David Marshall

Abstract:

Separation of stratified flow over a two-dimensional hill is inhibited or facilitated by acceleration or deceleration of the flow just outside the attached boundary layer. In this note, an expression is derived for this acceleration or deceleration in terms of streamline curvature and stratification. The expression is valid for linear as well as nonlinear deformation of the flow. For hills of vanishing aspect ratio a linear theory can be derived and a full regime diagram for separation can be constructed. For hills of finite aspect ratio scaling relationships can be derived that indicate the presence of a critical aspect ratio, proportional to the stratification, above which separation will occur as well as a second critical aspect ratio above which separation will always occur irrespective of stratification. © 2005 American Meteorological Society.

Abstract:

In this article the advantages and current status of unstructured mesh ocean modelling are reviewed. Future challenges are discussed along with the potential of resulting methods to make a significant impact on ocean modelling over the next decade. These methods are important because they are the only techniques that can simultaneously resolve both small and large scale ocean flows while smoothly varying resolution and conforming to complex coastlines and bathymetry. Realising the full potential of such methods will necessitate the use of dynamic mesh adaptivity. A number of techniques need to be combined and developed from different numerical modelling and geophysical fluid dynamics disciplines in order to create a powerful unstructured mesh ocean model. These are: Accurate and robust methods for the discretisation and advection of tracers, density and momentum; the choice of element/cell and satisfaction of the LBB stability condition; representation of hydrostatic and geostrophic balance; the ability to deal with sigma coordinate-like errors associated with the use of unstructured meshes; initial mesh generation to follow complex bathymetry and coastlines; sub-grid scale modelling on unstructured and possibly solution adaptive meshes; scalable solvers and parallel computing. A good solution to each problem is required, and thus the resulting model may be argued to be considerably more complex than traditionally used structured mesh models. It is these topics that are addressed here. © 2004 Elsevier Ltd. All rights reserved.

Abstract:

Great progress has been made in understanding the role of small- and mesoscale processes on the large-scale structure and circulation of the oceans. However, many questions remain regarding the sensitivity of the large-scale ocean circulation and hence the earth's climate, to rates of stirring, mixing, and dissipation supported by ocean eddies, internal waves, and boundary layers. Although such relatively small-scale oceanic phenomena are ubiquitous, we lack detailed knowledge about their interaction with the large-scale motions, as well as their interactions amongst themselves. Contributions are presented from observational, theoretical, and modeling studies that focus on small- and mesoscale ocean processes, and some parameterizations of these processes for use in studies of the large-scale circulation. The range of topics is relatively broad, with most focus on internal wave generation, flow-topography interaction, and small- and mesoscale processes involved in ocean mixing. General conclusions emphasize the notion of localized mixing and the importance of interaction between waves, eddies, and topography, and the importance of interactions between oceanic motions and the background density stratification. © 2004 Elsevier Ltd. All rights reserved.

Abstract:

There is a wide range of evidence from both models and palaeoclimatic data that indicates the possibility of abrupt changes in the oceanic meridional overturning circulation (MOC). However, much of our dynamical understanding of the MOC comes from steady-state models that rely upon the assumption of thermodynamic equilibrium and are therefore only valid on millennial time scales. Here a dynamical model for the global teleconnections of MOC anomalies on annual to multidecadal time scales is developed. It is based on a linear theory for the propagation of zonally integrated meridional transport anomalies in a reduced-gravity ocean and allows for multiple ocean basins connected by a circumpolar channel to the south. The theory demonstrates that the equator acts as a low-pass filter to MOC anomalies. As a consequence, MOC anomalies on decadal and shorter time scales are confined to the hemispheric basin in which they are generated and have little impact on the remainder of the global ocean. The linear theory is compared with the results of a global nonlinear numerical integration, which it reproduces to a good approximation. © 2004 American Meteorological Society.