NOTES AND CORRESPONDENCE Comments on ‘‘The Roles of the Horizontal Component of the Earth’s Angular Velocity in Nonhydrostatic Linear Models’’

Kasahara (2003) recently investigated the linear normal modes arising in a series of problems designed to elucidate the influence of the horizontal component of the Coriolis force in Cartesian tangent-plane approximations to the earth’s atmosphere or oceans. He suggests that when the horizontal component of the Coriolis force is included in the presence of horizontal rigid upper and and lower boundaries, ‘‘a distinct kind of wave oscillation emerges whose frequencies are very close to the inertial frequency,’’ and refers to these waves as ‘‘boundary-induced inertial (BII) modes.’’ In the case of a compressible stratified atmosphere he suggests dividing the normal modes into three types: ‘‘acoustic, inertio–gravity, and boundary-induced inertial modes.’’ The same three pairs of eigenmodes were also recently identified in essentially the same type of tangent-plane analysis by Thuburn et al. (2002b), although no BII modes were found in a related numerical analysis of eigenmodes on the full sphere (Thuburn et al. 2002a). The purpose of this comment is to clarify the nature and physical significance of BII modes within the context of the tangent-plane approximation. The distinction between gravity and acoustic waves is fundamental in that different physical processes (buoyancy and elastic restoring forces, respectively) are responsible for the propagation of each type of wave. No such distinction sets the BII mode apart from the inertio–gravity and acoustic modes; rather, as suggested by Kasahara, the mode appears in the set of normal modes due to the presence of the rigid upper and lower boundaries. Yet in contrast to a better known type of boundary-induced wave, the edge wave (in which the wave amplitude decays exponentially in the direction