14 Internal Solitary Waves System in the Mozambique Channel
273
Considering the relative positions of the ISWs signatures and the geometry of the
IT beam reflection, a region of low activity can be identified near the shelf-break
that lies behind the re-emergence of IT energy. This region is followed by another
area of ISW activity that closely coincides with the surfacing positions of the IT
rays. Similarly to the case in the Bay of Biscay, this suggests that there is a region of
elevated forcing near the shelf edge that is simultaneously generating ISWs directly
above, and IT rays that are propagating to the deeper ocean, reflecting from the sea
floor, and locally generating ISWs some 90 km farther offshore.
14.3 Mode 2 ISWs
14.3.1 Introduction
IWs propagation is naturally bounded, both above and below by the ocean’s surface
and bottom—thus confining them within a natural waveguide. However, the ocean’s
pycnocline can also be seen as another form of waveguide, since it confines the
higher frequency oscillations into interfacial waves (e.g. the ISWs seen in SAR imagery). The vertical confinement imposed by these boundaries results in horizontally
propagating waves, which nonetheless have a standing character in the vertical. In
this case, a classical Sturm-Liuville problem arises if the linear equations of motions
(under the Boussinesq and Traditional approximations) are solved with boundary
conditions for zero vertical velocities at the surface and bottom of the ocean. Therefore, IW solutions with an infinite number of modes can either exist in nature on their
own or in any number of combinations (see e.g. Gerkema and Zimmerman 2008 for
a detailed description on IW dynamics). The first case, usually results in low mode
propagation of IWs (like interfacial ITs or ISWs), while the second may result in an
increasing superposition of modes, which makes the spatial appearance of the IW
field to resemble a beam structure (like IT beams). In the particular case of SAR
imagery, ISWs are generally described as interfacial mode 1 waves of depression
(propagating along the pycnocline, and depressing it) that are usually ridding on the
troughs of the IT (which is also an interfacial disturbance of the pycnocline). However, recent attention has been given to a different set of observations, where SAR
surface signatures are not consistent with mode 1 ISWs, but rather suggest mode 2
solitary-like waves (for simplicity referred to in this chapter as mode 2 ISWs). In
fact, despite that first-mode internal waves are most commonly observed in the ocean,
higher-mode waveforms also occur under the proper conditions. A mode-2 wave is
best thought of in terms of a three-layer stratified ocean, when the middle-layer
thickness is relatively thinner than the upper and lower layers. In this configuration,
the wave travels as a bulge in the middle layer, displacing isopycnals upward into
the upper layer and downward into the bottom layer (see e.g. Shroyer et al. 2010c).
Cases of satellite observations and in situ measurements of mode 2 oceanic ISWs
are seldom, and they are hardly ever found in the literature. In fact, despite that they
have long been predicted in theory, it was not until recently that they were seen to
273
Considering the relative positions of the ISWs signatures and the geometry of the
IT beam reflection, a region of low activity can be identified near the shelf-break
that lies behind the re-emergence of IT energy. This region is followed by another
area of ISW activity that closely coincides with the surfacing positions of the IT
rays. Similarly to the case in the Bay of Biscay, this suggests that there is a region of
elevated forcing near the shelf edge that is simultaneously generating ISWs directly
above, and IT rays that are propagating to the deeper ocean, reflecting from the sea
floor, and locally generating ISWs some 90 km farther offshore.
14.3 Mode 2 ISWs
14.3.1 Introduction
IWs propagation is naturally bounded, both above and below by the ocean’s surface
and bottom—thus confining them within a natural waveguide. However, the ocean’s
pycnocline can also be seen as another form of waveguide, since it confines the
higher frequency oscillations into interfacial waves (e.g. the ISWs seen in SAR imagery). The vertical confinement imposed by these boundaries results in horizontally
propagating waves, which nonetheless have a standing character in the vertical. In
this case, a classical Sturm-Liuville problem arises if the linear equations of motions
(under the Boussinesq and Traditional approximations) are solved with boundary
conditions for zero vertical velocities at the surface and bottom of the ocean. Therefore, IW solutions with an infinite number of modes can either exist in nature on their
own or in any number of combinations (see e.g. Gerkema and Zimmerman 2008 for
a detailed description on IW dynamics). The first case, usually results in low mode
propagation of IWs (like interfacial ITs or ISWs), while the second may result in an
increasing superposition of modes, which makes the spatial appearance of the IW
field to resemble a beam structure (like IT beams). In the particular case of SAR
imagery, ISWs are generally described as interfacial mode 1 waves of depression
(propagating along the pycnocline, and depressing it) that are usually ridding on the
troughs of the IT (which is also an interfacial disturbance of the pycnocline). However, recent attention has been given to a different set of observations, where SAR
surface signatures are not consistent with mode 1 ISWs, but rather suggest mode 2
solitary-like waves (for simplicity referred to in this chapter as mode 2 ISWs). In
fact, despite that first-mode internal waves are most commonly observed in the ocean,
higher-mode waveforms also occur under the proper conditions. A mode-2 wave is
best thought of in terms of a three-layer stratified ocean, when the middle-layer
thickness is relatively thinner than the upper and lower layers. In this configuration,
the wave travels as a bulge in the middle layer, displacing isopycnals upward into
the upper layer and downward into the bottom layer (see e.g. Shroyer et al. 2010c).
Cases of satellite observations and in situ measurements of mode 2 oceanic ISWs
are seldom, and they are hardly ever found in the literature. In fact, despite that they
have long been predicted in theory, it was not until recently that they were seen to