The Dynamics of Flat Surface Internal Geophysical Waves with Currents

2016/11/20 by Alan Compelli, Rossen Ivanov · 1 citation
Physics and Astronomy · Mathematics · #physics.flu-dyn #math-ph #math.MP #msc:35Q35 #msc:37K05 #msc:74J30

paper · pdf · doi:10.1007/s00021-016-0283-4

published as J. Math. Fluid Mech. 19 (2017) pp 329 -- 344 · LaTeX, 21 pages, 1 figure, available online in J. Math. Fluid Mech. (2016)

arxiv created 2016/11/20 · arxiv updated 2018/11/09

Abstract

A two-dimensional water wave system is examined consisting of two discrete incompressible fluid domains separated by a free common interface. In a geophysical context this is a model of an internal wave, formed at a pycnocline or thermocline in the ocean. The system is considered as being bounded at the bottom and top by a flatbed and wave-free surface respectively. A current profile with depth-dependent currents in each domain is considered. The Hamiltonian of the system is determined and expressed in terms of canonical wave-related variables. Limiting behaviour is examined and compared to that of other known models. The linearised equations as well as long-wave approximations are presented.

Cited by

• Benjamin-Ono dynamics of internal waves with currents

Related

• Modelling intermediate internal waves with currents and variable bottom
• An Internal Wave as a Frequency Filter for Surface Gravity Waves on Water
• Higher-order integrable models for oceanic internal wave-current interactions
• Internal Gravity Waves in a Stratified Fluid with Smoothly Varying Bottom
• The dynamics of internal gravity waves in the ocean: theory and applications