The application of adaptive mesh modelling techniques to the study of open ocean deep convection

Abstract

The rapid cooling of the waters at high latitudes creates an unstable stratification which in turn leads to localised overturning (sinking) of the water column. This process is called open ocean deep convection (OODC). The process of OODC occurs in stages. Initially, individual convective elements known as plumes form and cold, dense water descends from the surface. Over time these plumes build up to produce a well-mixed 'chimney' of cold dense fluid. This chimney then slumps and sinks, and restratification (the return to a stable state throughout the water column) occurs.

It is widely accepted that OODC plays a main role in driving the thermohaline circulation (THC) and hence has a potentially major role in climate. However, the mechanisms of OODC itself are not fully understood, and there is much debate surrounding how it contributes to THC. One difficulty is that OODC tends to occur sporadically in only a few isolated regions around the globe, making direct observations difficult. As a result, theoretical and numerical investigations have become key to the development of our understanding of OODC. The scale on which OODC occurs presents a further issue, with traditional numerical representations (parameterisations) of OODC in global circulation models (GCMs) omitting convective detail due to resolution. Due to the scales on which OODC occurs, it has been difficult to numerically investigate the nature of OODC in the small scale at the same time as resolving basin scale circulation. With the advent of finite element methods and adaptive meshing techniques, it is now possible to study OODC in regional models without the need to parameterise. One such model, the Imperial College Ocean Model (ICOM) is employed in this thesis for these purposes. ICOM is a 3D finite element, non-hydrostatic model with an adaptive, unstructured mesh and non-uniform resolution, allowing modelling of the gyre circulation and resolution of OODC simultaneously. As the use of an adaptive, unstructured mesh model is novel in investigating Greenland Sea open ocean deep convection, it is of interest to assess the accuracy of the ICOM model, and the amount of numerical diffusion present. The classical fluid dynamics problem of parallel plate convection provides a simple test problem for this purpose. A series of tests investigating the linear stability of various temperature gradients were performed in order to diagnose the amount of numerical diffusivity associated with hexahedral, tetrahedral and adaptive meshes within ICOM, and ICOM was further compared with a leading GCM (MITgcm). The use of the linear instability problem was found to be a useful case against which to test numerical models in an attempt to diagnose implicit diffusivity and viscosity.

A series of experiments were conducted in order to identify any prevailing differences between model convection in fixed and adaptive mesh configurations, under varying durations of applied cooling, and using varying extents of horizontal cooling. The adaptive mesh proved to be highly suitable for studying the convective problem, it was less computationally expensive and free from the numerical instability observed on the fixed mesh. The sensitivity of model convection to the introduction of stratification was investigated. Uniform cooling was applied across the surface of a domain initialised with a weak stratification over the surface 1500m and a more strongly stratified region below, and the development of a convective layer was observed within the initial upper layer. Convection was constrained to the upper layer of stratification, and some penetrative convection was identified in the early stages of the model run.

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