{"id":376,"date":"2021-01-07T11:55:06","date_gmt":"2021-01-07T10:55:06","guid":{"rendered":"https:\/\/david-lannes.perso.math.cnrs.fr\/?p=376"},"modified":"2021-11-30T09:37:27","modified_gmt":"2021-11-30T08:37:27","slug":"modeling-shallow-water-waves","status":"publish","type":"post","link":"https:\/\/david-lannes.perso.math.cnrs.fr\/?p=376","title":{"rendered":"Modeling shallow water waves"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">D. Lannes, Nonlinearity 33 (2020), R1 <a href=\"https:\/\/david-lannes.perso.math.cnrs.fr\/wp-content\/uploads\/2021\/11\/modelinSW.pdf.zip\">Download<\/a> <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">We review here the derivation of many of the most important models that\nappear in the literature (mainly in coastal oceanography) for the description\nof waves in shallow water. We show that these models can be obtained\nusing various asymptotic expansions of the \u2018turbulent\u2019 and non-hydrostatic\nterms that appear in the equations that result from the vertical integration of\nthe free surface Euler equations. Among these models are the well-known\nnonlinear shallow water (NSW), Boussinesq and Serre\u2013Green\u2013Naghdi (SGN)\nequations for which we review several pending open problems. More recent\nmodels such as the multi-layer NSW or SGN systems, as well as the Isobe\u2013\nKakinuma equations are also reviewed under a unified formalism that should\nsimplify comparisons. We also comment on the scalar versions of the various\nshallow water systems which can be used to describe unidirectional waves in\nhorizontal dimension <em>d <\/em>= 1; among them are the KdV, BBM, Camassa\u2013Holm\nand Whitham equations. Finally, we show how to take vorticity effects into\naccount in shallow water modeling, with specific focus on the behavior of the\nturbulent terms. As examples of challenges that go beyond the present scope\nof mathematical justification, we review recent works using shallow water\nmodels with vorticity to describe wave breaking, and also derive models for\nthe propagation of shallow water waves over strong currents.\n<\/p>\n","protected":false},"excerpt":{"rendered":"<p>D. Lannes, Nonlinearity 33 (2020), R1 Download We review here the derivation of many of the most important models that appear in the literature (mainly in coastal oceanography) for the description of waves in shallow water. We show that these models can be obtained using various asymptotic expansions of the \u2018turbulent\u2019 and non-hydrostatic terms that [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1,5],"tags":[],"class_list":["post-376","post","type-post","status-publish","format-standard","hentry","category-non-classe","category-recent"],"_links":{"self":[{"href":"https:\/\/david-lannes.perso.math.cnrs.fr\/index.php?rest_route=\/wp\/v2\/posts\/376","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/david-lannes.perso.math.cnrs.fr\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/david-lannes.perso.math.cnrs.fr\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/david-lannes.perso.math.cnrs.fr\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/david-lannes.perso.math.cnrs.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=376"}],"version-history":[{"count":2,"href":"https:\/\/david-lannes.perso.math.cnrs.fr\/index.php?rest_route=\/wp\/v2\/posts\/376\/revisions"}],"predecessor-version":[{"id":430,"href":"https:\/\/david-lannes.perso.math.cnrs.fr\/index.php?rest_route=\/wp\/v2\/posts\/376\/revisions\/430"}],"wp:attachment":[{"href":"https:\/\/david-lannes.perso.math.cnrs.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=376"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/david-lannes.perso.math.cnrs.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=376"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/david-lannes.perso.math.cnrs.fr\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=376"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}