Waveguide structures encountered in underwater acoustics usually lead to nonseparable boundary value problems, which do not admit definition of conventional normal modes. However, it may nevertheless be possible to construct source‐free modelike wavefunctions for such configurations, which are intrinsically determined by the waveguide geometry, are mutually decoupled, and therefore propagate independently of one another when used in superposition. We call such wavefunctions intrinsic modes. For the special case of a wedge‐shaped ocean with penetrable bottom, we pursue an approach similar to our previous analysis [J. M. Arnold and L. B. Felsen, J. Acoust. Soc. Am. 73, 1105–1119 (1983)] to construct the intrinsic modes explicitly. Leading order asymptotic evaluation of an intrinsic mode for small bottom slope reveals its similarity to the conventional adiabatic mode, but with a uniform transition, through cutoff, between the bound and leaky mode regions. This construction proceeds without reference to any source of the acoustic field, thereby differing from our previous treatment wherein the existence of local modes was inferred from an independently calculated asymptotic form of a line source field. Moreover, by local normal mode expansion of an intrinsic mode, with the expansion coefficients derived from the next higher order asymptotic approximation, we demonstrate explicitly that the intrinsic mode can account for coupling between adiabatic modes, with coupling coefficients that are shown elsewhere to be consistent with those from conventional coupled mode theory.