Nonlinear transfer of internal-tide energy and the effect of rotation: an experimental study on bottom reflection, subharmonic resonance, and scattering at a thermocline.
| Project acronym: | |
| Name of Group Leader: | T. GERKEMA, Royal Netherlands Institute, Texel, The Netherlands |
| User-Project Title: | Nonlinear transfer of internal-tide energy and the effect of rotation: an experimental study on bottom reflection, subharmonic resonance, and scattering at a thermocline. |
| Facility: | Coriolis platform |
| Proceedings TA Project: | Nonlinear transfer of internal-tide energy and the effect of rotation: an experimental study on bottom reflection, subharmonic resonance, and scattering at a thermocline |
| Data Management Report: | Data Management Reports Page You will need to login to view this page |
Summary:
Internal waves in fluids owe their existence to the restoring forces of gravity (in a stably stratified fluid) and the Coriolis force (in rotating fluids). Examples are the inertio-gravity waves found in the ocean, for example at the tidal frequency, which are generated by tidal flow over large-scale topography, such as the continental slope. Internal waves propagate not only horizontally but also vertically. Thus, internal tides generated at the shelf edge will propagate downward, and reflect at the ocean bottom.
Internal tides are among the most energetic internal waves in the ocean, and play an important part in deep-ocean mixing, which in turn is a crucial chain in the maintenance of the meridional overturning circulation (Garrett & St. Laurent, 2002; Wunsch & Ferrari, 2004). Apart from this dissipation of internal-tide energy at small scales, there is a variety of ways in which this energy may be redistributed throughout the internal-wave spectrum. Three of these mechanisms, now well established theoretically but still in need of experimental and observational testing, are (A) the transfer to higher harmonics by nonlinear interaction, in particular by bottom reflection, (B) resonant generation of subharmonics, and (C) the generation of solitary waves due to scattering of an internal-tide beam at the thermocline. In the ocean, higher harmonics of the internal are often found in internal-wave spectra, but a direct link with mechanism (A) has not yet been established; possible indirect evidence of (B) has been found in observations showing an enhanced dissipation rate precisely at latitudes where this mechanism is thought to be at work on theoretical grounds (Hibiya & Nagasawa, 2004), while subharmonics were found in internal-tide beams in a numerical study (Gerkema et al, 2006b); mechanism (C) has been established both observationally (New & DaSilva, 2002) and theoretically (Gerkema, 2001).
Mechanism A
It has now been well established that nonlinear processes are at work at the junction of the incident and reflected waves, by which higher harmonics can be generated (i.e. waves at multiple frequency of the primary wave). This mechanism has been described analytically (e.g. Tabaei et al., 2005), and also numerically for internal tides (Gerkema et al., 2006a). In the latter paper, the effect of rotation was studied as well. In a sequel to this work (Gerkema et al., 2006b), in which a higher resolution was used, the dependence on rotation seemed fairly weak, whereas the earlier study had suggested that higher harmonics are stronger at lower latitudes (i.e. for weaker Coriolis effects). On the other hand, recent analytical work indicates that higher harmonics are weaker at lower latitudes, at least so far as single plane waves are concerned (Gerkema, 2006). These contradictory results form the primary motivation for this experimental work, in which the effect of the Coriolis force on the generation of higher harmonics will be studied using various rotation rates of the platform.
Mechanism B
A second goal concerns the generation of subharmonics. For a sufficiently low rate of rotation, waves having half the frequency of the primary wave can be generated by subharmonic resonance, a mechanism which is now thought to play a role in ocean mixing near the critical latitudes 30N/S in the ocean, and perhaps as well in the equatorial region spanned by these latitudes. Recent numerical experiments show that this process occurs already very close to the continental slope (Gerkema et al, 2006b), and this will now be verified in a laboratory setting.
Mechanism C
An internal-tide beam, propagating upward from the abyssal ocean toward the surface, undergoes a strong deformation as it encounters the (seasonal) thermocline, i.e. the part of the water column in which the stratification varies strongly. The beam scatters and creates a depression at the thermocline; this depression can develop into a train of solitary waves, due to nonlinear and nonhydrostatic processes (Gerkema, 2001). This mechanism is at work in for example the Central Bay of Biscay, where these solitary waves were observed (both by satellite and in-situ measurements) precisely where the internal-tide comes across the thermocline, which lies 50m below the surface (New & DaSilva, 2002). This mechanism has however never been studied experimentally, and it is one of the primary goals to study the effect of rotation (i.e. latitude in the oceanographic context) on the generation of solitary waves. Theoretical work indicates that rotation reduces the number of solitary waves generated from a depression (Gerkema, 2001). This idea will here be tested.
Click here for further information about this project on the CNRS website.
| Publication References |
| Internal-tide attractors in laboratory and numerical experiments, Journal of fluid Mechanics, in prep., L. Gostiaux, T. Gerkema, J. Sommeria and U. Harlander |
| Internal-tide attractors in laboratory and numerical experiments L. Gostiaux, T. Gerkema, J. Sommeria and U. Harlander, Journal of fluid Mechanics, in prep. |