dorsal/arxiv
View SchemaExplicit wave-averaged primitive equations using a Generalized Lagrangian Mean
| Authors | Fabrice Ardhuin, Nicolas Rascle, Kostas Belibassakis |
|---|---|
| Categories | |
| ArXiv ID | physics/0702067 |
| URL | https://arxiv.org/abs/physics/0702067 |
| DOI | 10.1016/j.ocemod.2007.07.001 |
Abstract
The generalized Langrangian mean theory provides exact equations for general wave-turbulence-mean flow interactions in three dimensions. For practical applications, these equations must be closed by specifying the wave forcing terms. Here an approximate closure is obtained under the hypotheses of small surface slope, weak horizontal gradients of the water depth and mean current, and weak curvature of the mean current profile. These assumptions yield analytical expressions for the mean momentum and pressure forcing terms that can be expressed in terms of the wave spectrum. A vertical change of coordinate is then applied to obtain glm2z-RANS equations (55) and (57) with non-divergent mass transport in cartesian coordinates. To lowest order, agreement is found with Eulerian-mean theories, and the present approximation provides an explicit extension of known wave-averaged equations to short-scale variations of the wave field, and vertically varying currents only limited to weak or localized profile curvatures. Further, the underlying exact equations provide a natural framework for extensions to finite wave amplitudes and any realistic situation. The accuracy of the approximations is discussed using comparisons with exact numerical solutions for linear waves over arbitrary bottom slopes, for which the equations are still exact when properly accounting for partial standing waves. For finite amplitude waves it is found that the approximate solutions are probably accurate for ocean mixed layer modelling and shoaling waves, provided that an adequate turbulent closure is designed. However, for surf zone applications the approximations are expected to give only qualitative results due to the large influence of wave nonlinearity on the vertical profiles of wave forcing terms.
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"abstract": "The generalized Langrangian mean theory provides exact equations for general\nwave-turbulence-mean flow interactions in three dimensions. For practical\napplications, these equations must be closed by specifying the wave forcing\nterms. Here an approximate closure is obtained under the hypotheses of small\nsurface slope, weak horizontal gradients of the water depth and mean current,\nand weak curvature of the mean current profile. These assumptions yield\nanalytical expressions for the mean momentum and pressure forcing terms that\ncan be expressed in terms of the wave spectrum. A vertical change of coordinate\nis then applied to obtain glm2z-RANS equations (55) and (57) with non-divergent\nmass transport in cartesian coordinates. To lowest order, agreement is found\nwith Eulerian-mean theories, and the present approximation provides an explicit\nextension of known wave-averaged equations to short-scale variations of the\nwave field, and vertically varying currents only limited to weak or localized\nprofile curvatures. Further, the underlying exact equations provide a natural\nframework for extensions to finite wave amplitudes and any realistic situation.\nThe accuracy of the approximations is discussed using comparisons with exact\nnumerical solutions for linear waves over arbitrary bottom slopes, for which\nthe equations are still exact when properly accounting for partial standing\nwaves. For finite amplitude waves it is found that the approximate solutions\nare probably accurate for ocean mixed layer modelling and shoaling waves,\nprovided that an adequate turbulent closure is designed. However, for surf zone\napplications the approximations are expected to give only qualitative results\ndue to the large influence of wave nonlinearity on the vertical profiles of\nwave forcing terms.",
"arxiv_id": "physics/0702067",
"authors": [
"Fabrice Ardhuin",
"Nicolas Rascle",
"Kostas Belibassakis"
],
"categories": [
"physics.ao-ph"
],
"doi": "10.1016/j.ocemod.2007.07.001",
"title": "Explicit wave-averaged primitive equations using a Generalized Lagrangian Mean",
"url": "https://arxiv.org/abs/physics/0702067"
},
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