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L. R. M. Maas et al.
description of tidal patterns, both in the world oceans as well as in coastal regions.
In fact, phase singularities, such as amphidromes, have been found in other settings
too: e.g. in the inertial wave patterns that appear in homogeneous-density fluids contained in uniformly-rotating, fully-enclosed cubes [4, 5, 18, 21, 27], as well as in
other branches of physics, like quantum mechanics [3].
In theoretical models, the simplest version of an amphidrome is obtained in a
tidal channel when two counter-propagating Kelvin waves form nodal points [29,
38]. Amphidromes also appear in semi-analytical models of rotationally-modified
surface gravity waves, both in half-infinite channels and in rectangular basins [32,
33, 38], as well as in numerical models of more realistically-shaped basins [15],
although they are then mixed with Poincaré waves.
Due to the advent of satellite altimetry, however, spatial patterns of combined
Kelvin and Poincaré waves could be directly observed in whole-field measurements
of the Ocean [7], albeit at three kilometer resolution along and still more crudely
across the satellite track. It revealed that on the open ocean, tides are of smallamplitude, a few decimeter at most, in line with the strength of the tidal forcing.
Amplification is restricted to coastal regions, first of all due to the exponential character of Kelvin waves, induced by the Coriolis force, but occurring especially when
a bay co-oscillates, as when in resonance with a basin mode [10].
Away from the equator, open ocean tides combine propagating, coastally-trapped
Kelvin waves with Poincaré waves. Together these display amphidromic points that
are traversed mostly in cyclonic (anti-clockwise) sense in the Northern Hemisphere,
and vice versa in the Southern Hemisphere. However, at times, ocean tides instead
display sloshing, and are then dominated by standing Poincaré waves that show a
behaviour complementary to that of Kelvin waves, exhibiting off-coastal elevation
maxima, betrayed by near-uniform phases. One example for the semidiurnal M2 tide
is seen in Fig. 1 in the Mozambique Channel. It has a maximum and nearly uniform
phase in the narrows. A more striking example, though, can be found in the central
Indian Ocean, where the tidal maximum at 75 ◦ E, 19 ◦ S lies close to a phase saddle
point at 71 ◦ E, 9.6 ◦ S, the point where two 260-degrees-phase-lines cross each other
(see star in Fig. 1). The uniformity in phase near this local tidal maximum implies
that over a large area the semidiurnal tide simply rises and sinks in unison. Notice the
4 amphidromes surrounding this mid Indian Ocean maximum, some lying actually
on land (like on Sri Lanka and Madagascar).
The altimetry-derived barotropic tides are based on the Oregon State University
Tidal Inversion Software (OTIS) [12]. In this work, we use the TPX08-ATLAS product, which is provided for 9 tidal constituents (M2, S2, N2, K2, K1, O1, P1, Q1
and M4), with a horizontal resolution of 1/30 ◦ (http://volkov.oce.orst.edu/tides), see
Table 1, although we will not consider M4 tides here.
What will be relevant for the present study is the behaviour of the tide in the
Mozambique Channel, as well as along a transect at 23 ◦ S, east of Madagascar,
where our instruments are located. Taking a cursory look at these two regions, Fig. 1
shows that we may expect quite different behaviour. In the Mozambique Channel,
the semidiurnal M2 tide—usually the strongest tidal component—has a standing
character, testified by its near-uniform phase, and an amplified tidal elevation which
L. R. M. Maas et al.
description of tidal patterns, both in the world oceans as well as in coastal regions.
In fact, phase singularities, such as amphidromes, have been found in other settings
too: e.g. in the inertial wave patterns that appear in homogeneous-density fluids contained in uniformly-rotating, fully-enclosed cubes [4, 5, 18, 21, 27], as well as in
other branches of physics, like quantum mechanics [3].
In theoretical models, the simplest version of an amphidrome is obtained in a
tidal channel when two counter-propagating Kelvin waves form nodal points [29,
38]. Amphidromes also appear in semi-analytical models of rotationally-modified
surface gravity waves, both in half-infinite channels and in rectangular basins [32,
33, 38], as well as in numerical models of more realistically-shaped basins [15],
although they are then mixed with Poincaré waves.
Due to the advent of satellite altimetry, however, spatial patterns of combined
Kelvin and Poincaré waves could be directly observed in whole-field measurements
of the Ocean [7], albeit at three kilometer resolution along and still more crudely
across the satellite track. It revealed that on the open ocean, tides are of smallamplitude, a few decimeter at most, in line with the strength of the tidal forcing.
Amplification is restricted to coastal regions, first of all due to the exponential character of Kelvin waves, induced by the Coriolis force, but occurring especially when
a bay co-oscillates, as when in resonance with a basin mode [10].
Away from the equator, open ocean tides combine propagating, coastally-trapped
Kelvin waves with Poincaré waves. Together these display amphidromic points that
are traversed mostly in cyclonic (anti-clockwise) sense in the Northern Hemisphere,
and vice versa in the Southern Hemisphere. However, at times, ocean tides instead
display sloshing, and are then dominated by standing Poincaré waves that show a
behaviour complementary to that of Kelvin waves, exhibiting off-coastal elevation
maxima, betrayed by near-uniform phases. One example for the semidiurnal M2 tide
is seen in Fig. 1 in the Mozambique Channel. It has a maximum and nearly uniform
phase in the narrows. A more striking example, though, can be found in the central
Indian Ocean, where the tidal maximum at 75 ◦ E, 19 ◦ S lies close to a phase saddle
point at 71 ◦ E, 9.6 ◦ S, the point where two 260-degrees-phase-lines cross each other
(see star in Fig. 1). The uniformity in phase near this local tidal maximum implies
that over a large area the semidiurnal tide simply rises and sinks in unison. Notice the
4 amphidromes surrounding this mid Indian Ocean maximum, some lying actually
on land (like on Sri Lanka and Madagascar).
The altimetry-derived barotropic tides are based on the Oregon State University
Tidal Inversion Software (OTIS) [12]. In this work, we use the TPX08-ATLAS product, which is provided for 9 tidal constituents (M2, S2, N2, K2, K1, O1, P1, Q1
and M4), with a horizontal resolution of 1/30 ◦ (http://volkov.oce.orst.edu/tides), see
Table 1, although we will not consider M4 tides here.
What will be relevant for the present study is the behaviour of the tide in the
Mozambique Channel, as well as along a transect at 23 ◦ S, east of Madagascar,
where our instruments are located. Taking a cursory look at these two regions, Fig. 1
shows that we may expect quite different behaviour. In the Mozambique Channel,
the semidiurnal M2 tide—usually the strongest tidal component—has a standing
character, testified by its near-uniform phase, and an amplified tidal elevation which