ON THE IRREVERSIBILITY OF INTERNAL-WAVE DYNAMICS DUE TO WAVE-TRAPPINGBY MEAN FLOW INHOMOGENEITIES .1. LOCAL ANALYSIS

The propagation of guided internal waves on non-uniform large-scale fl ows of arbitrary geometry is studied within the framework of linear in viscid theory in the WKB-approximation. Our study is based on a set of Hamiltonian ray equations, with the Hamiltonian being determined from the Taylor-Goldstein boundary-value problem for a stratified shear fl ow. Attention is focused on the fundamental fact that the generic smoo th non-uniformities of the large-scale flow result in specific singula rities of the Hamiltonian. Interpreting wave packets as particles with momenta equal to their wave vectors moving in a certain force field, one can consider these singularities as infinitely deep potential hole s acting quite similarly to the 'black holes' of astrophysics. It is s hown that the particles fall for infinitely long time, each into its o wn 'black hole'. In terms of a particular wave packet this falling imp lies infinite growth with time of the wavenumber and the amplitude, as well as wave motion focusing at a certain depth. For internal-wave-fi eld dynamics this provides a robust mechanism of a very specific conse rvative and moreover Hamiltonian irreversibility. This phenomenon was previously studied for the simplest model of the flow non-uniformity, parallel shear flow (Badulin, Shrira & Tsimring 1985), where the term 'trapping' for it was introduced and the basic features were establish ed. In the present paper we study the case of arbitrary flow geometry. Our main conclusion is that although the wave dynamics in the general case is incomparably more complicated, the phenomenon persists and re tains its most fundamental features. Qualitatively new features appear as well, namely, the possibility of three-dimensional wave focusing a nd of 'non-dispersive' focusing. In terms of the particle analogy, the latter means that a certain group of particles fall into the same hol e. These results indicate a robust tendency of the wave field towards an irreversible transformation into small spatial scales, due to the p resence of large-scale flows and towards considerable wave energy conc entration in narrow spatial zones.