The interaction of mode-1 internal tides with a geostrophic current

Yangxin He, University of Waterloo, Department of Applied Math, Waterloo, ON, Canada and Kevin G Lamb, Univ Waterloo, Waterloo, ON, Canada
We examine the reflection and transmission of mode-1 internal
tides (ITs) propagating across a geostrophic current, such as the Gulf
Stream, in a two dimensional setting. The current is modeled as an idealized Gaussian function with width
and length . Depending on the current parameters and the Coriolis parameter , the effective frequency
can be smaller or larger than the IT frequency
, resulting in weak or strong reflections from the ITs impinging
on the current. Our analysis is mainly focused on 1) the reflection coefficient of the ITs
from the current and 2) the energy in the linear modes , where is the modal
number, produced after the waves propagate through the
current. There exists a region of and , that
maximizes and , respectively. The values of and
slowly decrease as and move away from the region. A linear theory of from internal waves normally incident on a linear barotropic current is presented.