Deep-Ocean Tides in the South-West Indian Ocean . . .
173
amplitudes each, we take their average values as observed tidal amplitudes, Z j , in
computing their admittance, Z j ∕ ̄
Z j . The tidal potential coefficients, C j , of the eight
tidal frequencies Ω j : (Q1, O1, P1, K1, N2, M2, S2, K2), are given by [29] and
read C j = (0.072, 0.377, 0.176, 0.530, 0.174, 0.908, 0.423, 0.115). With these coefficients, along the transects in the Mozambique Channel (í µí¼ ≈ 16.75 ◦ S) and East
of Madagascar (í µí¼ ≈ 22.90
◦ S), the admittance of these tidal components, Z j ∕ ̄
Z j , has
been determined, shown in the second and third column of Table 1, respectively.
Admittances indeed vary fairly smoothly, particularly in the Mozambique Channel
where semidiurnal amplitudes are all resonantly amplified, peaking with an amplification factor of about 5.9, at a frequency in between S2 and K2.
The response at the diurnal frequencies in the Mozambique Channel is about the
same as in the tidal potential (admittance close to 1), albeit picking up at frequencies
below the lowest diurnal frequency considered here, Q1.
The tides derived from BPRs along the transect East of Madagascar are all
suppressed compared to their presence in the tidal potential. The semidiurnal components are weak because of the proximity of an amphidromic point close to the transect; the diurnal components vary at a larger scale, and amplify towards the equator.
Deep Versus Mid-depth Pressure-Measurements of Tides
BPRs of tides show harmonic constants to be very stable. This is surprising as internal tides might well be present at the bottom too. These could lead to a modulation of
tidal amplitudes and phases. Consider e.g. a two-layer ocean with upper and lower
layer depths h 1 and h 2 and corresponding densities í µí¼ 1 and í µí¼ 2 , respectively. Then
the hydrostatic pressure at the bottom is given by a stationary part í µí¼ 1 gh 1 + í µí¼ 2 gh 2
and a variable part due to elevations of free surface, í µí¼ , or interface, í µí¼, given by
gí µí¼ 1 í µí¼ + g(í µí¼ 2 − í µí¼ 1 )í µí¼. Expressed as elevation, by dividing by gí µí¼ 1 , this perturbation
pressure reads í µí¼ + í µí»¿í µí¼. It shows that pressure perturbations due to large interface
elevations í µí¼ ≫ í µí¼ might still be moderate due to weakness of the density contrast,
í µí»¿ ≡ í µí¼ 2 ∕í µí¼ 1 − 1 ≪ 1. When the ocean is continuously-stratified, higher internal modal
structures may appear within the sea. The net pressure perturbation at the bottom
due to internal displacements can then be less than those within the water column
as isopycnal elevations at one depth can be compensated by depressions at another.
Judging from the near-bottom stability of the tides, internal tides are weak at the
bottom either for the above reason, or because their presence is precluded by the
presence of a thick bottom boundary layer at the top of which internal waves reflect,
higher up in the water column.
Observations from pressure recorders, mounted higher in the water column do
show the presence of internal tides. In fact, they often dominate the pressure signal,
especially East of Madagascar, see the second and fourth row of Fig. 13, showing
amplitudes at intermediate depths four times those found at the bottom. Mooring
lmc8, on the East side of Mozambique Channel, is exceptional in showing hardly any
173
amplitudes each, we take their average values as observed tidal amplitudes, Z j , in
computing their admittance, Z j ∕ ̄
Z j . The tidal potential coefficients, C j , of the eight
tidal frequencies Ω j : (Q1, O1, P1, K1, N2, M2, S2, K2), are given by [29] and
read C j = (0.072, 0.377, 0.176, 0.530, 0.174, 0.908, 0.423, 0.115). With these coefficients, along the transects in the Mozambique Channel (í µí¼ ≈ 16.75 ◦ S) and East
of Madagascar (í µí¼ ≈ 22.90
◦ S), the admittance of these tidal components, Z j ∕ ̄
Z j , has
been determined, shown in the second and third column of Table 1, respectively.
Admittances indeed vary fairly smoothly, particularly in the Mozambique Channel
where semidiurnal amplitudes are all resonantly amplified, peaking with an amplification factor of about 5.9, at a frequency in between S2 and K2.
The response at the diurnal frequencies in the Mozambique Channel is about the
same as in the tidal potential (admittance close to 1), albeit picking up at frequencies
below the lowest diurnal frequency considered here, Q1.
The tides derived from BPRs along the transect East of Madagascar are all
suppressed compared to their presence in the tidal potential. The semidiurnal components are weak because of the proximity of an amphidromic point close to the transect; the diurnal components vary at a larger scale, and amplify towards the equator.
Deep Versus Mid-depth Pressure-Measurements of Tides
BPRs of tides show harmonic constants to be very stable. This is surprising as internal tides might well be present at the bottom too. These could lead to a modulation of
tidal amplitudes and phases. Consider e.g. a two-layer ocean with upper and lower
layer depths h 1 and h 2 and corresponding densities í µí¼ 1 and í µí¼ 2 , respectively. Then
the hydrostatic pressure at the bottom is given by a stationary part í µí¼ 1 gh 1 + í µí¼ 2 gh 2
and a variable part due to elevations of free surface, í µí¼ , or interface, í µí¼, given by
gí µí¼ 1 í µí¼ + g(í µí¼ 2 − í µí¼ 1 )í µí¼. Expressed as elevation, by dividing by gí µí¼ 1 , this perturbation
pressure reads í µí¼ + í µí»¿í µí¼. It shows that pressure perturbations due to large interface
elevations í µí¼ ≫ í µí¼ might still be moderate due to weakness of the density contrast,
í µí»¿ ≡ í µí¼ 2 ∕í µí¼ 1 − 1 ≪ 1. When the ocean is continuously-stratified, higher internal modal
structures may appear within the sea. The net pressure perturbation at the bottom
due to internal displacements can then be less than those within the water column
as isopycnal elevations at one depth can be compensated by depressions at another.
Judging from the near-bottom stability of the tides, internal tides are weak at the
bottom either for the above reason, or because their presence is precluded by the
presence of a thick bottom boundary layer at the top of which internal waves reflect,
higher up in the water column.
Observations from pressure recorders, mounted higher in the water column do
show the presence of internal tides. In fact, they often dominate the pressure signal,
especially East of Madagascar, see the second and fourth row of Fig. 13, showing
amplitudes at intermediate depths four times those found at the bottom. Mooring
lmc8, on the East side of Mozambique Channel, is exceptional in showing hardly any