Internal solitary waves in the Red Sea : An unfolding mystery

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2010; see also Jackson, 2007). Here, we give a preliminary account of some of the available observations of oceanic ISWs in the Red Sea to elucidate three mysterious aspects. First, these ISWs occur repeatedly only over a particular 80 km stretch where the Red Sea is deepest (about ~ 1,500 m deep, along the sea's main axis). Second, they occur in spite of the surface tide-generally seen as their source-being very weak. Third, the ISWs originate from the deep parts of the Red Sea and not from the nearest shelf edge, as is common. Given these unusual characteristics, the source and generation mechanism of these ISWs are unclear at present.
We propose three possible explanations that we hope will motivate further studies focusing, in particular, on modeling and in situ measurements of these waves' temporal and spatial characteristics.
Large tidal-period internal waves (internal tides) are well known to result from the interaction of strong surface (or astronomic) tides with steep seafloor or shelf-break topography. Subsequently, these internal tides propagate as interfacial waves and steepen as they propagate away from the shelf break; ISWs then develop, usually phase locked to the internal tides' troughs (see, e.g., Pingree et al., 1986;Gerkema, 1996;Alford et al., 2010). When the maximum surface tidal current at the internal wave generation site is significantly less than the phase speed of the generated internal tides, it is generally accepted that linear theory should provide a good approximate description of the internal tides (see, e.g., Vlasenko et al., 2005)    In addition to imaging spectrometers, such as MODIS and MERIS that operate in the visible wavelengths of the electromagnetic spectrum, ISWs are also detectable in radar images (e.g., Alpers, 1985) Pingree et al., 1986;da Silva et al., 2011). When we assume that ISW generation occurs at the same tidal phase   Note, however, that the slopes of the linear fits to the filled circles are slightly less steep than those for the SAR data (which is particularly noticeable for east-propagating waves), meaning that, during the period of this sequence, the phase speeds were smaller (1.1 m s -1 and 0.9 m s -1 for east-and west-propagating waves, respectively).

resonant interfacial Tides
It is well known that (interfacial) internal tides can generate ISWs through nonlinear effects as they evolve in time (e.g., Gerkema, 1996). Often, these waves occur on the abrupt interface between a buoyant surface layer and a denser layer beneath, and such waves are termed

local generation
Several physical mechanisms can generate ISWs in the ocean, and their generation in the Red Sea as a result of nonlinear evolution of an interfacial tide is just one possibility. Another mechanism is known as "local generation, " in which tidal beams impinge on the pycnocline from below (see New and Pingree, 1992;Gerkema, 2001;New and da Silva, 2002).
In a gently and continuously stratified ocean, the deep layers below the mixed layer exhibit a buoyancy frequency (N) that varies slowly with depth (z), which permits internal tide energy to propagate as beams (or "rays") inclined to the horizontal. The slope of these rays to the horizontal (s), is determined by the strength of N, in a relation that also includes the wave frequency (σ) and the Coriolis frequency (f ) that is related to Earth's rotation: .
In nature, these tidal beams have been observed to reflect off the seafloor and propagate upward, toward the surface.
Near the sea surface, the beams may produce large interfacial solitons where they hit the pycnocline from below (New and Pingree, 1992). But, where do these beams form in the first place? where N is large enough to support them, and propagate in the same horizontal direction as the incident beam. New and Pingree (1992) first proposed this kind of ISW generation for the central region of the Bay of Biscay, where the stratification is sufficiently strong in summer to allow for ISW propagation. Our knowledge of regions where ISWs appear to have been generated by this same local mechanism has been increasing in recent years, now including the Iberian Peninsula (Azevedo et al., 2006;da Silva et al., 2007) and Mozambique Channel (da Silva et al., 2009). Numerical and laboratory experiments have been successful in reproducing the local generation of ISWs under controlled conditions (e.g., Grisouard et al., 2011;Mercier et al., in press), and we now believe that the local generation mechanism is more widely applicable in the ocean than previously thought.  et al., 2008). In this case, in addition to latitude, the angle of propagation in the horizontal plane is also needed (i.e., the orientation north of east, which is 40° in the present case). For each ray, a vertical arrow pointing downward in Figure 4b indicates the horizontal position where it encounters the pycnocline for the first time. We thus see that the ray originating from the western slope (i.e., at left in Figure 4b), marked in red, reaches the pycnocline to the right of the position where the blue ray (which comes from the right) surfaces for the first time (see blue ray and blue vertical arrow in Figure 4b). This would explain why the ISWs appear to originate from the center of the basin, yet are due to local generation. In this view, then, the (internal tide) rays lie at the origin of the ISWs.
Note that the three-layer, summer stratification in the Red Sea could potentially inhibit the local generation mechanism of ISWs. The reason is that the strength of the pycnocline is a critical " isWs are preseNT oNly oVer The red sea's CeNTral, deepesT parT, suggesTiNg They eiTher Break as They propagaTe oNTo The shelf or dissipaTe rapidly. " factor for the evolution of ISWs through the internal tide beam mechanism (e.g., Gerkema, 2001;Akylas et al., 2007;Grisouard et al., 2011;Mercier et al., in press). In addition, the lower pycnocline may distort the rays before they reach the upper one. ISWs. Such a boosting mechanism actually exists, as we illustrate in Figure 5.
Here, we idealize the Red Sea by crudely modeling the trough cross section below the pycnocline as a parabolic basin.
Moreover, we assume the basin to be filled with a uniformly stratified fluid, which guarantees that internal waves of tidal frequency propagate with a fixed inclination relative to the horizontal. In propagate. rays (dashed) maintain fixed inclinations relative to the horizontal, and move rightward and leftward from X 0 . Both rays approach the limit cycle (wave attractor), displayed in red, and eventually propagate in the same direction, indicated by long red arrows (from Maas and lam, 1995). (b) laboratory experiment showing observed spatial distribution of the amplitude of density perturbations due to internal waves generated by weakly rocking a tank sideways. Notice that in this experiment the surface (transition between blue and orange at the top) is a free surface. Courtesy of Jeroen Hazewinkel. (c) simple wave attractor predicted by ray-tracing simulations in the frequency range 0.85-0.95 × 10 -4 rad s -1 for the stratification of the study region in winter. rays are launched at X 0 . dominates defocusing. The amplification mechanism that we appeal to requires weak friction at the bottom and within the water column so that the internal tide may survive a few reflections from the pycnocline and the bottom. In theory, as Figure 5a shows, this ray and all other rays appear to approach a unique limit cycle (red lines), leading to a pileup of internal tidal energy. Internal waves are steered to this particular location regardless of where they are forced within the trough. For this reason, this limit cycle is referred to as a wave attractor (Maas and Lam, 1995;Maas, 2005). During  (Hazewinkel et al., 2010) also reveal the propagating nature of the internal waves, continuously approaching the attractor where, lacking a pycnocline, they are absorbed by viscous dissipation (Hazewinkel et al., 2008).
The ray pattern in Figure 5c shows While for any given ratio of basin aspect ratio (depth H, divided by halfwidth L) to ray slope s, wave attractors exist in nontrivially shaped, stratified basins, such as the parabola (Figure 5a) or Red Sea trough (Figure 5c), the shape of these ray pattern cycles can range from simple (as in Figure 5) to very complicated. We expect that only the simpler ones, discussed in the previous paragraph, are physically relevant (but see Hazewinkel et al., 2010). Although, theoretically, interfacial wave resonance, discussed earlier, occurs for discrete frequencies, wave attractors of a shape displayed in Figure 5 occur over a finite frequency σ-interval (see previous paragraph). These attractor intervals again define resonant situations, but the condition under which resonance occurs now appears fuzzy. This means that the resonance condition is more easily met in practice.