Schematic side view of the wave tank.
Simulated (BIM) swash layers at the time of maximum runup, depicted with true aspect ratio. In the lower panel the two fields of view (FOV) for PIV measurements are shown.
Upper panel: Definition sketch of wave tank and deep water acoustic gauge. The vertical scale is exaggerated in the sketch. Lower panel: Elevation time series from experiments (exp.), Boussinesq model (Bouss.) and full potential theory (BIM). The model times series start at a finite elevation because the initial conditions in the model are partly situated in front of the gauge location.
Runup data for θ = 10°.
Runup data for θ = 12° from Langsholt. 51
The shoreline excursion as function of time. The runup height is then s(t)sin θ, where θ is the beach inclination.
Image showing part of the shoreline before start of runup, with water to the right. The front of the wave has reached the shoreline, but it has not yet been set it into motion.
Boundary layers in the runup, with outer flow from full potential theory. The lines normal to the s axis show profile locations, while nonlinear and linear profiles are dashed and solid, respectively. Also the free surface is depicted as a bold solid line. Upper panel: A/d = 0.0985, t = 7.40 s. 1 m on the s-axis corresponds to 5.84 m/s. Lower panels: A/d = 0.295, 1 m on the s-axis corresponds to 3.89 m/s. The two lower panels correspond to t = 6.70 s and t = 7.30 s, respectively.
Measured (dots) and simulated (fully drawn lines) velocity profiles in the boundary layer. Dashes correspond to time simulated profiles with time shifts 0.05 s and 0.02 s, respectively, in the left and right panels. The measurement is made 7 cm in-land and the PIV data are averaged over a distance of approximately 0.5 cm along the beach. Left panel: A/d = 0.0977 for times 6.90 s, 7.20 s, 7.40 s, 7.60 s, and 7.80 s. Right panel: A/d = 0.292 for times 5.70 s, 6.00 s, 6.10 s, 6.30 s, and 6.80 s.
Measured (dots) and simulated (BIM, fully drawn lines) velocity profiles in the boundary layer in the upper field of view for A/d = 0.292 and times 6.34 s, 6.40 s, 6.58 s, 6.75 s, and 7.00 s.
Instantaneous streamlines based on PIV velocities approximately 0.8 m from the equilibrium shoreline. Upper left, upper right, lower left, and lower right panels correspond to t = 6.40 s, t = 6.43 s, t = 6.75 s, and t = 7.11 s, respectively. The units on the s and z axes are m and mm, respectively.
A uniform plug retarded by gravity. The shape of the fluid body is irrelevant as long as the boundary layer is thinner than the flow depth.
Velocity profiles at t = 0.4696 s across the viscous boundary layer at various s-positions (i.e., τξ values) along the beach as indicated on the abscissa. The runup-plug enters the beach with velocity U 0 = 1 m/s and the total runup-time is 0.5870s in this case, giving the runup-length 0.2935 m. It is remarked that the profiles are shifted to their s locations and that the velocity is zero at z = 0 for all profiles.
Entrainment velocity profile along the outer edge of the viscous boundary layer.
The wedge-shaped fluid body that surpasses observed inundation. Left panel shows the volume at equilibrium, while the right panel shows the volume at the time, according to the Boussinesq model, at maximum runup. The experimental position for maximum inundation is marked by + in the right panel. The case A/d = 0.098 has been used for illustration.
Normalized volume transport defect computed from simulated velocity profiles in the boundary layer.
The ratio N L for τ = 0.5 at various locations in the boundary layer.
The ratio N L for τ = 0.9 at various locations in the boundary layer is displayed in the figure.
Reynold numbers for solitary waves with d = 0.2 m and θ = 10°.
Maximum runup height to amplitude (R/A). Exp., BIM, and Bouss. correspond to the experiments and the two models, respectively.
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