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This paper considers two-dimensional gravity solitary waves moving through a body of density stratified water lying below vacuum. The fluid domain is assumed to lie above an impenetrable flat ocean bed, while the interface between the water and vacuum is a free boundary where the pressure is constant. We prove that, for any smooth choice of upstream velocity field and density function, there exists a continuous curve of such solutions that includes large-amplitude surface waves. Furthermore, following this solution curve, one encounters waves that come arbitrarily close to possessing points of horizontal stagnation.
We also provide a number of results characterizing the qualitative features of solitary stratified waves. In part, these include bounds on the wave speed from above and below, some of which are new even for constant density flow; an a priori bound on the velocity field and lower bound on the pressure; a proof of the nonexistence of monotone bores in this physical regime; and a theorem ensuring that all supercritical solitary waves of elevation have an axis of even symmetry.
@article{AIHPC_2018__35_2_517_0,
author = {Chen, Robin Ming and Walsh, Samuel and Wheeler, Miles H.},
title = {Existence and qualitative theory for stratified solitary water waves},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {517--576},
publisher = {Elsevier},
volume = {35},
number = {2},
year = {2018},
doi = {10.1016/j.anihpc.2017.06.003},
mrnumber = {3765551},
zbl = {1408.35135},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2017.06.003/}
}
TY - JOUR AU - Chen, Robin Ming AU - Walsh, Samuel AU - Wheeler, Miles H. TI - Existence and qualitative theory for stratified solitary water waves JO - Annales de l'I.H.P. Analyse non linéaire PY - 2018 SP - 517 EP - 576 VL - 35 IS - 2 PB - Elsevier UR - http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2017.06.003/ DO - 10.1016/j.anihpc.2017.06.003 LA - en ID - AIHPC_2018__35_2_517_0 ER -
%0 Journal Article %A Chen, Robin Ming %A Walsh, Samuel %A Wheeler, Miles H. %T Existence and qualitative theory for stratified solitary water waves %J Annales de l'I.H.P. Analyse non linéaire %D 2018 %P 517-576 %V 35 %N 2 %I Elsevier %U http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2017.06.003/ %R 10.1016/j.anihpc.2017.06.003 %G en %F AIHPC_2018__35_2_517_0
Chen, Robin Ming; Walsh, Samuel; Wheeler, Miles H. Existence and qualitative theory for stratified solitary water waves. Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 2, pp. 517-576. doi: 10.1016/j.anihpc.2017.06.003
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