On the energetics of stratified turbulent mixing, irreversible thermodynamics, Boussinesq models and the ocean heat engine controversy

In this paper, the available potential energy (APE) framework of Winters et al. (J. Fluid Mech., vol. 289, 1995, p. 115) is extended to the fully compressible Navier– Stokes equations, with the aims of clarifying (i) the nature of the energy conversions taking place in turbulent thermally stratified fluids; and (ii) the role of surface buoyancy fluxes in the Munk & Wunsch (Deep-Sea Res., vol. 45, 1998, p. 1977) constraint on the mechanical energy sources of stirring required to maintain diapycnal mixing in the oceans. The new framework reveals that the observed turbulent rate of increase in the background gravitational potential energy GPEr , commonly thought to occur at the expense of the diffusively dissipated APE, actually occurs at the expense of internal energy, as in the laminar case. The APE dissipated by molecular diffusion, on the other hand, is found to be converted into internal energy (IE), similar to the viscously dissipated kinetic energy KE. Turbulent stirring, therefore, does not introduce a new APE/GPEr mechanical-to-mechanical energy conversion, but simply enhances the existing IE/GPEr conversion rate, in addition to enhancing the viscous dissipation and the entropy production rates. This, in turn, implies that molecular diffusion contributes to the dissipation of the available mechanical energy ME =APE +KE, along with viscous dissipation. This result has important implications for the interpretation of the concepts of mixing efficiency γmixing and flux Richardson number Rf , for which new physically based definitions are proposed and contrasted with previous definitions. The new framework allows for a more rigorous and general re-derivation from the first principles of Munk & Wunsch (1998, hereafter MW98)’s constraint, also valid for a non-Boussinesq ocean: G(KE) ≈ 1 − ξ Rf ξ Rf Wr, forcing = 1 + (1 − ξ )γmixing ξ γmixing Wr, forcing , where G(KE) is the work rate done by the mechanical forcing, Wr, forcing is the rate of loss of GPEr due to high-latitude cooling and ξ is a nonlinearity parameter such that ξ =1 for a linear equation of state (as considered by MW98), but ξ <1 otherwise. The most important result is that G(APE), the work rate done by the surface buoyancy fluxes, must be numerically as large as Wr, forcing and, therefore, as important as the mechanical forcing in stirring and driving the oceans. As a consequence, the overall mixing efficiency of the oceans is likely to be larger than the value γmixing =0.2 presently used, thereby possibly eliminating the apparent shortfall in mechanical stirring energy that results from using γmixing =0.2 in the above formula.

Voronoi, Delaunay, and Block-Structured Mesh Refinement for Solution of the Shallow-Water Equations on the Sphere

Alternative meshes of the sphere and adaptive mesh refinement could be immensely beneficial for weather and climate forecasts, but it is not clear how mesh refinement should be achieved. A finite-volume model that solves the shallow-water equations on any mesh of the surface of the sphere is presented. The accuracy and cost effectiveness of four quasi-uniform meshes of the sphere are compared: a cubed sphere, reduced latitude–longitude, hexagonal–icosahedral, and triangular–icosahedral. On some standard shallow-water tests, the hexagonal–icosahedral mesh performs best and the reduced latitude–longitude mesh performs well only when the flow is aligned with the mesh. The inclusion of a refined mesh over a disc-shaped region is achieved using either gradual Delaunay, gradual Voronoi, or abrupt 2:1 block-structured refinement. These refined regions can actually degrade global accuracy, presumably because of changes in wave dispersion where the mesh is highly nonuniform. However, using gradual refinement to resolve a mountain in an otherwise coarse mesh can improve accuracy for the same cost. The model prognostic variables are height and momentum collocated at cell centers, and (to remove grid-scale oscillations of the A grid) the mass flux between cells is advanced from the old momentum using the momentum equation. Quadratic and upwind biased cubic differencing methods are used as explicit corrections to a fast implicit solution that uses linear differencing.

Why the western Pacific subtropical high has extended westward since the late 1970s

The western Pacific subtropical high (WPSH) is closely related to Asian climate. Previous examination of changes in the WPSH found a westward extension since the late 1970s, which has contributed to the inter-decadal transition of East Asian climate. The reason for the westward extension is unknown, however. The present study suggests that this significant change of WPSH is partly due to the atmosphere's response to the observed Indian Ocean-western Pacific (IWP) warming. Coordinated by a European Union's Sixth Framework Programme, Understanding the Dynamics of the Coupled Climate System (DYNAMITE), five AGCMs were forced by identical idealized sea surface temperature patterns representative of the IWP warming and cooling. The results of these numerical experiments suggest that the negative heating in the central and eastern tropical Pacific and increased convective heating in the equatorial Indian Ocean/ Maritime Continent associated with IWP warming are in favor of the westward extension of WPSH. The SST changes in IWP influences the Walker circulation, with a subsequent reduction of convections in the tropical central and eastern Pacific, which then forces an ENSO/Gill-type response that modulates the WPSH. The monsoon diabatic heating mechanism proposed by Rodwell and Hoskins plays a secondary reinforcing role in the westward extension of WPSH. The low-level equatorial flank of WPSH is interpreted as a Kelvin response to monsoon condensational heating, while the intensified poleward flow along the western flank of WPSH is in accord with Sverdrup vorticity balance. The IWP warming has led to an expansion of the South Asian high in the upper troposphere, as seen in the reanalysis.

A comparison of conservative upwind difference schemes for the Euler equations

Numerical results are presented and compared for three conservative upwind difference schemes for the Euler equations when applied to two standard test problems. This includes consideration of the effect of treating part of the flux balance as a source, and a comparison of different averaging of the flow variables. Two of the schemes are also shown to be equivalent in their implementation, while being different in construction and having different approximate Jacobians. (C) 2006 Elsevier Ltd. All rights reserved.

Upwind solution of singular differential equations arising from steady channel flows

We study ordinary nonlinear singular differential equations which arise from steady conservation laws with source terms. An example of steady conservation laws which leads to those scalar equations is the Saint–Venant equations. The numerical solution of these scalar equations is sought by using the ideas of upwinding and discretisation of source terms. Both the Engquist–Osher scheme and the Roe scheme are used with different strategies for discretising the source terms.