## Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

## If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

# The square root depth wave equations

C. J. Cotter, D. D. Holm and J. R. Percival
Proceedings: Mathematical, Physical and Engineering Sciences
Vol. 466, No. 2124 (8 December 2010), pp. 3621-3633
Stable URL: http://www.jstor.org/stable/40998102
Page Count: 13
Preview not available

## Abstract

We introduce a set of coupled equations for multi-layer water waves that removes the ill-posedness of the multi-layer Green-Naghdi (MGN) equations in the presence of shear. The new well-posed equations are Hamiltonian and in the absence of imposed background shear, they retain the same travelling wave solutions as MGN. We call the new model the square root depth $(\sqrt D )$ equations from the modified form of their kinetic energy of vertical motion. Our numerical results show how the $\sqrt D$ equations model the effects of multi-layer wave propagation and interaction, with and without shear.

• 3621
• 3622
• 3623
• 3624
• 3625
• 3626
• 3627
• 3628
• 3629
• 3630
• 3631
• 3632
• 3633