Long wave runup on piecewise linear topographies

We study long-wave evolution and runup on piecewise linear one- and two-dimensional bathymetries analytically and experimentally with the objective of understanding certain coastal effects of tidal waves. We develop a general solution method for determining the amplification factor of different ocean topographies consisting of linearly varying and constant-depth segments to study how spectral distributions evolve over bathymetry, and apply our results to study the evolution of solitary waves. We find asymptotic results which suggest that solitary waves often interact with piecewise linear topographies in a counter-intuitive manner. We compare our analytical predictions with numerical results, with results from a new set of laboratory experiments from a physical model of Revere Beach, and also with the data on wave runup around an idealized conical island. We find good agreement between our theory and the laboratory results for the time histories of free-surface elevations and for the maximum runup heights. Our results suggest that, at least for simple piecewise linear topographies, analytical methods can be used to calculate effectively some important physical parameters in long-wave runup. Also, by underscoring the effects of the topographic slope at the shoreline, this analysis qualitatively suggests why sometimes predictions of field-applicable numerical models differ substantially from observations of tsunami runup.


Analytical solution for the propagation of finite crested long waves over a sloping beach
Yağmur, Ahmed Sabri; Kanoğlu, Utku; Department of Aerospace Engineering (2022-2-10)
The analytical solution of shallow water-wave equations, both linear and nonlinear, is widely used to provide an insightful understanding of the coastal effect of long waves. These solutions are generally carried out for two-dimensional (1 space + 1 time) propagation, even though there are a limited number of analytical solutions for the three-dimensional (2 space + 1 time) propagation. Three-dimensional propagation of long waves over a sloping beach is considered here. The analytical solution is obtained u...
Sharghivand, Naeimeh; Aşık, Mehmet Zülfü; Department of Engineering Sciences (2022-8-11)
In this study, the N-wave profile is fitted to the seafloor deformation for a large set of earthquake scenarios, i.e., assuming that the seafloor deformation resulting from an earthquake instantaneously transfers to the sea surface. Hence, the N-wave parameters are identified with respect to the earthquake source parameters allowing to express the initial tsunami profile in terms of the earthquake source parameters. Then, the maximum tsunami runup is presented through the earthquake fault plane parameters u...
Analytical solutions for evolution and runup of longwaves over a sloping beach
Ceylan, Nihal; Kanoğlu, Utku; Department of Engineering Sciences (2019)
The initial value problem of the linear evolution and runup of long waves on a plane beach is analyzed analytically. The shallow water-wave equations are solved by integral transform and eigenvalue expansion methodologies. The results from linear solutions are compared with the solution of the nonlinear shallow water-wave equations confirming the runup invariance, i.e. nonlinear and linear theories produce same maximum runup. Then, existing analytical nonlinear solution for shoreline motion is implemented f...
Performance Assessment of NAMI DANCE in Tsunami Evolution and Currents Using a Benchmark Problem
Velioglu, Deniz; Kian, Rozita; Yalçıner, Ahmet Cevdet; Zaytsev, Andrey (2016-09-01)
Numerical modeling of tsunami evolution, propagation, and inundation is complicated due to numerous parameters involved in the phenomenon. It is important to assess the performance of numerical codes that solve tsunami motion, as well as flow and velocity patterns. NAMI DANCE is a computational tool developed for the modeling of long waves. It provides numerical modeling and efficient visualization of tsunami generation, propagation, and inundation mechanisms and computes the tsunami parameters. In the theo...
Tsunami hydrodynamics in coastal zones
Özer, Ceren; Yalçıner, Ahmet Cevdet; Department of Civil Engineering (2012)
This study analyzes the parameter “hydrodynamic demand” that is also defined by the square of Froude Number representing the damage of tsunami waves on structures and coastlines, and other hydrodynamic parameters, i.e., the distribution of instantaneous flow depths, runup values and the direction of maximum currents, occurred during tsunami inundation by using advanced numerical modeling. The analyses are performed on regular-shaped basins with different bottom slopes and real-shaped topographies using diff...
Citation Formats
U. Kanoğlu, “Long wave runup on piecewise linear topographies,” JOURNAL OF FLUID MECHANICS, pp. 1–28, 1998, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/48471.