In non-rotating fluids, boundary-layer separation occurs when the nearly inviscid flow just outside a viscous boundary-layer experiences an appreciable deceleration due to a region of adverse pressure gradient. The fluid ceases to flow along the boundary due to a flow recirculation region close to the boundary. The flow is then said to be "detached." In recent decades, attention has shifted to the study of boundary-layer separation in a rotating reference frame due to its significance in Geophysical Fluid Dynamics (GFD). Since the Earth is a rotating sphere, the so-called β-plane approximation f = f0 + βy is often used to account for the inherent meridional variation of the Coriolis parameter, f, while still solving the governing equations on a plane. Numerical simulations of currents on the β-plane have been useful in understanding ocean currents such as the Gulf Stream, the Brazil Current, and the Antarctic Circumpolar Current to name a few. In this thesis, we first consider the problem of prograde flow past a cylindrical obstacle on the β-plane. The problem is governed by the barotropic vorticity equation and is solved using a numerical method that is a combination of a finite difference method and a spectral method. A modified form of the β-plane approximation is proposed to avoid computational difficulties. Results are given and discussed for flow past a circular cylinder at selected Reynolds numbers (Re) and non-dimensional β-parameters (β^). Results are then given and discussed for flow past an elliptic cylinder of a fixed aspect ratio (r = 0.2) and at two angles of inclination (90°, 15°) at selected Re and β^. In general, it is found that the β-effect acts to suppress boundary-layer separation and to allow Rossby waves to form in the exterior flow field. In the asymmetrical case of an inclined elliptic cylinder, the β-effect was found to constrain the region of vortex shedding to a small region near the trailing edge of the cylinder. The shed vortices were found to propagate around the trailing edge instead of in the expected downstream direction, as observed in the non-rotating case. The second problem considered in this thesis is the separation of western boundary currents from a curved coastline. This problem is also governed by the barotropic vorticity equation, and it is solved on an idealized model domain suitable for investigating the effects that boundary curvature has on the tendency of a boundary current to separate. The numerical method employed is a two-dimensional Chebyshev spectral collocation method and yields high order accuracy that helps to better resolve the boundary-layer dynamics in comparison to low-order methods. Results are given for a selection of boundary curvatures, non-dimensional β-parameters (β^), Reynolds numbers (Re), and Munk Numbers (Mu). In general, it is found than an increase in β^ will act to suppress boundary-layer separation. However, a sufficiently sharp obstacle can overcome the β-effect and force the boundary current to separate regardless of the value of β^. It is also found that in the inertial limit (small Mu, large Re) the flow region to the east of the primary boundary current is dominated by strong wave interactions and large eddies which form as a result of shear instabilities. In an interesting case of the inertial limit, strong waves were found to interact with the separation region, causing it to expand and propagate to the east as a large eddy. This idealized the mechanism by which western boundary currents such as the Gulf Stream generate eddies in the world's oceans.

Le golfe de Gascogne (GdG), un milieu riche en processus physiques a été étudié à partir de simulations numériques. L’étude est construite autour d'échelles allant du GdG à la sous méso-échelle. Dans la première partie, nous avons examiné la variabilité interannuelle de la température et de la salinité de surface sur une période de 53 ans : nous avons pu décrire deux tendances en lien avec I'Atlantique Nord-Est. Le refroidissement et la dessalure jusqu'en 1976 seraient liés à la grande anomalie de salinité, le réchauffement et la salinification actuels liés à I'augmentation de CO2 atmosphérique. Le GdG se caractérise par un courant de pente, lberian Poleward Current (lPC) : sa variabilité serait liée au vent du Sud-Ouest qui renforce l'lPC par un courant géostrophique dans le Bassin lbérique. L’un des résultats intéressant trouvé dans les simulations et confìrmé par les observations est l'apparition des anomalies froides liées à des upwellings en alternance avec des anomalies chaudes "La Navidad". Ces upwellings seraient liés au vent de Nord dans le Bassin lbérique mais au courant d'Ouest le long des côtes Nord espagnoles. Dans une deuxième partie, nous nous sommes attachés à la méso et sous méso-échelle à travers la détection des tourbillons et la variabilité des spectres d'énergie. Un indice basé sur le rapport entre I'anomalie de densité de surface et I'anomalie de niveau de la mer permet de détecter les tourbillons de subsurface et de les distinguer des tourbillons de surface. Une application de cet indice à partir des données satellites confirme le potentiel de détection des Slope Water Oceanic eDDIES (tourbillons de subsurface caractéristiques du GdG). La description de l'énergie cinétique turbulente (EKE) dans le GdG montre une variabilité spatiale avec un maximum le long de la côte Nord espagnole liée à I'lPC. Les pentes des spectres (k-4.2 pour la SSH, en k-2.4 pour la SST et en k-2.4 pour l'énergie cinétique) sont différents des observations satellites, mais comparables avec les précédentes études. Ces pentes de spectres ont également une variabilité saisonnière avec un maximum en hiver et un minimum en été, liée au cycle saisonnier de I'EKE. / The Bay of Biscay (BoB), an environment rich in physical processes has been studied from numerical simulations. Thestudy is built around scales from the size of BoB until sub mesoscale.ln the first part, we examined the interannual variability of the sea surface temperature and saliniÇ over a period of 53years: we were able to describe two trends related to the North-East Atlantic. Cooling and freshening until 1976 thatcould be related to the Great Salinity Anomaly and current salinification related to the atmospheric increase of CO2.The Bay of Biscay is characterized by a slope current, the lberian Poleward Current (lPC): its variability is linked to theSouth West wind strengthens the IPC by a geostrophic current in the lberian Basin. One of the interesting results foundin simulations and confirmed by observations is the appearance of cold anomalies related to upwellings and alternatingwith warm anomalies 'La Navidad'. These upwellings could be linked to the north wind in the lberian Basin but to the West current along the northern Spanish coast.ln the second part, we are committed to the meso and sub mesoscale eddies through a method of detection and throughthe variability of energy spectra. An index based on the ratio of surface density anomaly and sea level anomaly allowsdetecting subsurface vortices and distinguishing them from the surface ones. The application of this index from thesatellite data confirms the detection potential of Slope Water Oceanic Eddies (subsurface vortices of BoB).The description of the Eddy Kinetic Energy (EKE) in the BoB. shows a spatial variability with maximum along the Spanishnorth coast linked to the lPC. The slopes of the spectra (k-4.2 for SSH, k-2.4 for SST and k-2.4 for the kinetic energy) are different from satellite observations, but comparable with previous studies. These spectral slopes have a seasonalvariability with a maximum in winter and minimum in summe¡ related to the seasonal cycle of EKE.

Indiana University-Purdue University Indianapolis (IUPUI) / We numerically investigate the underlying physics of two peculiar phenomena, which are axis-switching and saddle-back velocity profile, in both laminar and turbulent rectangular jets using lattice Boltzmann method (LBM). Previously developed computation protocols based on single-relaxation-time (SRT) and multiple-relaxation-time (MRT) lattice Boltzmann equations are utilized to perform direct numerical simulation (DNS) and large eddy simulation (LES) respectively. In the first study, we systematically study the axis-switching behavior in low aspect-ratio (AR), defined as the ratio of width over height, laminar rectangular jets with <italic>AR=1</italic> (square jet), 1.5, 2, 2.5, and 3. Focuses are on various flow properties on transverse planes downstream to investigate the correlation between the streamwise velocity and secondary flow. Three distinct regions of jet development are identified in all the five jets. The <italic>45&deg</italic> and <italic>90&deg</italic> axis-switching occur in characteristic decay (CD) region consecutively at the early and late stage. The half-width contour (HWC) reveals that <italic>45&deg</italic> axis-switching is mainly contributed by the corner effect, whereas the aspect-ratio (elliptic) feature affects the shape of the jet when <italic>45&deg</italic> axis-switching occurs. The close examinations of flow pattern and vorticity contour, as well as the correlation between streamwise velocity and vorticity, indicate that <italic>90&deg</italic> axis-switching results from boundary effect. Specific flow patterns for <italic>45&deg</italic> and <italic>90&deg</italic> axis-switching reveal the mechanism of the two types of axis-switching respectively. In the second study we develop an algorithm to generate a turbulent velocity field for the boundary condition at jet inlet. The turbulent velocity field satisfies incompressible continuity equation with prescribed energy spectrum in wave space. Application study of the turbulent velocity profile is on two turbulent jets with <italic>Re=25900</italic>. In the jets with <italic>AR=1.5</italic>, axis-switching phenomenon driven by the turbulent inlet velocity is more profound and in better agreement with experimental examination over the laminar counterpart. Characteristic jet development driven by both laminar and turbulent inlet velocity profile in square jet (<italic>AR=1</italic>) is also examined. Overall agreement of selected jet features is good, while quantitative match for the turbulence intensity profiles is yet to be obtained in future study. In the third study, we analyze the saddle-back velocity profile phenomenon in turbulent rectangular jets with AR ranging from 2 to 6 driven by the developed turbulent inlet velocity profiles with different turbulence intensity (<italic>I</italic>). Saddle-back velocity profile is observed in all jets. It has been noted that the saddle-back's peak velocities are resulted from the local minimum mixing intensity. Peak-center difference <italic>&Delta_pc</italic> and profound saddle-back (PSB) range are defined to quantify the saddle-back level and the effects of AR and <italic>I</italic> on saddle-back profile. It is found that saddle-back is more profound with larger AR or slimmer rectangular jets, while its relation with <italic>I</italic> is to be further determined.

Sedimentation rates and compositions of sinking particles were investigated at three sites on the Beaufort slope and one in Canada Basin during the period 1990-1994 using moored sequential sediment traps. A method was developed to identify the terrigenous and biogenic components of the fluxes. The physical context including ice cover, ocean currents, river inputs, winds, air temperature, incident light, and nutrient availability provide essential information to the interpretation of the particle fluxes and to the understanding of shelf-basin sediment transport in this area. Eddies, internal waves, upwelling and downwelling, and the state of the ice cover all played important and overlapping roles in the pattern of observed fluxes. A peak in the flux of highly terrigenous material under complete ice cover in mid-winter to the northwest of Mackenzie Trough was associated with predominantly downwelling conditions and the passage of a series of eddies and internal waves. A prolonged spring diatom bloom occurred in the mid-slope area and was clearly associated with an early opening of the ice on the east side of the shelf. Higher fluxes at the Canada Basin site were associated with a large eddy clearly identifiable from the current-T-S record and also from the composition of the suspended material carried with it. At the base of the slope (2700 m), the composition was highly terrigenous and remarkably consistent. Higher up the slope (700 m), biogenic peaks in the summer diluted the terrigenous material briefly, but it appears that there is a constant background of highly terrigenous material. There was a high degree of variability between sites and over the slope there was not enough data to asses the inter-annual variability. In Canada Basin, the inter-annual variability was closely linked to the extent of open water in the summer period. At all sites, lateral transport is clearly indicated by the increase in flux with depth. The data robustly demonstrate the need for detailed knowledge of physical processes for informed interpretation of particle fluxes and sediment transport in this area.