Baroclinic Responses Caused by Barotropic Rossby-Wave Incident to Steep Bottom Topography : A Semi-analytical Study

Baroclinic responses caused by barotropic Rossby-wave incident to steep bottom topography are modeled for two-layer ocean with a meridionally running bottom topography (ridge), which is Gaussian shape in zonal direction. The model is governed by linear geostrophic equations under rigid-rid and beta-plane approximations, and is solved semi-analytically. The baroclinic waves are generated west of the topography due to the barotropic wave incidents to the topography. The dependencies of modeled baroclinic responses are studied with respect to model parameters, such as topography shape or width, layer thickness, frequency and meridional wave number of the incidental barotropic Rossby waves. The shape of the bottom topography strongly influences the amplitudes of the baroclinic responses. When topography height is changed with fixed other model parameters, the interface amplitude increases as the ridge height is increased. In particular, the rate of the amplitude increase is quite high for the bottom topography hight larger than the one third of the lower layer thickness. For a fixed topography height, the interface amplitude takes a maximum as the topography width is changed. The topography width at the maximal amplitude is roughly 3.2 times as large as the wave length of free baroclinic Rossby wave around a limit of small topography height, and is increased linearly when the topography height is increased. The wave length of the free baroclinic waves is proportional to the period. Hence, the interface amplitude is dependent on the period of the incidental barotropic waves, and takes its maxima at specific period. With layer thickness suitable to for the mid-latitude Pacific or Atlantic Ocean, the maximal amplitude occurs in a period range between one and five years. These results imply that the baroclinic wave generation is the most energetic from intrannual to annual periods, consistent with the findings of the satellite observations. Furthermore, different topographies with different horizontal scales, such as narrow Emperor Sea Mountains and relatively wide Shatsky and Hess Rises in the North Pacific, are expected to have different influences on baroclinic wave generations at a specific timescale.