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Waves, which arise when restoring forces act on small perturbations, are ubiquitous in fluids. Their counterpart, mean flows, capture the remainder of the motion and are often characterised by a slower evolution and larger scale patterns. Waves and mean flows, which are typically separated by time- or space-averaging, interact, and this interaction is central to many fluid-dynamical phenomena. Wave-mean flow interactions can be classified into dissipative interactions and non-dissipative interactions. The former is important for small-scale flows, the latter for large-scale flows. In this thesis these two kinds of interactions are studied in the context of microfluidics and geophysical applications. Viscous wave-mean flow interactions are studied in two microfluidic problems. Both are motivated by the rapidly increasing number of microfluidic devices that rely on the mean-flow generated by dissipating acoustic waves - acoustic streaming - to drive small-scale flows. The first problem concerns the effect of boundary slip on steady acoustic streaming, which we argue is important because of the high frequencies employed. By applying matched asympototics, we obtain the form of the mean flow as a function of a new non-dimensional parameter measuring the importance of the boundary slip. The second problem examined is the development of a theory applicable to experiments and devices in which rigid particles are manipulated or used as passive tracers in an acoustic wave field. Previous work obtained dynamical equations governing the mean motion of such particles in a largely heuristic way. To obtain a reliable mean dynamical equation for particles, we apply a systematic multiscale approach that captures a broad range of parameter space. Our results clarify the limits of validity of previous work and identify a new parameter regime where the motion of particles and of the surrounding fluid are coupled nonlinearly. Non-dissipative wave-mean flow interactions are studied in two geophysical fluid problems. (i) Motivated by the open question of mesoscale energy transfer in the ocean, we study the interaction between a mesoscale mean flow and near-inertial waves. By applying generalized Lagrangian mean theory, Whitham averaging and variational calculus, we obtain a Hamiltonian wave-mean flow model which combines the familiar quasi-geostrophic model with the Young & Ben Jelloul model of near-inertial waves. This research unveils a new mechanism of mesoscale energy dissipation: near-inertial waves extract energy from the mesoscale ow as their horizontal scale is reduced by differential advection and refraction so that their potential energy increases. (ii) We study the interaction between topographic waves and an unidirectional mean flow at an inertial level, that is, at the altitude where the Doppler-shifted frequency of the waves match the Coriolis parameter. This interaction can be described using linear theory, using a combination of WKB and saddle-point methods, leading to explicit expressions for the mean-flow response. These demonstrate, in particular, that this response is switched on asymptotically far downstream from the topography, in contrast to what is often assumed in parameterisation.

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Thesis (PhD (Civil Engineering))--Stellenbosch University, 2008. / The velocity, density and turbulence profiles of a horizontal, saline gravity current were measured experimentally. Stable stratfication damped the turbulence and prevented the gravity current from becoming self-similar. The velocity and density prfiles were measured simultaneously and non-intrusively with particle image velocimetry scalar (PIV-S) technology. The application of the PIV-S technology had to be extended in order to measure the continuously stratified gravity current. Measurement of the Reynolds fluxes and Reynolds stresses revealed the anisotropic turbulent transport of mass and momentum within the gravity current body. These measurements also allowed the interaction between turbulence and stratification to be studied. The measured profiles were used to evaluate the accuracy of a gravity current model which did not assume self-similarity. The gravity current model was based on a Reynolds-averaged Navier-Stokes (RANS) multispecies mixture model. The Reynolds flux and Reynolds stress profiles did not show self-similarity with increasing downstream distance. Comparison of the vertical and horizontal Reynolds fluxes showed that gravity strongly damped the vertical flux. At a downstream location, where the bulk Richardson number was supercritical, the shear production profile had a positive inner (near bed) peak and a positive outer peak, while the buoyancy production pro le had a negative outer peak. Further downstream, where the bulk Richardson number was near-critical, the outer shear and buoyancy production peaks disappeared, due to the continuous damping of the turbulence intensities by the stable stratification. However, near bed shearing allowed the inner shear production peak to remain. Sensitivity analyses of different turbulence models for the gravity current model showed that the standard k -e turbulence model, as well as the Renormalization Group theory (RNG) k -e turbulence model, generally underpredicted the mean streamwise velocity profile and overpredicted the excess density pro le. The flux-gradient hypothesis, used to provide closure for the Reynolds uxes, modelled the vertical Reynolds ux reasonably, but not the horizontal flux. This did not compromise the results, since the horizontal gravity current had the characteristics of a boundary-layer ow, where the horizontal flux does not contribute significantly to the flow structure. It was shown that the gravity current model, implementing the standard k -e turbulence model with a constant turbulent Schmidt number of ot = 1;3, produced profiles which were within 10% - 20% of the measured profiles.

The mean flowfield and time-dependent characteristics of a Mach 5 cylinder-induced transitional shock-wave/boundary-layer interaction have been studied experimentally. The objectives of the study were to: (i) provide a detailed description of the mean flow structure of the interaction, and (ii) characterize the unsteadiness of the interaction based on fluctuating pressure measurements. / text

This dissertation presents a series of laboratory experiments to study flow and mixing properties of multiphase plumes. The particle image velocimetry (PIV) and laserinduced fluorescence (LIF) techniques are developed to measure two-dimensional velocity and concentration fields of multiphase plumes. The developed measurement techniques are applied to bubble plumes in different ambient conditions. The problems and errors in the two-phase PIV application to a bubble plume case are addressed through a comparative study between the optical separation method using fluorescent particles and a new phase separation method using vector postprocessing. The study shows that the new algorithm predicts well the instantaneous and time-averaged velocity profiles and has errors comparable to those for image masking techniques. The phase separation method developed in the previous section is applied to study the mean flow characteristics of a bubble plume in quiescent and unstratified condition. The entrainment coefficients representing the mixing properties of a bubble plume are calculated to lie between 0.08 near the plume source and 0.05 in the upper region, and to depend on the non-dimensional quantity us/(B/z)1/3, where us is the bubble slip velocity, B is the initial buoyancy flux, and z is the height from the diffuser. Further, the LIF technique is investigated to measure the scalar concentration field around a bubble plume in quiescent, unstratified condition. This new application to bubble plumes accounts for light scattering by bubbles using an attenuation coef- ficient that is proportional to the local void fraction. Measured scalar concentration fields show similar trend in concentration fluctuation to turbulent plume cases. Finally, the velocity and concentration field measurements using the developed two-phase PIV and LIF methods are applied for a bubble plume in a density-stratified ambient. The turbulent flow characteristics induced by a bubble plume in a stratified ambient water are studied. The plume fluctuation frequency is measured as about 0.1 Hz and compares well to plume wandering frequency measured in unstratified plume cases.

The scattering of waves by a finite thin plate in a two-dimensional wave guide and an array of finite thin plates, in the presence of subsonic mean flow, are formulated using a mode matching technique. The influence of mean flow on trapped modes in the vicinity of a finite thin plate in a two-dimensional wave guide is then investigated by putting the amplitude of the forcing term to zero in the scattering problem. The conditions for complex resonances are found, and numerical results are computed. The influence of mean flow on Rayleigh-Bloch modes is investigated by using a similar methodology. The condition for embedded trapped modes to exist is introduced next, and then numerical results for embedded trapped modes without mean flow are presented. Complex resonances without mean flow are then found by fixing the geometry of the waveguide. The influence of mean flow on complex resonances and embedded trapped modes is investigated subsequently. In addition, the investigation of scattering coefficients is discussed when the frequency of an incident wave is near the real part of the frequency of complex resonances or embedded trapped modes. Embedded trapped modes near an indentation in a strip wave guide, which may correspond to a two-dimensional acoustic wave guide or a channel of uniform water depth in water waves, are also found. Modes are sought which are either symmetric or anti-symmetric about the centreline of the guide and the centre of the indentation. In each case, a simple approximate solution is found numerically. Full solutions are then found by using a Galerkin approach in which the singularity near the indentation edge is modelled by choosing proper special functions. The final part of the thesis is devoted to spinning modes (Rayleigh-Bloch modes) in a cylindrical waveguide in the presence of radial fins. A mode matching technique is used to obtain the potential, and the coefficients in the expansion are found numerically by using an efficient Galerkin procedure. In addition, an existence proof for modes symmetric about the centre of the guide and the centre of the section with radial fins is given by applying a variational approach. The connection between Rayleigh-Bloch modes and trapped modes is discussed thereafter, and numerical results for a number of geometric configurations are presented.

Every type of current meter is different and has its proper characteristics. Knowing the performance of a current meter is essential in order to use it properly either for field or laboratory measurements (such as in the Offshore Technology Research Center wave basin). A study of the MAVS (Modular Acoustic Velocity Sensor) in a wave basin is a first step essential for later deployment in real studies. This thesis is based on data obtained from different series of laboratory measurements conducted in the OTRC wave basin. The objective of the first part of the study was to characterize the MAVS frequency response using benchmarks such as tow tests or wave tests. These benchmarks allowed us not only to characterize the sensor but also to eventually correct some of the measurement distortions due to flow blockage, vortex shedding, or vibrations of the mounting structure, for example. After the preliminary study was done, we focused on the potential use of the MAVS in the OTRC wave basin. Indeed, in the case of a study of a scale model in the wave basin, the stresses applied to the model have to be accurately known. In the case of current-induced loads, this includes contributions from both the mean flow and the turbulence. Thus, after correcting the values measured by the MAVS, a mapping of the current jet was executed to determine its three-dimensional structure in the wave basin. Knowing the structure of the current in the OTRC wave basin, it was then possible to define a domain in which the current can be considered uniform with a certain tolerable error. This domain of uniformity will allow us to validate the use of the OTRC wave basin to study large models such as FPSOs (Floating Production, Storage and Offloading Units).

Un des mécanismes proposés pour expliquer l'origine de la variabilité climatique sur des périodes décennales à multidécennales est une oscillation propre de la circulation océanique thermohaline. Son mécanisme s'apparente aux modes de bassin basse fréquence et grande échelle qui résultent de l'interaction entre les ondes lentes planétaires et les ondes rapides de bord au cours du processus d'ajustement du bassin. Toutefois, la plupart des études de ce prototype oscillation décennale ont été menées dans des contextes simplifiés quasi-géostrophiques, à gravité réduite ou à fond plat. On se propose dans ce travail de thèse d'étudier l'effet de la topographie du fond et de la circulation moyenne sur les caractéristiques des modes de bassin baroclines. On utilise un modèle shallow water à deux couches verticales avec surface libre. Différentes bathymétries analytiques type fond plat, dorsale médio-océanique et pentes continentales sont étudiées.L'obtention des vecteurs propres du modèle linéarisé par analyse de stabilité linéaire autour d'un état au repos révèle que (1) la sélection de ces modes à basse résolution s'établit par la dissipation explicite introduite dans le modèle, (2) la période décennale et l'amortissement du mode le moins amorti sont faiblement sensibles à la topographie. Les budgets d'énergie et de vorticité de ces modes sont calculés dans le but de rationaliser le rôle amortisseur de la topographie via la conversion d'énergie qui a lieu entre les modes barotrope et barocline. En effet, une circulation barotrope, absente à fond plat, émerge à travers l'interaction entre le mode barocline à fond plat et la topographie. Toutefois, cette conversion d'énergie sous l'effet JEBAR demeure faible comparée aux processus visqueux.En présence d'une circulation stationnaire forcée par le vent et les flux de chaleur, les intégrations temporelles du modèle nonlinéaire perturbé par des structures baroclines cohérentes type tourbillons gaussiens montrent la forte interaction entre le vortex et la topographie. Cette interaction se manisfeste par : (1) une accélération de la vitesse de phase vers l'ouest par rapport au résultat à fond plat, (2) une circulation barotrope construite par la conversion de l'énergie barocline en barotrope, et (3) un déplacement méridien de l'anomalie dépendant de son signe même en l'absence d'advection nonlinéaire.Par ailleurs, le mode majeur de variabilité barocline, fortement amorti par la topographie et la dissipation dans la configuration non forcée paraît renforcé par l'écoulement stationnaire qui diminue son taux d'amortissement. Sa période d'oscillation développe une dépendance à la migration méridienne de l'advection zonale par l'écoulement moyen: elle est raccourcie (T ̴ 16 ans) pour le forçage par le vent et rallongée (T ̴ 22 ans) pour le forçage par les flux de chaleur. / One of the potential mechanisms at the origin of climatic variability on decadal to multidecadal timescales is the thermohaline oscillation corresponding to large-scale and low frequency basin modes that result from the interaction between long planetary waves and fast inertia-gravity waves during the adjustment process. However, most of the studies dealing with this decadal oscillation were carried out in a simplified flat bottom or reduced-gravity quasigeostrophic context.This dissertation aims to study the effect of bottom topography and mean flow on the characteristics of the gravest baroclinic basin modes in a mid-latitude idealized ocean basin. To that end, we make use of a two-layer shallow water (SW) model. Different bathymetries such as a flat bottom, a mid-ocean ridge and continental slopes are studied. Getting the eigenvectors from the linearized model through linear stability analysis around a state of rest reveals that (1) the selection of these modes is set by the explicit dissipation introduced in the model, (2) the oscillation period and decay rate are weakly sensitive to the form and height of the topography. Vorticity and energy budgets are computed in order to give a rationale for the decaying role of the topography via energy conversion from the baroclinic to the barotropic mode. Indeed, the barotropic flow absent in a flat bottom, results accurately from the interaction of the flat-bottomed baroclinic motion with the topographic height. However, the energy conversion under the JEBAR effect remains weaker with respect to the frictional processes.A stationary circulation is now included through wind or thermal forcing. Temporal integrations of the nonlinear model perturbed by coherent baroclinic structures with a gaussian eddy form show the strong interaction between the vortex and the topography. This interaction implies: (1) a westward acceleration of the zonal phase speed (with respect to the classic flat-bottom result), (2) a barotropic circulation built up by the conversion of the baroclinic energy into a barotropic one, and (3) an eddy sign-dependent meridional migration, even in the absence of nonlinear advection. Moreover, the decadal basin mode strongly damped by the topography and the dissipation shows a decrease of its decay rate by the large scale stationary forcing. Its oscillation period is found to be a strong function of the meridional migration of the eastward advection by the mean flow: it is shortened (T ̴ 16 yrs) in the wind-forced experiment and lengthened (T ̴ 22 yrs) with a thermal forcing.

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