This thesis contains a thorough investigation of the properties of freely decaying turbulence in a rotating shallow water layer on a sphere. A large number of simulations, covering an extensive range of Froude and Rossby numbers, have been carried out using a novel numerical algorithm that exploits the underly- ing properties of the flow. In general these flows develop coherent structures; vortices interact, merge and migrate polewards or equatorwards depending or their sign, leaving behind regions of homogenized potential vorticity separated by sharp zonal jets. In the first half of the thesis we investigate new ways of looking at these structures. In the second half of the thesis we examine the properties of the potential vorticity (PV) induced, balanced component and the residual, unbalanced component of the flows. Cyclone-anticyclone asymmetry has long been observed in atmospheric and oceanic data, laboratory experiments and numerical simulations. This asymmetry is usually seen to favour anticyclonic vorticity with the asymmetry becoming more pronounced at higher Froude numbers (e.g. Polvani et al. [1994a]). We find a similar result but note that the cyclones, although fewer, are significantly more intense and coherent. We present several ways of quantifying this across the parameter space. Potential vorticity homogenization is an important geophysical mechanism responsible for sharpening jets through the expulsion of PV gradients to the edge of flow structures or domains. Sharp gradients of PV are obvious in contour plots of this field as areas where the contours are bunched together. This suggests that we can estimate the number of zonal jets by performing a cluster analysis on the mean latitude of PV contours (this diagnostic is also examined by Dritschel and McIntyre [2007]). This provides an estimate rather than an exact count of the number of jets because the jets meander signficantly. We investigate the accuracy of the estimates provided by different clustering techniques. We find that the properties of the jets defy such simple classification and instead demand a more local examination. We achieve this by examining the palinstrophy field. This field, calculated by taking the gradient of the PV, highlights the regions where PV contours come closer together, exactly what we would expect in regions of strong jets. Plots of the palinstrophy field reveal the complex structure of these features. The potential vorticity field is even more central to the flow evolution than the strong link with jets suggests. From a knowledge of the spatial distribution of PV, it is possible to diagnose the balanced components of all other fields. These components will not contain inertia-gravity waves but will contain the dominant, large scale features of the flow. This inversion, or decomposition into balanced (vortical) and unbalanced (wave) components, is not unique and can be defined to varying orders of accuracy. We examine the results of four dfferent definitions of this decomposition, two based on truncations of the full equations and two based on an iterative procedure applied to the full equations. We find the iterative procedure to be more accurate in that it attributes more of the flow to the PV controlled, balanced motion. However, the truncated equations perform surprisingly well and do not appear to suffer in accuracy at the equator, despite the fact that the scaling on which they are based has been thought to break down there. We round off this study by considering the impact of the unbalanced motion on the flow. This is accomplished by splitting the integration time of the model into intervals τ < t < τ+dτ and comparing, at the end of each interval, the balanced components of the flow obtained by a) integrating the model from t = 0 and b) integrating the full equations, initialised at t = τ with the balanced components from a) at t = τ. We find that any impact of the unbalanced component of the flow is less than the numerical noise of the model.

Thesis. 1978. M.S.--Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND AERONAUTICS. / Includes bibliographical references. / M.S.

Research into the fluidic precessing jet, used in industrial burners, has been carried out within the School of Mechanical Engineering at the University of Adelaide for over a decade. The flow field generated by the fluidic precessing jet (FPJ) is extremely complex, and there are many questions yet to be answered about the mechanisms by which precession influences the mixing of the jet and ambient fluid, and hence combustion. Some may be answered by studying a non-reacting precessing jet. The mechanical precessing jet (MPJ) nozzle generates a precessing jet for which the exit conditions are well known, unlike the fluidic precessing jet. The non-reacting flow from this 'mechanical analogue' of the FPJ forms the basis of the current study. The MPJ provides a means of controlling and changing the structure of turbulence in a precessing jet by varying its precessional frequency. The characteristics of the MPJ flow are primarily determined by a Strouhal number of precession, and may be categorised as belonging to either a 'low Strouhal number' or 'high Strouhal number' regime of behaviour. The fundamental aim of studying the mechanical precessing jet flow is to determine the influence of the structure of turbulent motions, and in particular the large scale motions, on jet mixing. The analyses presented in this thesis lead to a better understanding of the underlying mechanisms of precession-enhanced turbulent mixing and combustion. Simultaneously collected phase-averaged velocity and concentration fields of the MPJ flow are presented, and correlations between the fields analysed, for one low and one high Strouhal number. Additionally, because the turbulent flow produced by the MPJ nozzle is unsteady in nature and instantaneous realisations of the flow may differ significantly from the mean flow patterns, planar velocity and concentration measurements which show instantaneous flow structure over the entire field are presented. The phase-averaged velocity and concentration field data have enabled new analytical models of the MPJ trajectory to be developed, and the behaviour of the major flow features, including the stability of the counter-rotating vortex pair, to be studied. The strong entrainment and mixing characteristics of the MPJ flow are also illustrated. The data and analysis strongly suggest that the initial trajectory of the jet is essentially radial, during which the jet experiences axial compression. At larger radius the jet experiences axial stretching. A counter- rotating vortex pair is seen to form approximately two potential core lengths from the jet exit, where the jet appears to bend sharply towards the axis of rotation. These vortices dominate the jet motion in the near field and eventually merge in the transition region of the flow. The inner vortex of the counter-rotating vortex pair mixes at approximately half the rate of the outer vortex, thus delivering a rich fuel mixture to the transition region when the MPJ is used as a burner. This may explain in part earlier observations of highly radiant, fuel-rich flames in the transition region. This study also outlines the development of an experimental technique for the simultaneous measurement of velocity and concentration in a plane. The medium is air, and the technique combines Particle Image Velocimetry (PIV) and Planar Laser Induced Fluorescence (PLIF) of acetone vapour in a unique manner. / Thesis (Ph.D.)--School of Mechanical Engineering, 2004.

One microfilm reel (16 mm.) in pocket / Bibliography: leaves 194-201 / xiii, 212, 6 leaves, [9] leaves of plates : ill. (some col.) ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Mechanical Engineering, 1987

A plane jet is a statistically two-dimensional flow, with the dominant flow in the streamwise (x) direction, spread in the lateral (y) direction and zero entrainment in the spanwise (z) direction respectively (see Figure 1). A plane jet has several industrial applications, mostly in engineering environments, although seldom is a jet issuing through a smooth contoured nozzle encountered in real life. Notably, the Reynolds number and boundary conditions between industrial and laboratory environments are different. In view of these, it is important to establish effects of nozzle boundary conditions as well as the influence of Reynolds number, on jet development. Such establishments are essential to gain an insight into their mixing field, particularly relevant to engineering applications. To satisfy this need, this thesis examines the influence of boundary conditions, especially those associated with the formation of the jet and jet exit Reynolds number, on the flow field of a turbulent plane air jet by measuring velocity with a hot wire anemometer. A systematic variation is performed, of the Reynolds number Re over the range 1,500≤Re ≤16,500, the inner-wall nozzle contraction profile r* over the range 0≤r*≤3.60 and nozzle aspect ratio AR over the range 15≤AR≤72 (see notation for symbols). An independent assessment of the effect of sidewalls on a plane jet is also performed. Key outcomes are as follows: (1) Effects of Reynolds number Re: Both the mean and turbulence fields show significant dependence on Re. The normalized initial mean velocity and turbulence intensity profiles are Re-dependent. An increase in the thickness of boundary layer at the nozzle lip with a decrease in Re is evident. This dependence appears to become negligible for Re ≥10,000. The centerline mean velocity decay and jet spreading rates are found to decrease as Re is increased. Furthermore, the mean velocity field appears to remain sensitive to Reynolds number at Re = 16,500. Unlike the mean velocity field, the turbulent velocity field has a negligible Re-dependence for Re ≥10,000. An increase in Reynolds number leads to an increase in the entrainment rate in the near field but a reduced rate in the far field. The centerline skewness and the flatness factors show a systematic dependence on Reynolds number too. (2) Effects of the inner-wall nozzle exit contraction profile r*: The inner-wall nozzle exit contraction profile r* influences the initial velocity and turbulence intensity profiles. Saddle-backed mean velocity profiles are evident for the sharp-edged orifice configuration (r* ≈ 0) and top hat profiles emerge when r* ≥1.80. As r* is increased from 0 to 3.60, both the near and the far field decay and the spreading rates of the plane jet are found to decrease. Hence, the sharp-edged orifice-jet (r* ≈ 0) decays and spreads more rapidly than the jet through a radially contoured configuration (r* ≈ 3.60). The asymptotic values of the center-line turbulence intensity, skewness and flatness factors of the velocity fluctuations increase as r* tends toward zero. The non-dimensional vortex shedding frequency of StH ≈ 0.39, is higher for the sharp-edged orifice nozzle (r*≈ 0), than for the radially contoured (r* ≈ 3.60) nozzle whose StH ≈ 0.24. Thus, the vortex shedding should be strongly dependent on flow geometry and on nozzle boundary conditions. (3) Effects of nozzle aspect ratio AR: The initial velocity and turbulence intensity profiles are slightly dependent on nozzle aspect ratio of the plane air jet. It is believed that a coupled influence of the nozzle aspect ratio and sidewalls produce changes in the initial flow field. The axial extent over which a statistically 'two-dimensional' flow is achieved, is found to depend upon nozzle aspect ratio. This could be possibly due to the influence of the evolving boundary layer on the sidewalls or due to increased three-dimensionality, whose influence becomes significantly larger as nozzle aspect ratio is reduced. A statistically two dimensional flow is only achieved over a very limited extent for AR = 15. In the self-similar region, the rates of centreline velocity decay, spreading of the mean velocity field and jet entrainment increase with an increase in nozzle aspect ratio. An estimate of the critical jet aspect ratio, where three-dimensional effects first emerge and its axial location is made. Results show that the critical aspect ratio increases with nozzle aspect ratio up to AR <30. For AR≥30, the critical aspect ratio based on jet half width, attains a constant value of about 0.15. Thus, it appears that when the width of the flow approximately equals the spacing between the sidewalls, the plane air jet undergoes a transition from 2-D to 3-D. A distinct hump of the locally normalized turbulence intensity at an axial distance between 10 to 12 nozzle widths downstream, characterizes the centerline turbulence intensity for all nozzle aspect ratios. This hump is smaller when nozzle aspect ratio is larger. (4) Effects of the sidewalls: A jet issuing from a nozzle of AR = 60 and measured at Re = 7,000 is tested with sidewalls, i.e. plane-jet and without sidewalls, i.e. free-rectangular-jet. It is found that the entire flow field behaves differently for the two cases. The initial velocity profiles are top hat for both jets. The free rectangular jet decays and spreads more rapidly in both the near and far field. It is found that the free rectangular jet behaves statistically two-dimensional up to a shorter axial distance (x/H = 70) as opposed to the plane jet whose two-dimensional region extends up to x/H = 160. Also noted are that the axial extent of the two-dimensional region depends strongly on nozzle aspect ratio. Beyond the 2-D region, the free rectangular jet tends to behave, statistically, like a round jet. The locally normalized centerline turbulence intensity also depend on sidewalls. Turbulence intensity for the plane jet asymptotes closer to the nozzle (around x/H = 30) whereas for the free rectangular jet, turbulence intensity varies as far downstream as x/H = 100, and then asymptotes. A constant StH of 0.36 is found for the free rectangular jet whereas an StH of 0.22 is obtained for the plane jet. It is noted that the effects of jet exit Reynolds number, inner-wall nozzle exit contraction profile, nozzle aspect ratio and sidewalls on the plane air jet are all non-negligible. The effect of viscosity is expected to weaken with increased Reynolds number and this may contribute to the downstream effects on the velocity field. Both the nozzle contraction profile and nozzle aspect ratio provide different exit boundaries for the jet. Such boundary conditions not only govern the formation of the initial jet but also its downstream flow properties. Hence, the initial growth of the shear layers and the structures within these layers are likely to evolve differently with different boundary conditions. Thus, the interaction of the large-scale structures with the surroundings seems to depend on nozzle boundary conditions and consequently, influences the downstream flow. In summary, the present study supports the notion that the near and far fields of the plane jet are strongly dependent on Reynolds number and boundary conditions. Therefore, the present thesis contains immensely useful information that will be helpful for laboratory-based engineers in selection of appropriate nozzle configurations for industrial applications. / Thesis (Ph.D.)--School of Mechanical Engineering, 2005.

Jets in crossflow are used in a wide range of engineering applications and have been studied for more than 60 years. The transversal penetration and structure of a jet placed in a crossflow is known to be strongly three-dimensional. It is believed that, by using a pulsed jet inclined in the crossflow direction, the momentum transport can be controlled in two very efficient ways: the pulse can increase the jet penetration and the mixing downstream, while the inclination avoids the creation of a reverse flow at the jet exit and may extend the mixing area further downstream. Although some results are available in the literature focusing on components of this problem, none addresses the combination of these two factors. Moreover, most of these studies use elaborate flow visualizations and 2-D velocity measurement methods that may not be adequate to elucidate the complexity of such a flow. This study addresses these issues by using stereoscopic PIV measurements for a steady and fully modulated jet at a constant mean velocity ratio, V[subscript r], of 3.4. For the steady jet case, the effect of the jet Reynolds number, Re[subscript j], is investigated. For the pulsed case, the effect of a low pulsing frequency is considered as well as the pulse duty cycle. For each case, the mean three-component velocity field is examined. Proper Orthogonal Analysis (POD) of vorticity and turbulent kinetic energy are used to further evaluate the vortical and turbulent characteristics of the jet. In addition, a vortex detection algorithm, and 3D rendering of the flow streamlines are used to study the near field vortical flow structure of the jet flow. / Graduation date: 2006

published_or_final_version / Civil and Structural Engineering / Master / Master of Philosophy

Motivated by a practical interest in noise generated by turbofan engine, this thesis studies the stability of parallel coaxial jets with velocity and temperature profiles characteristic of the exhaust region of the engine. Because the bypass stream mixes with both the exhaust and the ambient air, these profiles contain thin layers in which the velocity and temperature may vary rapidly. As a consequence, multiple instability modes are possible. In accordance with Rayleigh's theorem for axisymmetric incompressible shear flows, it follows that there are three possible modes, only two of which are unstable. To complement the study of parallel flow stability, this thesis also includes the derivation of the amplitude evolution equation for slowly varying axisymmetric incompressible flows.

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