The reflection of linear surface waves by sinusoidal bottom undulations is considered in the case where the incident wave is not necessarily close to the resonant frequency. For finite detuning away from the resonant frequency, two previous solutions are shown to give results which are inconsistent with direct numerical solutions, especially when the results are extended to oblique incidence. The correction to the methods is given, and various consequences of the new results are examined.

1.
J. T.
Kirby
, “
A general wave equation for waves over rippled beds
,”
J. Fluid Mech.
162
,
171
(
1986
).
2.
J. C. W. Berkhoff, “Computation of combined refraction-diffraction,” Proceedings of the 13th International Conference on Coastal Engineering, Vancouver, 1972 (ASCE, New York, 1972), pp. 471–190.
3.
A. G.
Davies
and
A. D.
Heathershaw
, “
Surface-wave propagation over sinusoidally varying topography
,”
J. Fluid Mech.
144
,
419
(
1984
).
4.
J. T. Kirby and J. P. Anton, “Bragg reflection of waves by artificial bars,” Proceedings of the 22nd International Conference on Coastal Engineering, Delft, 1990 (ASCE, New York, 1990), pp. 757–768.
5.
C. C.
Mei
, “
Resonant reflection of surface water waves by periodic sandbars
,”
J. Fluid Mech.
152
,
315
(
1985
).
6.
R. A.
Dalrymple
and
J. T.
Kirby
, “
Water waves over ripples
,”
J. Waterway Port Coast. Ocean Eng.
112
,
309
(
1986
).
7.
C. C.
Mei
,
T.
Hara
, and
M.
Naciri
, “
Note on Bragg scattering of water waves by parallel bars on the seabed
,”
J. Fluid Mech.
186
,
147
(
1988
).
8.
A. G.
Davies
,
E.
Guazzelli
, and
M.
Belzons
, “
The propagation of long waves over an undulating bed
,”
Phys. Fluids A
1
,
1331
(
1989
).
9.
J. T.
Kirby
, “
Propagation of surface waves over an undulating bed
,”
Phys. Fluids A
1
,
1898
(
1989
).
10.
T. B.
Benjamin
,
B.
Boczar-Karakiewicz
, and
W. G.
Pritchard
, “
Reflection of water waves in a channel with corrugated bed
,”
J. Fluid Mech.
185
,
249
(
1987
).
11.
P. L.-F.
Liu
, “
Resonant reflection of water waves in a long channel with corrugated boundaries
,”
J. Fluid Mech
179
,
371
(
1987
).
12.
S. B.
Yoon
and
P. L.-F.
Liu
, “
Resonant reflection of shallow-water waves due to corrugated boundaries
,”
J. Fluid Mech.
180
,
451
(
1987
).
13.
J. T.
Kirby
and
P.
Vengayil
, “
Non-resonant and resonant reflection of long waves in varying channels
,”
J. Geophys. Res.
93
,
10782
(
1988
).
14.
N. Booij, “Gravity waves on water with non-uniform depth and current,” Report 81–1, Department of Civil Engineering, Delft University of Technology, 1981.
15.
P. L.-F.
Liu
, “
Viscous effects on evolution of Stokes waves
,”
J. Waterway, Port Coast. Ocean Eng.
112
,
55
(
1986
).
16.
M.
Belzons
,
V.
Rey
, and
E.
Guazzelli
, “
Subharmonic Bragg resonance for surface water waves
,”
Europhys. Lett.
16
,
189
(
1991
).
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