TY - JOUR

T1 - On the existence and qualitative theory of stratified solitary water waves

AU - Chen, Robin Ming

AU - Walsh, Samuel

AU - Wheeler, Miles H.

PY - 2016/6/1

Y1 - 2016/6/1

N2 - In this note, we announce new results on the existence of two-dimensional solitary waves moving through a body of density stratified water lying beneath air. The fluid domain is assumed to lie above an impenetrable flat ocean bed, while the interface between the air and water is a free boundary where the pressure is constant. We prove that, for any smooth choice of upstream velocity and density distribution, there exists a continuous curve of such solutions that includes large-amplitude waves that come arbitrarily close to having a (horizontal) stagnation point. Additionally, we provide several results characterizing the qualitative features of solitary stratified waves. In part, these include: estimates on the Froude number, velocity, and pressure, some of which are new, even for the constant density case; a proof of the nonexistence of monotone bores in this physical regime; and a theorem ensuring that all supercritical stratified solitary waves of elevation have an axis of even symmetry.

AB - In this note, we announce new results on the existence of two-dimensional solitary waves moving through a body of density stratified water lying beneath air. The fluid domain is assumed to lie above an impenetrable flat ocean bed, while the interface between the air and water is a free boundary where the pressure is constant. We prove that, for any smooth choice of upstream velocity and density distribution, there exists a continuous curve of such solutions that includes large-amplitude waves that come arbitrarily close to having a (horizontal) stagnation point. Additionally, we provide several results characterizing the qualitative features of solitary stratified waves. In part, these include: estimates on the Froude number, velocity, and pressure, some of which are new, even for the constant density case; a proof of the nonexistence of monotone bores in this physical regime; and a theorem ensuring that all supercritical stratified solitary waves of elevation have an axis of even symmetry.

UR - http://www.scopus.com/inward/record.url?scp=84963569422&partnerID=8YFLogxK

U2 - 10.1016/j.crma.2016.03.004

DO - 10.1016/j.crma.2016.03.004

M3 - Article

AN - SCOPUS:84963569422

VL - 354

SP - 601

EP - 605

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

SN - 1631-073X

IS - 6

ER -