Physical oceanography

Abstract:

Flow in the world's oceans occurs at a wide range of spatial scales, from a fraction of a metre up to many thousands of kilometers. In particular, regions of intense flow are often highly localised, for example, western boundary currents, equatorial jets, overflows and convective plumes. Conventional numerical ocean models generally use static meshes. The use of dynamically-adaptive meshes has many potential advantages but needs to be guided by an error measure reflecting the underlying physics. A method of defining an error measure to guide an adaptive meshing algorithm for unstructured tetrahedral finite elements, utilizing an adjoint or goal-based method, is described here. This method is based upon a functional, encompassing important features of the flow structure. The sensitivity of this functional, with respect to the solution variables, is used as the basis from which an error measure is derived. This error measure acts to predict those areas of the domain where resolution should be changed. A barotropic wind driven gyre problem is used to demonstrate the capabilities of the method. The overall objective of this work is to develop robust error measures for use in an oceanographic context which will ensure areas of fine mesh resolution are used only where and when they are required. © 2006 Elsevier Ltd. All rights reserved.

Abstract:

The problem of western boundary current separation is investigated using a barotropic vorticity model. Specifically, a boundary current flowing poleward along a boundary containing a cape is considered. The meridional gradient of the Coriolis parameter (the β effect), the strength of dissipation, and the geometry of the cape are varied. It is found that 1) all instances of flow separation arc coincident with the presence of a flow deceleration, 2) an increase in the strength of the β effect is able to suppress flow separation, and 3) increasing coastline curvature can overcome the suppressive β effect and induce separation. These results are supported by integrated vorticity budgets, which attribute the acceleration of the boundary current to the β effect and changes in flow curvature. The transition to unsteady final model states is found to have no effect upon the qualitative nature of these conclusions. © 2005 American Meteorological Society.

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.