Abstract
By means of a variety of approaches, the present study points out the challenges in understanding equatorial ocean dynamics (±2.5º).
Standard theory, in fact, fails in accurately describing such a big portion of our ocean.
This is mainly because at the equator rotation and density stratification combine uniquely, causing approximations commonly used in Physical Oceanography to break down.
Measurements have also long shown that the oceans differ in the equatorial belt compared to offequatorial regions, but a complete understanding of the observed features is still lacking.
In this work, we explore the consequences of restoring the nontraditional terms (related to the horizontal component of the Coriolis force) back in the classical set of equations. For the surface and interfacial wave case, we study the resulting nonseparable equations of motion, finding new analytical wave solutions. Disappointingly, we are not able to reconcile these new solutions with the traditional theory.
Exploring the role of lowlatitude internal waves analytically is impossible. Here a threedimensional, internal wave ray tracing algorithm is developed and applied to the spherical shell and to the full fluid sphere as paradigmatic examples of geometries of geophysical (and astrophysical) relevance. In the spherical shell, we observe the trapping of rays (frequencies) first to meridional planes, and second to internal wave attractors. The occurrence of these attractors in the equatorial region is suggestive of a role they might play in the real ocean, collecting energy from offequatorial regions towards the equator. A comparison between results obtained with the new algorithm and the old wave solutions can be only done in the idealised full sphere case. This is in fact one of the very few domains where analytical solutions for internal waves are known. Threedimensional ray tracing is shown to be a robust tool to evaluate the regularity (or nonregularity) of a system, extending to threedimensional frameworks the correspondence, valid in twodimensions, periodic orbits = regular solutions, attractors = singular solutions, chaotic orbits = null solutions. The threedimensional ray tracing also unveils a new class of solutions, zonally propagating, and underlines the importance of the critical latitudes in shaping the wave field.
Eventually, we turn to ocean observations, using a set of hydrographic and current data collected in the western Atlantic Ocean between the equator and 2.5º N, from December 2007 to July 2009. We isolate various equatorial features, brought to light by different and independent measurements: small vertical structure in the current field, anomalous mixing properties and latitudinally varying nearinertial wave polarization properties. Their spatial superposition suggests the existence of an “equatorial boundary layer”, whose transition to offequatorial regions is observed to take place at about 1.5º N.
The notion of “equatorial boundary layer” can be of help both from a theoretical and observational point of view, when apparently unrelated features come together, indeed making the lowlatitude belt a distinct place from the more familiar midlatitude regions.
Standard theory, in fact, fails in accurately describing such a big portion of our ocean.
This is mainly because at the equator rotation and density stratification combine uniquely, causing approximations commonly used in Physical Oceanography to break down.
Measurements have also long shown that the oceans differ in the equatorial belt compared to offequatorial regions, but a complete understanding of the observed features is still lacking.
In this work, we explore the consequences of restoring the nontraditional terms (related to the horizontal component of the Coriolis force) back in the classical set of equations. For the surface and interfacial wave case, we study the resulting nonseparable equations of motion, finding new analytical wave solutions. Disappointingly, we are not able to reconcile these new solutions with the traditional theory.
Exploring the role of lowlatitude internal waves analytically is impossible. Here a threedimensional, internal wave ray tracing algorithm is developed and applied to the spherical shell and to the full fluid sphere as paradigmatic examples of geometries of geophysical (and astrophysical) relevance. In the spherical shell, we observe the trapping of rays (frequencies) first to meridional planes, and second to internal wave attractors. The occurrence of these attractors in the equatorial region is suggestive of a role they might play in the real ocean, collecting energy from offequatorial regions towards the equator. A comparison between results obtained with the new algorithm and the old wave solutions can be only done in the idealised full sphere case. This is in fact one of the very few domains where analytical solutions for internal waves are known. Threedimensional ray tracing is shown to be a robust tool to evaluate the regularity (or nonregularity) of a system, extending to threedimensional frameworks the correspondence, valid in twodimensions, periodic orbits = regular solutions, attractors = singular solutions, chaotic orbits = null solutions. The threedimensional ray tracing also unveils a new class of solutions, zonally propagating, and underlines the importance of the critical latitudes in shaping the wave field.
Eventually, we turn to ocean observations, using a set of hydrographic and current data collected in the western Atlantic Ocean between the equator and 2.5º N, from December 2007 to July 2009. We isolate various equatorial features, brought to light by different and independent measurements: small vertical structure in the current field, anomalous mixing properties and latitudinally varying nearinertial wave polarization properties. Their spatial superposition suggests the existence of an “equatorial boundary layer”, whose transition to offequatorial regions is observed to take place at about 1.5º N.
The notion of “equatorial boundary layer” can be of help both from a theoretical and observational point of view, when apparently unrelated features come together, indeed making the lowlatitude belt a distinct place from the more familiar midlatitude regions.
Original language  English 

Awarding Institution 

Supervisors/Advisors 

Award date  26 Jan 2016 
Publisher  
Print ISBNs  9789462992627 
Publication status  Published  26 Jan 2016 
Keywords
 Equator
 Ocean
 Waves
 Internal waves
 observations
 theory
 ray dynamics
 boundary layer
 GFD