:
  https://doi.org/10.1016/j.amc.2016.01.005
• Document Type:
  Journal Article
• Funding:
  Grant no. NA08OAR4320751
• Rights Information:
  Accepted Manuscript
• Compliance:
  CHORUS
• Main Document Checksum:
  urn:sha256:99553cc87a23d9bd0cc0c6bf405397fb8ea087d23778e40d9f6249d58c6f8ac0
• Download URL:
  https://repository.library.noaa.gov/view/noaa/49476/noaa_49476_DS1.pdf
• File Type:
  [PDF - 565.84 KB ]