doi:10.1016/S0378-3839(99)00046-0
Copyright © 1999 Elsevier Science B.V. All rights reserved
Separation of incident and reflected waves over sloping bathymetry
T. E. Baldock* and D. J. Simmonds1
School of Civil and Structural Engineering, University of Plymouth, Palace St., Plymouth, PL1 2DE, UK
Received 3 May 1999;
accepted 15 June 1999.
Available online 7 January 2000.
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Abstract
An existing 2D method for separating incident and reflected waves over a horizontal bed [Frigaard, P., Brorsen, M., 1995. A time domain method for separating incident and reflected irregular waves. Coastal Eng., 24, 205–215.] is modified to account for normally incident linear waves propagating over a bed with arbitrary 2D bathymetry. Linear shoaling is used to determine the amplitude and phase change between two measurement positions; thereafter the existing technique can be applied. Comparisons between the existing and modified methods are made using numerically simulated data. Errors in the reflection coefficient are found to be small for large reflection coefficients, but may become large if reflection is low. However, if an accurate assessment of the amplitude of the incident and reflected wave trains is required, the bathymetry must be accounted for in order to avoid significant errors (up to 90% for cases considered).
Author Keywords: Waves; Reflection; Sloping bathymetry; Beaches
Fig. 1. (a) Calculated reflection coefficient, β=1/40, R=0.8, f=0.0488 Hz. – · –, Depth (rhs); – □ – SB; – × – HB. (b) Calculated incident and reflected wave amplitudes, β=1/40, R=0.8, f=0.0488 Hz. – · – Depth (rhs); □ ai (SB);
ai (HB); ◊ ar (SB); × ar (HB); —— ai (LS); - - - ar, (LS). (c) Error in incident and reflected wave amplitudes, β=1/40, R=0.8, f=0.0488 Hz. – · – Depth (rhs); –
– ai (HB); – × – ar (HB).
Fig. 2. (a) Calculated reflection coefficient, β=1/40, R=0.1, f=0.513 Hz. – · – Depth (rhs); – □ – SB; – × – HB. (b) Calculated incident and reflected wave amplitudes, β=1/40, R=0.1, f=0.513 Hz. – · – Depth (rhs); □ ai (SB);
ai (HB); ◊ ar (SB); × ar (HB); —— ai (LS); - - - ar, (LS). (c) Error in incident and reflected wave amplitudes, β=1/40, R=0.1, f=0.513 Hz. – · – Depth (rhs); –
– ai (HB); – × – ar (HB).
Fig. 3. (a) Calculated reflection coefficient, β=1/10, R=0.8, f=0.0488 Hz. – · – Depth (rhs); – □ – SB; – × – HB. (b) Calculated incident and reflected wave amplitudes, β=1/10, R=0.8, f=0.0488 Hz. – · – Depth (rhs); □ ai (SB);
ai (HB); ◊ ar (SB); × ar (HB); —— ai (LS); - - - ar, (LS). (c) Error in incident and reflected wave amplitudes, β=1/10, R=0.8 ,f=0.0488 Hz. – · – Depth (rhs); –
– ai (HB); – × – ar (HB).
Fig. 4. (a) Calculated reflection coefficient, β=1/10, R=0.1, f=0.513 Hz. – · – Depth (rhs); – □ – SB; – × – HB. (b) Calculated incident and reflected wave amplitudes, β=1/10, R=0.1, f=0.513 Hz. – · – Depth (rhs); □ ai (SB);
ai (HB); ◊ ar (SB); × ar (HB); —— ai (LS); - - - ar, (LS). (c) Error in incident and reflected wave amplitudes, β=1/10, R=0.1, f=0.513 Hz. – · – Depth (rhs); –
– ai (HB); – × – ar (HB).