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Appl. Math."],"published-print":{"date-parts":[[2023,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A new family of non-hydrostatic layer-averaged models for the non-stationary Euler equations is presented in this work, with improved dispersion relations. They are a generalisation of the layer-averaged models introduced in Fern\u00e1ndez-Nieto et al. (Commun Math Sci 16(05):1169\u20131202, 2018), named LDNH models, where the vertical profile of the horizontal velocity is layerwise constant. This assumption implies that solutions of LDNH can be seen as a first order Galerkin approximation of Euler system. Nevertheless, it is not a fully (<jats:italic>x<\/jats:italic>,\u00a0<jats:italic>z<\/jats:italic>) Galerkin discretisation of Euler system, but just in the vertical direction (<jats:italic>z<\/jats:italic>). Thus, the resulting model only depends on the horizontal space variable (<jats:italic>x<\/jats:italic>), and therefore specific and efficient numerical methods can be applied (see Escalante-Sanchez et al. in J Sci Comput 89(55):1\u201335, 2021). This work focuses on particular weak solutions where the horizontal velocity is layerwise linear on <jats:italic>z<\/jats:italic> and possibly discontinuous across layer interfaces. This approach allows the system to be a second-order approximation in the vertical direction of Euler system. Several closure relations of the layer-averaged system with non-hydrostatic pressure are presented. The resulting models are named LIN-NH<jats:inline-formula><jats:alternatives><jats:tex-math>$$_k$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mrow\/>\n                    <mml:mi>k<\/mml:mi>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> models, with <jats:inline-formula><jats:alternatives><jats:tex-math>$$k=0,1,2$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>k<\/mml:mi>\n                    <mml:mo>=<\/mml:mo>\n                    <mml:mn>0<\/mml:mn>\n                    <mml:mo>,<\/mml:mo>\n                    <mml:mn>1<\/mml:mn>\n                    <mml:mo>,<\/mml:mo>\n                    <mml:mn>2<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. Parameter <jats:italic>k<\/jats:italic> indicates the degree of the vertical velocity profile considered in the approximation of the vertical momentum equation. All the introduced models satisfy a dissipative energy balance. Finally, an analysis and a comparison of the dispersive properties of each model are carried out. We show that Models LIN-NH<jats:inline-formula><jats:alternatives><jats:tex-math>$$_1$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mrow\/>\n                    <mml:mn>1<\/mml:mn>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and LIN-NH<jats:inline-formula><jats:alternatives><jats:tex-math>$$_2$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mrow\/>\n                    <mml:mn>2<\/mml:mn>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> provide a better dispersion relation, group velocity and shoaling than LDNH models.<\/jats:p>","DOI":"10.1007\/s40314-023-02309-7","type":"journal-article","created":{"date-parts":[[2023,5,11]],"date-time":"2023-05-11T09:35:17Z","timestamp":1683797717000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Non-hydrostatic layer-averaged approximation of Euler system with enhanced dispersion properties"],"prefix":"10.1007","volume":"42","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7602-5920","authenticated-orcid":false,"given":"C.","family":"Escalante","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"E. 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