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George Mellor
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George Mellor

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George Mellor

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In response to the comments of Ardhuin et al., the formulation of Mellor has been revised. Solutions of the model equations are now consistent with known deep-water behavior and agree with the shallow water, analytical–numerical experiment put forward by Ardhuin et al.

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George Mellor
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George Mellor

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The results of the subject paper are reviewed wherein credible Langmuir cells are produced by a numerical solution of the primitive fluid dynamic equations with a free surface. Whereas it is a major achievement, the claim that the same results support the general application of the so-called vortex force equations is challenged.

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George Mellor
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George Mellor

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The paper focuses on the consequences of including surface and subsurface, wind-forced pressure–slope momentum transfer into the oceanic water column, a transfer process that competes with now-conventional turbulence transfer based on mixing coefficients. Horizontal homogeneity is stipulated as is customary when introducing a new surface boundary layer model or significantly new vertical momentum transfer physics to an existing model. An introduction to pressure–slope momentum transfer is first provided by a phase-resolved, vertically dependent analytical model that excludes turbulence transfer. There follows a discussion of phase averaging; an appendix is an important adjunct to the discussion. Finally, a coupled wave–circulation model, which includes pressure–slope and turbulence momentum transfer, is presented and numerically executed. The calculated temperatures compare well with measurements from ocean weather station Papa.

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George Mellor

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Surface wave equations appropriate to three-dimensional ocean models apparently have not been presented in the literature. It is the intent of this paper to correct that deficiency. Thus, expressions for vertically dependent radiation stresses and a definition of the Doppler velocity for a vertically dependent current field are obtained. Other quantities such as vertically dependent surface pressure forcing are derived for inclusion in the momentum and wave energy equations. The equations include terms that represent the production of turbulence energy by currents and waves. These results are a necessary precursor for three-dimensional ocean models that handle surface waves together with wind- and buoyancy-driven currents. Although the third dimension has been added here, the analysis is based on the assumption that the depth dependence of wave motions is provided by linear theory, an assumption that is the basis of much of the wave literature.

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George Mellor

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The comments of Ardhuin et al. concerning the papers by Mellor from 2003 and 2015 are reviewed. It is found that the comments do not impact the validity of these papers.

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George Mellor

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There exist different theories representing the effects of surface gravity waves on oceanic flow fields. In the past, the author has conjectured that the vertically integrated, two-dimensional fluid equations of motion put forward by Longuet-Higgins and Stewart are correct and that theories that differ from their theory cannot be entirely correct; this paper explores these differences. Longuet-Higgins and Stewart deduced vertically integrated, two-dimensional equations featuring a wave radiation stress term in the fluid dynamic, momentum equation. More recently, the author has proposed vertically dependent, three-dimensional equations that have required correction but when vertically integrated, agreed with the earlier, two-dimensional equations. This paper derives both vertically independent and vertically dependent equations from the same base and, importantly, using the same expression for pressure in the belief that the paper will contribute to the understanding and clarification of this seemingly difficult topic in ocean dynamics. An error in the classical papers by Longuet-Higgins and Stewart has been detected. Although the final phase-averaged result was correct, the error has had consequences in the development of vertically dependent equations. The prognostic equations in this paper are for the Eulerian current plus Stokes drift; toward the end of the paper these equations are contrasted with prognostic equations for the Eulerian current alone.

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