Coupled-mode field computations for media with locally reacting irregular boundaries

Abstract

Coupled-mode methods have been used in underwater acoustics to compute three-dimensional sound propagation and scattering. Significant computational simplifications are possible for media with a lateral variation restricted to cylindrically symmetric anomalies, such as seamounts, and also for media which are invariant in one of the horizontal directions. Typically, the upper and lower depth boundaries of the medium have then been horizontal and flat. This paper generalizes the discrete coupled-mode method with a reflection- (or scattering-) matrix formulation to media with irregular and locally reacting boundaries. Horizontal and vertical segments thereby approximate a sloping boundary. Incorporation of the boundary conditions in a correct way necessitates modifications of the basic equation systems. Additional coupling matrices appear, involving integration of normal-mode products over the depth increments for adjacent regions of the medium. The paper includes three computational examples. One is from underwater acoustics with an island that rises above the sea level. The other two are from atmospheric acoustics with sound propagation over a locally reacting irregular ground surface. Using nonlinear optimization, it is possible to select a suitable artificial absorbing medium termination for a mode representation of the field.

Coupled-mode separation of multiply scattered wavefield components in two-dimensional waveguides

“…The issue here, cf. [46,Sec. IV E], is to design an artificial medium truncation, ending at z = z b , providing negligible reflections. Recalling figure 1b and equation (3.3), the reflections from the downwards directed plane wave must be minimized.…”

“…With the chosen normalization of the normal modes and the basic wave functions, reciprocity arguments of the same type as in [46,Sec. VI] show that all modal reflection matrices R n and R n are symmetric.…”

“…Concerning §4.2, the integrations over the pertinent depth intervals must be reconsidered; cf. the difference between Secs IV and III in [46]. In §4.…”

“…It follows, cf. [46, eqns (35)–(36)], that there are coefficient column vectors bolda¯n=falsefalse{false(a¯nfalse)mfalsefalse}, bolda¯nL=falsefalse{false(a¯nLfalse)mfalsefalse}, bolda¯nR=falsefalse{false(a¯nRfalse)mfalsefalse} for waves to the right (increasing x ) with x -reference at x n −1 , and b n = {( b n ) m }, boldbnL=falsefalse{false(bnLfalse)mfalsefalse}, boldbnR=falsefalse{false(bnRfalse)mfalsefalse} for waves to the left (decreasing x ) with x -reference at x n , such that, within strip region n ,right left.5emthickmathspacetruev(x,z)=Φn…”

Internal tide generation from non-uniform barotropic body forcing

“…The analytical step is the exact reformulation of the hydrodynamic problem as an infinite coupled-mode system (CMS) of equations accomplished by means of an exact, local eigenfunction expansion of the stream function. This approach, also called coupled-mode theory, has been applied to various non-uniform waveguide problems in acoustics (Brekhovskikh & Godin 1992;Desaubies & Dysthe 1995;Maurel, Mercier & Félix 2014;Ivansson 2021), elasticity (Maupin 1988;Pagneux & Maurel 2006;He et al 2019) and water waves (Porter & Staziker 1995;Athanassoulis & Belibassakis 1999;Papoutsellis, Charalampopoulos & Athanassoulis 2018) among other disciplines. In the context of ITs, Griffiths & Grimshaw (2007) derived a CMS from Euler's equations using a local vertical mode decomposition and calculated 2-D ITs over a shelf topography.…”