Non-Reflecting Internal Wave Beam Propagation in the Deep Ocean

It is well-known that internal waves can propagate downwards in the interior of the oceanic (e.g. Gill, 1982) and this process has been studied experimentally in the laboratory (e.g. Stevens and Imberger, 1994). Moreover, it is well-known that a monochromatic internal wave is an exact solution of the fully nonlinear Euler equations for a stratified fluid (in the Boussinesq approximation) with a constant buoyancy (Brunt-Vaisala) frequency, and such a wave propagates without change in amplitude and direction (Miropolsky, 2001). In the general case of the arbitrary distribution of the buoyancy frequency with depth an internal wave will transform and generate internal reflections. However, various observations (De Witt et al, 1986; Pingree and New, 1989, 1991) and numerical simulations (Morozov and Pisarev, 2002; Gerkema, 2002, 2004, Gerkema et al., 2006; Johnston and Merrifield, 2003; Holloway and Merrifield, 2003; Vlasenko et al, 2003) of a nonlinear internal wave field in the ocean show that internal waves of tidal period propagate as beams with no visible internal reflection. Fig. 1 demonstrates such behavior of internal wave beams in the Bay of Biscay (Gerkema et al, 2004). Here we analyze theoretically the penetration of internal waves in an ocean with continuous stratification in background density and a shear current. We will show that for certain specific vertical distributions of the oceanic stratification internal waves can be considered as traveling waves which propagate without any internal reflection. Further these profiles can represent real oceanic data rather well. This confirms that the internal reflection of internal waves in the deep ocean is