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- Author or Editor: George Mellor x
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Abstract
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.
Abstract
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.
Abstract
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.
Abstract
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.
Abstract
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.
Abstract
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.
Abstract
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.
Abstract
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.
Abstract
There have been several numerical models developed to represent the phase-averaged flow in the surf zone, which is characterized by kD less than unity, where k is wavenumber and D is the water column depth. The classic scenario is that of surface gravity waves progressing onto a shore that create an offshore undertow current. In fact, in some models, flow velocities are parameterized assuming the existence of an undertow. The present approach uses the full vertically dependent continuity and momentum equations and the vertically dependent wave radiation stress in addition to turbulence equations. The model is applied to data that feature measurements of wave properties and also cross-shore velocities. In this paper, both the data and the model application are unidirectional and the surface stress is nil, representing the simplest surf zone application. Breaking waves are described empirically. Special to the surf zone, it is found that a simple empirical adjustment of the radiation stress enables a favorable comparison with data. Otherwise, the model applies to the open ocean with no further empiricism. A new bottom friction algorithm had been derived and is introduced in this paper. In the context of the turbulence transport model, the algorithm is relatively simple.
Abstract
There have been several numerical models developed to represent the phase-averaged flow in the surf zone, which is characterized by kD less than unity, where k is wavenumber and D is the water column depth. The classic scenario is that of surface gravity waves progressing onto a shore that create an offshore undertow current. In fact, in some models, flow velocities are parameterized assuming the existence of an undertow. The present approach uses the full vertically dependent continuity and momentum equations and the vertically dependent wave radiation stress in addition to turbulence equations. The model is applied to data that feature measurements of wave properties and also cross-shore velocities. In this paper, both the data and the model application are unidirectional and the surface stress is nil, representing the simplest surf zone application. Breaking waves are described empirically. Special to the surf zone, it is found that a simple empirical adjustment of the radiation stress enables a favorable comparison with data. Otherwise, the model applies to the open ocean with no further empiricism. A new bottom friction algorithm had been derived and is introduced in this paper. In the context of the turbulence transport model, the algorithm is relatively simple.
