Horizontal Transport and Mixing and their connection with Dynamical and Biological Processes in the Ocean

Abstract

Horizontal transport and mixing processes are central to the study of the physical, chemical, and biological dynamics of the ocean. Correct understanding and precise modelling of them are relevant from a theoretical viewpoint and crucial for a range of practical issues, such as plankton dynamics or the fate of pollutant spills. In this regard, the last few years have seen the appearance of interesting new developments on the Lagrangian description of transport and mixing phenomena, many of them coming from the area of nonlinear dynamics. Such approaches do not aim at predicting individual tracer trajectories, but at locating spatial structures that are known from dynamical systems theory to act as templates for the whole flow (Leong and Ottino, 1989; Wiggins, 1992). This is mainly due to the capacity of the Lagrangian diagnostics to exploit the spatiotemporal variability of the velocity field by following fluid particle trajectories, at difference of Eulerian ones which analyze frozen snapshots of data. Among these Lagrangian techniques, a powerful class consists in the computation of local Lyapunov exponents (LLE) which measure the relative dispersion of transported particles. In particular, there are the so called finite-size Lyapunov exponents (FSLEs) where one computes the time taken by two trajectories, initially separated by a finite distance, to reach a larger final finite distance. LLEs are attracting the attention of the oceanographic community. The main reasons for this interest are the following: a) they identify and display the dynamical structures in the flow that strongly organizes fluid motion (Lagrangian Coherent Structures (LCSs)) like vortices, barriers to transport, fronts, etc ; b) they are relatively easy to compute; c) they provide extra information on characteristics time-scales for the ocean flow dynamics; d) they are able to reveal oceanic structures below the nominal resolution of the velocity field being analyzed; and e) the FSLEs are specially suited to analyze transport in closed areas. Despite the growing number of applications of Lyapunov exponents, a systematic analysis of many of their properties and their efficiency in diagnosing ocean transport properties at different scales is still lacking. The objective of this thesis have been centered in the study of physical and biological processes in the ocean related to transport and mixing from the Lagrangian point of view. The study has been made with the idea of characterizing transport properties and coherent structures at different scales, from coastal to planetary scales. After some introduction and background in the two first chapters, in Chapter 3 we address the following questions: How do errors in the velocity field propagate onto the FSLE? Is the sub-grid information that they provide valid or just an artifact? How do they transform under changes in scale? To do this, we compute the FSLEs at different spatial resolutions and analyze their scaling properties and their response to different sources of error both in the velocity data and in the way that particle trajectories are computed. In order to keep close to the oceanographic applications we use numerical data of the marine surface velocity of the Mediterranean Sea. Once the reliability of FSLE diagnostics in ocean flows has been studied, we focus in applying this tool to analyze marine transport properties, from a particular coastal area to the global ocean. In Chapter 4, the near-surface velocity field obtained from an ocean general circulation model has been analyzed using FSLEs in order to address the following questions: Can we classify the ocean in regions of different stirring by means of FSLEs? How is the relationship between Lagrangian and Eulerian descriptors? Can we obtain the same transport information from both perspectives? We characterize the stirring properties of Northern and Southern Hemispheres, then the main oceanic basins and currents. We study the relation between averages of FSLE and some Eulerian descriptors such as Eddy Kinetic Energy and vorticity over different regions. These relations are useful to characterize the dynamics of different ocean areas. Chapter 5 is dedicated to study flow structures and transport in the coastal area of the Bay of Palma, Spain, in terms of FSLE and residence times. Can we detect small coastal LCSs? Are these structures relevant in the flow dynamics of a coastal region? How can we characterize the transport between the coast and the open ocean? We investigate the character of the semi-persistent detected LCSs. Fluid interchange between the Bay of Palma and the open ocean is studied by computing particle trajectories and residence times for different months. We examine the connection between LCSs and regions of different residence times. Finally, in Chapter 6 we focus on the influence of transport processes on marine ecosystems in prominent Eastern Boundary Upwelling zones. Particularly, we analyze the physical factors which drive the planktonic productivity in the Benguela upwelling system. Recent studies, both based on remote sensed data and coupled models, showed a reduction of biological productivity due to vigorous horizontal stirring in upwelling areas. In order to better understand this phenomenon, we have considered a system of oceanic flow in the Benguela area coupled with a simple biogeochemical model of Nutrient-Phyto-Zooplankton (NPZ) type. Our modelling approach confirms that in the south Benguela there is a reduction of biological activity when stirring is increased. Two-dimensional offshore advection and north-south differences in the growth rate of phytoplankton seem to be the dominant processes involved.