Large amplitude internal waves (IW) have emerged in the past 30 years as a prominent feature of many shelf and coastal areas around the world. Already at the end of the 1960's, Ziegenbein (1969) and Halpern (1971) reported the existence of tidally generated internal waves in the Strait of Gibraltar and in Massachusetts Bay. By now, nonlinear internal waves have been reported on the New England shelf (Colosi et al., 1999), on the Malin shelf (Small et at., 1999) in the Celtic Sea (Holt and Thorpe, 1997), near the Oregon coast (Trevorrow, 1998), in the East and South China Seas (Liu et al., 1998), in the Bay of Biscay (New and Pingree, 1992), in the Strait of Messina (Brandt et al., 1996), in the Sulu Sea (Apel et al., 1985), on the Scotian shelf (Sandstrom and Elliot, 1984), in the Gulf of California (Fu and Holt, 1984), in the New York Bight (Liu, 1988) and in the Andaman Sea (Osborne and Burch, 1980).
Of the three stages of the life of a nonlinear IW - generation, propagation and dissipation/shoaling, the issue of propagation is probably the best understood. Using the amplitude of the wave and the wavenumber relative to an appriate depth as parameters, several sets of equations can be derived from the Euler equations (nglecting viscosity) representing different regimes (shallow vs. deep water, small amplitude vs. large amplitude, etc.). References... At least some of these simplified equations are amenable to analytical solutions, in the form of waves of fixed shape traveling at a speed which is a non linear function of the amplitude (unlike linear waves) as well as the wavenumber.
The generation problem is more complicate and it has been subject to fewer investigations. Often, the timing of the waves strongly suggest a tidal origin, such as in Massachusetts Bay (Chereskin, 1983). In most cases, it is the barotropic tidal flow over some topographic feature (such as a sill) that injects energy into the wave field, although the exact details are often complicated by other factors, such as areas where the flow becomes supercritical, local instabilities etc (Farmer and Armi, 1999, 2000). This problem has been modeled with success in the past solving directly the Euler (or Navier-Stokes) equations (Hibiya, Lamb).
The literature on shoaling and dissipation is even scarcer, with few observation of shoaling of IW reported by Sandstrom and Oakey (1995) over the Scotian shelf. Yet the problem of dissipation has far reaching implications for a variety of applications. Here we will just mention that there is still a considerable amount of uncertainty as to what dissipates the huge amount of energy contained in the tides of the global ocean (Munk and Wunsch, 1998). Currently two mechanisms are being proposed: one postulates that the tidal flow over mid-ocean ridges creates internal waves which in turn become unstable, cascading energy towards the dissipating scales (several sessions of the AGU-ASLO 2000 Ocean Sciences meeting were specifically devoted to this problem), while the other considers the ISWs generated on the continental shelfs as the primary way through which energy is fed into the dissipative scales (see e.g. MacKinnon and Gregg, 2000). Also, the very distribution of dissipation on the shelf might be highly intermittent, with localized regions where shoaling/overturning raises the local level of dissipation several orders of magnitude above the background (Nash and Moum, 2000). Probably both mechanisms contribute to the total budget, the question being what their relative contribution is.
In this paper we use a model to study the global problem of generation, propagation and dissipation of ISWs in Massachusetts Bay, where a detailed set of observations was carried on in the summer of 1998. The rest of the paper is oganized as follows: The second section describes the data collected in the Bay; the third section describes the model and the environmental conditions; the fourth section presents the results from the modeling effort, exploring the effects of variation in environmental conditions; in the fifth section we discuss the results of the model in conjuction with the observed field and provide a summary. A detailed analysis of the approximations used to derive the model is provided in the Appendix.