Kelvin wave reflection at an oscillating boundary with applications to the North Sea

A numerical model study of parameters influencing tidal currents in the Irish Sea

“…This can be readily illustrated (calculation 4) by increasing k to 0.01, with viscosity determined using (24), 'with K 2 = 2.5 x 10 -5, 2 orders of magnitude below its normally accepted va!ue. It is evident from a comparison of Figure 5 with Figure 4a, that increasing bottom friction from (k =' 0.005 to 0.01) in the three-dimensional model has not moved the amphidrome further against .the coast, as is predicted from analytical work with two-dimensional models [Brown, 1987[Brown, , 1989 unrealistically high values (of the order of 50 cm higher than observed in the eastern Irish Sea; Figure 5) with this reduced viscosity. Also, as is to be expected, with a shift in the position of the amphidrome, the phase distribution changes (compare Figures 4a and 5).…”

“…The influence of bed friction upon the location of tidal amphidromes is well known [Brown, 1987[Brown, , 1989, with increasing bottom friction coefficient causing the amphidrome off the east coast of Ireland (Figure 4a) to move closer to the coast. (Pugh [1981] has shown that increased frictional effects can be associated with weather effects.)…”

A numerical model study of parameters influencing tidal currents in the Irish Sea

“…This can be readily illustrated (calculation 4) by increasing k to 0.01, with viscosity determined using (24), 'with K 2 = 2.5 x 10 -5, 2 orders of magnitude below its normally accepted va!ue. It is evident from a comparison of Figure 5 with Figure 4a, that increasing bottom friction from (k =' 0.005 to 0.01) in the three-dimensional model has not moved the amphidrome further against .the coast, as is predicted from analytical work with two-dimensional models [Brown, 1987[Brown, , 1989 unrealistically high values (of the order of 50 cm higher than observed in the eastern Irish Sea; Figure 5) with this reduced viscosity. Also, as is to be expected, with a shift in the position of the amphidrome, the phase distribution changes (compare Figures 4a and 5).…”

“…The influence of bed friction upon the location of tidal amphidromes is well known [Brown, 1987[Brown, , 1989, with increasing bottom friction coefficient causing the amphidrome off the east coast of Ireland (Figure 4a) to move closer to the coast. (Pugh [1981] has shown that increased frictional effects can be associated with weather effects.)…”

The Importance of Long Wave Reflections in Tidal Modelling on a Continental Shelf

“…The sensitivity analysis is also limited by the necessity to assume the boundary conditions are correct, as mentioned in section 3 the phase at the English Channel also affects the position of the amphidrome (Brown 1987) however this does not affect the shelf model results and the boundary conditions do match the phase of the elevations observed at Dover on the UK side of the English Channel boundary. Further work should compare bathymetry sources to gauge the potential size of this error and analyse standing/ propagating waves at more locations covering a larger spatial domain to increase confidence in the results and to improve understanding of how the magnitude of the reflections has changed over time.…”

Horizontally viscous effects in a tidal basin: extending Taylor's problem

“…The resulting amphidromic system displays elevation and current amphidromic points alternatingly on the centreline of the basin, provided the channel is sufficiently narrow for all Poincaré modes to be evanescent (LeBlond & Mysak 1978). Taylor's strongly idealized model qualitatively reproduces the main features of tides in large-scale basins like the North Sea (Brown 1987).…”

A numerical model study of parameters influencing tidal currents in the Irish Sea

“…This can be readily illustrated (calculation 4) by increasing k to 0.01, with viscosity determined using (24), 'with K 2 = 2.5 x 10 -5, 2 orders of magnitude below its normally accepted va!ue. It is evident from a comparison of Figure 5 with Figure 4a, that increasing bottom friction from (k =' 0.005 to 0.01) in the three-dimensional model has not moved the amphidrome further against .the coast, as is predicted from analytical work with two-dimensional models [Brown, 1987[Brown, , 1989 unrealistically high values (of the order of 50 cm higher than observed in the eastern Irish Sea; Figure 5) with this reduced viscosity. Also, as is to be expected, with a shift in the position of the amphidrome, the phase distribution changes (compare Figures 4a and 5).…”

“…The influence of bed friction upon the location of tidal amphidromes is well known [Brown, 1987[Brown, , 1989, with increasing bottom friction coefficient causing the amphidrome off the east coast of Ireland (Figure 4a) to move closer to the coast. (Pugh [1981] has shown that increased frictional effects can be associated with weather effects.)…”

The Importance of Long Wave Reflections in Tidal Modelling on a Continental Shelf

“…The sensitivity analysis is also limited by the necessity to assume the boundary conditions are correct, as mentioned in section 3 the phase at the English Channel also affects the position of the amphidrome (Brown 1987) however this does not affect the shelf model results and the boundary conditions do match the phase of the elevations observed at Dover on the UK side of the English Channel boundary. Further work should compare bathymetry sources to gauge the potential size of this error and analyse standing/ propagating waves at more locations covering a larger spatial domain to increase confidence in the results and to improve understanding of how the magnitude of the reflections has changed over time.…”

Horizontally viscous effects in a tidal basin: extending Taylor's problem

“…The resulting amphidromic system displays elevation and current amphidromic points alternatingly on the centreline of the basin, provided the channel is sufficiently narrow for all Poincaré modes to be evanescent (LeBlond & Mysak 1978). Taylor's strongly idealized model qualitatively reproduces the main features of tides in large-scale basins like the North Sea (Brown 1987).…”

A numerical model study of parameters influencing tidal currents in the Irish Sea

“…This can be readily illustrated (calculation 4) by increasing k to 0.01, with viscosity determined using (24), 'with K 2 = 2.5 x 10 -5, 2 orders of magnitude below its normally accepted va!ue. It is evident from a comparison of Figure 5 with Figure 4a, that increasing bottom friction from (k =' 0.005 to 0.01) in the three-dimensional model has not moved the amphidrome further against .the coast, as is predicted from analytical work with two-dimensional models [Brown, 1987[Brown, , 1989 unrealistically high values (of the order of 50 cm higher than observed in the eastern Irish Sea; Figure 5) with this reduced viscosity. Also, as is to be expected, with a shift in the position of the amphidrome, the phase distribution changes (compare Figures 4a and 5).…”

“…The influence of bed friction upon the location of tidal amphidromes is well known [Brown, 1987[Brown, , 1989, with increasing bottom friction coefficient causing the amphidrome off the east coast of Ireland (Figure 4a) to move closer to the coast. (Pugh [1981] has shown that increased frictional effects can be associated with weather effects.)…”

The Importance of Long Wave Reflections in Tidal Modelling on a Continental Shelf

“…The sensitivity analysis is also limited by the necessity to assume the boundary conditions are correct, as mentioned in section 3 the phase at the English Channel also affects the position of the amphidrome (Brown 1987) however this does not affect the shelf model results and the boundary conditions do match the phase of the elevations observed at Dover on the UK side of the English Channel boundary. Further work should compare bathymetry sources to gauge the potential size of this error and analyse standing/ propagating waves at more locations covering a larger spatial domain to increase confidence in the results and to improve understanding of how the magnitude of the reflections has changed over time.…”

Horizontally viscous effects in a tidal basin: extending Taylor's problem

“…The resulting amphidromic system displays elevation and current amphidromic points alternatingly on the centreline of the basin, provided the channel is sufficiently narrow for all Poincaré modes to be evanescent (LeBlond & Mysak 1978). Taylor's strongly idealized model qualitatively reproduces the main features of tides in large-scale basins like the North Sea (Brown 1987).…”