Search Results

You are looking at 1 - 10 of 43 items for

  • Author or Editor: George Mellor x
  • Refine by Access: All Content x
Clear All Modify Search
George Mellor

Abstract

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.

Full access
George Mellor
Full access
George Mellor

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.

Full access
George Mellor

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.

Full access
George Mellor

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.

Full access
George Mellor

Abstract

A turbulence closure model is applied to the case of an oscillating boundary layer; model calculations compare favorably with data. Wave-induced oscillations can be temporally resolved in a one-dimensional model but not in three-dimensional ocean models, and, indeed, statistical wave models, working in consort with ocean models, can only provide information on expected wave periods and amplitudes. Therefore, in this paper, a way has been found to parameterize the effects of bottom flow oscillations; it entails augmenting the turbulence shear production as a function of amplitude and period of the oscillation, the bottom shear stress of the mean current flow, and the angle between the directions of the oscillations and the mean flow. The more conventional method of solving for an apparent wall roughness is also investigated in an appendix.

Full access
George Mellor

Abstract

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.

Full access
George Mellor

Abstract

Full access
George Mellor
Full access
George Mellor

Abstract

Three-dimensional, interacting current and surface gravity wave equations have recently been derived and compared with their counterpart vertically integrated equations; they are in the form of sigma-coordinate equations. The purpose of this paper is to examine some of the consequences of these equations including energy transfer between mean energy, wave energy, and turbulence energy, to frame some outstanding research issues, to provide a Cartesian version of the sigma-coordinate equations, and to compare with other formulations of wave–current interaction. In general, the paper is intended to set the stage for the development of numerical coupled surface wave and three-dimensional general circulation models. These models often include a flow-dependent turbulence-based viscosity.

Full access