A new oceanic climatology to calculate ocean heat content (OHC) was developed for application year-round in the Atlantic Ocean basin. The Systematically Merged Atlantic Regional Temperature and Salinity (SMARTS) Climatology blends temperature and salinity fields from the World Ocean Atlas 2001 (WOA) and Generalized Digital Environmental Model v.3.0 (GDEM) at 1/4° resolution. This higher resolution climatology better resolves features in the Gulf of Mexico (GOM), including the Loop Current and eddy structures, than the previous coarser 1/2° products. Daily mean isotherm depths of the 20° C (D20) and 26° C (D26) (and their mean ratio), reduced gravity (e.g., 2-layer model), mixed layer depth (MLD), and OHC were estimated from the blended climatology. Using SMARTS with satellite-derived surface height anomaly and SST fields, daily values of D20, D26, MLD, and OHC were calculated from 1998 to 2010 using a two-layer model approach. Airborne and ship-deployed eXpendable BathyThermographs (XBT), long-term moorings, and Argo profiling floats provided the in-situ data to blend and assess the SMARTS Climatology. A clear, direct relationship emerged from the detailed analysis between satellite-derived and in-situ measurements of isotherm depths and OHC. This new climatological approach created a more accurate estimation of isotherm depths and OHC from satellite radar altimetry measurements, which can be used in hurricane intensity forecasts from the Statistical Hurricane Intensity Prediction Scheme (SHIPS). The Mainelli (2000) technique of calculating OHC was reexamined to most accurately project sea surface height anomalies (SSHA) into changes in depths of D20, D26, and MLD. SSHA surface features were tracked to determine realistic drift velocities ingested into the objective analysis algorithm. The former OHC algorithm assumed a climatological MLD, however observations show large temporal variability of MLD. Using a SSHA-dependent MLD for the OHC estimation improves the two-layer model by 5%. Upper ocean thermal structure estimations improved by 25% using the SMARTS Climatology as compared to that of Mainelli (2000).

The present understanding of the structure and dynamics of turbulent boundary layers on aerodynamically smooth walls has been clarified over the last decade or so. However, the dynamics of turbulent boundary layers over rough surfaces is much less well known. Nevertheless, there are many industrial and environmental flow applications that require understanding of the mean velocity and turbulence in the immediate vicinity of the roughness elements.</p> <p>This thesis reports the effects of surface roughness on the flow characteristics in a turbulent boundary layer. Both experimental and numerical investigations are used in the present study. For the experimental study, comprehensive data sets are obtained for two-dimensional zero pressure-gradient turbulent boundary layers on a smooth surface and ten different rough surfaces created from sand paper, perforated sheet, and woven wire mesh. The physical size and geometry of the roughness elements and freestream velocity were chosen to encompass both transitionally rough and fully rough flow regimes. Three different probes, namely, Pitot probe, single hot-wire, and cross hot-film, were used to measure the velocity fields in the turbulent boundary layer. A Pitot probe was used to measure the streamwise mean velocity, while the single hot-wire and cross hot-film probes were used to measure the fluctuating velocity components across the boundary layer. The flow Reynolds number based on momentum thickness, , ranged from 3730 to 13,550. The data reported include mean velocity, streamwise and wall-normal turbulence intensities, Reynolds shear stress, triple correlations, as well as skewness and flatness factors. Different scaling parameters were used to interpret and assess both the smooth- and rough-wall data at different Reynolds numbers, for approximately the same freestream velocity. The appropriateness of the logarithmic law and power law proposed by George and Castillo (1997) to describe the mean velocity in the overlap region was also investigated. The present results were interpreted within the context of the Townsends wall similarity hypothesis. </p> <p>Based on the mean velocity data, a novel correlation that relates the skin friction to the ratio of the displacement and boundary layer thicknesses, which is valid for both smooth- and rough-wall flows, was proposed. In addition, it was also found that the application of a mixed outer scale caused the velocity profile in the outer region to collapse onto the same curve, irrespective of Reynolds numbers and roughness conditions. The present results showed that there is a common region within the overlap region of the mean velocity profile where both the log law and power law are indistinguishable, irrespective of the surface conditions. For the power law formulation, functional relationships between the roughness shift, and the power law coefficient and exponent were developed for the transitionally rough flows. The present results also suggested that the effect of surface roughness on the turbulence field depends to some degree on the specific characteristics of the roughness elements and also the component of the Reynolds stress tensor being considered. </p> <p>In the case of the numerical study, a new wall function formulation based on a power law was proposed for smooth and fully rough wall turbulent pipe flow. The new formulation correctly predicted the friction factors for smooth and fully rough wall turbulent pipe flow. The existing two-layer model realistically predicted the velocity shift on a log-law plot for the fully rough turbulent boundary layer. The two-layer model results also showed the effect of roughness is to enhance the level of turbulence kinetic energy and Reynolds shear stress compared to that on a smooth wall. This enhanced level extends into the outer region of the flow, which appears to be consistent with present and recent experimental results for the boundary layer.

The present understanding of the structure and dynamics of turbulent boundary layers on aerodynamically smooth walls has been clarified over the last decade or so. However, the dynamics of turbulent boundary layers over rough surfaces is much less well known. Nevertheless, there are many industrial and environmental flow applications that require understanding of the mean velocity and turbulence in the immediate vicinity of the roughness elements.</p> <p>This thesis reports the effects of surface roughness on the flow characteristics in a turbulent boundary layer. Both experimental and numerical investigations are used in the present study. For the experimental study, comprehensive data sets are obtained for two-dimensional zero pressure-gradient turbulent boundary layers on a smooth surface and ten different rough surfaces created from sand paper, perforated sheet, and woven wire mesh. The physical size and geometry of the roughness elements and freestream velocity were chosen to encompass both transitionally rough and fully rough flow regimes. Three different probes, namely, Pitot probe, single hot-wire, and cross hot-film, were used to measure the velocity fields in the turbulent boundary layer. A Pitot probe was used to measure the streamwise mean velocity, while the single hot-wire and cross hot-film probes were used to measure the fluctuating velocity components across the boundary layer. The flow Reynolds number based on momentum thickness, , ranged from 3730 to 13,550. The data reported include mean velocity, streamwise and wall-normal turbulence intensities, Reynolds shear stress, triple correlations, as well as skewness and flatness factors. Different scaling parameters were used to interpret and assess both the smooth- and rough-wall data at different Reynolds numbers, for approximately the same freestream velocity. The appropriateness of the logarithmic law and power law proposed by George and Castillo (1997) to describe the mean velocity in the overlap region was also investigated. The present results were interpreted within the context of the Townsends wall similarity hypothesis. </p> <p>Based on the mean velocity data, a novel correlation that relates the skin friction to the ratio of the displacement and boundary layer thicknesses, which is valid for both smooth- and rough-wall flows, was proposed. In addition, it was also found that the application of a mixed outer scale caused the velocity profile in the outer region to collapse onto the same curve, irrespective of Reynolds numbers and roughness conditions. The present results showed that there is a common region within the overlap region of the mean velocity profile where both the log law and power law are indistinguishable, irrespective of the surface conditions. For the power law formulation, functional relationships between the roughness shift, and the power law coefficient and exponent were developed for the transitionally rough flows. The present results also suggested that the effect of surface roughness on the turbulence field depends to some degree on the specific characteristics of the roughness elements and also the component of the Reynolds stress tensor being considered. </p> <p>In the case of the numerical study, a new wall function formulation based on a power law was proposed for smooth and fully rough wall turbulent pipe flow. The new formulation correctly predicted the friction factors for smooth and fully rough wall turbulent pipe flow. The existing two-layer model realistically predicted the velocity shift on a log-law plot for the fully rough turbulent boundary layer. The two-layer model results also showed the effect of roughness is to enhance the level of turbulence kinetic energy and Reynolds shear stress compared to that on a smooth wall. This enhanced level extends into the outer region of the flow, which appears to be consistent with present and recent experimental results for the boundary layer.

Oceanic waves registered by satellite observations often have curvilinear fronts and propagate over various currents. In this thesis, we study long linear and weakly-nonlinear ring waves in a stratified fluid in the presence of a depth-dependent horizontal shear flow. It is shown that despite the clashing geometries of the waves and the shear flow, there exists a linear modal decomposition, which can be used to describe distortion of the wavefronts of surface and internal waves, and systematically derive a 2+1-dimensional cylindrical Korteweg-de Vries (cKdV)-type equation for the amplitudes of the waves. The general theory is applied to the case of the waves in a two-layer fluid with a piecewise-constant shear flow, with an emphasis on the effect of the shear flow on the geometry of the wavefronts. The distortion of the wavefronts is described by the singular solution (envelope of the general solution) of the nonlinear first order differential equation, constituting generalisation of the dispersion relation in this curvilinear geometry. There exists a striking difference in the shape of the wavefronts: the wavefront of the surface wave is elongated in the shear flow direction while the wavefront of the interfacial wave is squeezed in this direction. We solve the derived 2+1-dimensional cKdV-type equation numerically using a finite-difference scheme. The effects of nonlinearity and dispersion are studied by considering numerical results for surface and interfacial ring waves generated from a localised source with and without shear flow and the 2D dam break problem. In these examples, the linear and nonlinear surface waves are faster than interfacial waves, the wave height decreases faster at the surface, the shear flow leads to the wave height decreasing slower downstream and faster upstream, and the effect becomes more prominent as the shear flow strengthens.

The objective of this preliminary study was to determine the potential of diffuse correlation spectroscopy (DCS) for assessment of coagulation depth. Coagulation of tissue can occur due to a number of different reasons such as thermal or electrical burns or radiofrequency ablation. DCS is a non-invasive optical technique which can be used to determine the optical and dynamic properties of tissue by fitting a theoretical model of photon propagation in multiply scattering tissue to experimental data obtained from measurements. The DCS measurements were performed on two-layered phantom models that represent healthy tissue with high flow properties with a layer of coagulated tissue with low flow properties on top. Three different phantom models were prepared using gelatin-Intralipid gels, PDMS, and nylon as an upper layer, and an Intralipid solution was used for the bottom layer for all three phantoms. DCS measurements were performed on all three phantom models with varying thicknesses of the upper layers, and varying source-detector separations. The acquired data from the DCS measurement were analyzed in MATLAB in order to obtain the electric field temporal autocorrelation function. A theoretical model describing photon propagation in a two-layered medium was fitted to the obtained data in order to extract the desired parameters. The results showed that the thickness of the gelatin-Intralipid gels could be extracted within a 0.5 mm certainty and the thickness of the PDMS phantoms could also be extracted within approximately 0.7 mm. For the nylon phantoms, the results obtained were not good because the fitting was not successful and the thickness was not extracted appropriately. There is potential in DCS for assessment of burn wound depth but further research and development has to be done in the field in order to obtain more accurate and reliable results.

Ce travail est consacré à la modélisation mathématique et numérique des écoulements eau-air en conduite qui interviennent notamment dans les centrales de production d’électricité ou les réseaux d’eaux usées. On s’intéresse particulièrement aux écoulements mixtes caractérisés par la présence de régimes stratifiés pilotés par des ondes gravitaires lentes, de régimes en charge ou secs (conduite remplie d’eau ou d’air) pilotés par des ondes acoustiques rapides, et de poches d’air piégées. Une modélisation précise de ces écoulements est nécessaire afin de garantir le bon fonctionnement du circuit hydraulique sous-jacent. Alors que la plupart des modèles disponibles dans la littérature se concentrent sur la phase eau en négligeant la présence de l’air, un modèle bicouche compressible prenant en compte les interactions eau-air est proposé dans cette thèse. Sa construction réside dans l’intégration des équations d’Euler barotropes sur la hauteur de chaque phase et dans l’application de la contrainte hydrostatique sur le gradient de pression de l’eau. Le modèle obtenu est hyperbolique et satisfait une inégalité d’entropie en plus d’autres propriétés mathématiques notables, telles que l’unicité des relations de saut ou la positivité des hauteurs et densités de chaque phase. Au niveau discret, la simulation d’écoulements mixtes avec le modèle bicouche compressible soulève plusieurs défis en raison de la disparité des vitesses d’ondes caractérisant chaque régime, des processus de relaxation rapide sous-jacents, et de la disparition de l’une des phases dans les régimes en charge ou sec. Une méthode à pas fractionnaires implicite-explicite est alors développée en s’appuyant sur la relaxation rapide en pression et sur le mimétisme avec les équations de Saint-Venant pour la dynamique lente de la phase eau. En particulier, une approche par relaxation permet d’obtenir une stabilisation du schéma en fonction du régime d’écoulement. Plusieurs cas tests sont traités et démontrent la capacité du modèle proposé à gérer des écoulements mixtes incluant la présence de poches d’air piégées. / The present work is dedicated to the mathematical and numerical modelling of transient air-water flows in pipes which occur in piping systems of several industrial areas such as nuclear or hydroelectric power plants or sewage pipelines. It deals more specifically with the so-called mixed flows which involve stratified regimes driven by slow gravity waves, pressurized or dry regimes (pipe full of water or air) driven by fast acoustic waves and entrapped air pockets. An accurate modelling of these flows is necessary to guarantee the operability of the related hydraulic system. While most of available models in the literature focus on the water phase neglecting the air phase, a compressible two-layer model which accounts for air-water interactions is proposed herein. The derivation process relies on a depth averaging of the isentropic Euler set of equations for both phases where the hydrostatic constraint is applied on the water pressure gradient. The resulting system is hyperbolic and satisfies an entropy inequality in addition to other significant mathematical properties, including the uniqueness of jump conditions and the positivity of heights and densities for each layer. Regarding the discrete level, the simulation of mixed flows with the compressible two-layer model raises key challenges due to the discrepancy of wave speeds characterizing each regime combined with the fast underlying relaxation processes and with phase vanishing when the flow becomes pressurized or dry. Thus, an implicit-explicit fractional step method is derived. It relies on the fast pressure relaxation in addition to a mimetic approach with the shallow water equations for the slow dynamics of the water phase. In particular, a relaxation method provides stabilization terms activated according to the flow regime. Several test cases are performed and attest the ability of the compressible two-layer model to deal with mixed flows in pipes involving air pocket entrapment.