Internal waves describe the (linear) response of an incompressible stably stratified
fluid to small perturbations. The inclination of their group velocity with respect
to the vertical is completely determined by their frequency. Therefore the
reflection on a sloping boundary cannot follow Descartes’ laws, and it is
expected to be singular if the slope has the same inclination as the group
velocity. We prove that in this critical geometry the weakly viscous and weakly
nonlinear wave equations have actually a solution which is well approximated
by the sum of the incident wave packet, a reflected second harmonic and
some boundary layer terms. This result confirms the prediction by Dauxois
and Young, and provides precise estimates on the time of validity of this
approximation.
PDF Access Denied
We have not been able to recognize your IP address
54.146.97.79
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our
journal-recommendation form.
Or, visit our
subscription page
for instructions on purchasing a subscription.