Within turbulence there are many phenomena which are currently unsolved. In the solar wind temperature anisotropies and low growth rates instability have a dominant role in defining the turbulent behaviour of plasma. Due to the non- linearity of the equations involved in the description of the physics of plasmas numerical simulations are a fundamental tool to study the dynamics of turbulent phenomena. In particular, hybrid codes are widely used in space plasma applications due to their ability to simulate large regions of volume maintaining some kinetic effects. However, due to the sensitivity to the initial level of noise in the simulation, low growth rate instabilities are particularly difficult to simulate. Particle in Cell-hybrid simulations require too many particles to reduce the initial noise, while Vlasov-hybrid simulations require too many grid points to fully discretize spatial and velocity phase spaces. We present here a Vlasov-hybrid algorithm and code implementation where the distribution function is expanded in series of Hermite functions. Thanks to the properties of these it is possible to project the Vlasov equation to find an equation for each coefficient of the expansion. These coefficients are advanced in time using a Current Advance Method algorithm with splitting method for the Vlasov operator. The former is treated explicitly, while the latter is treated implicitly with a GMRES solver. The current is advanced with a temporal ODE derived taking moments of the Vlasov equation. A 1D3V code is implemented, tested and used to study low growth rate instabilities such as a proton cyclotron instability and a ion/ion right hand resonant instability with small relative velocity drift between beam and core populations. The results are compared with existing hybrid algorithms that we implemented. A 2D3V parallelized version of the code is implemented and described here. Initial results are presented and future improvements are discussed.

The dynamics of different classes of turbulent and miscible fountains are stud- ied: from classic axisymmetric fountains issuing from round sources, to confined fountains propagating in a quasi-two-dimensional environment, to line fountains which form when release conditions are approximately two-dimensional at the source. Each class is characterised by distinct dynamical behaviour, which this the- sis analyses both through theoretical arguments and experimental measurements. A model for the entrainment of ambient fluid into a fluctuating fountain top is developed and implemented into a first complete description for round fountains. The solutions of the resulting 'three-region-model' lie in improved agreement with available data and, uniquely, do not diverge near the top of the fountain. Next, con- fined fountains (unexplored to date) are classified into four flow regimes and their behaviour collapsed according to a single governing parameter that captures the severity of confinement. Finally, new experiments on line foutains shed light on the quasi-steady structure of these flows, revealing (and motivating) a strong con- nection between their motion in the vertical and lateral planes. Round, confined and line fountains are then contrasted in the conclusions, where we reflect on what is required to progress towards a unified theory of turbulent fountains.

Typescript (photocopy) / ix, 240 leaves : ill. ; 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, 1978

<p>In this work we have focused on the statistical properties of turbulence.</p><p>This has been done in two different settings; one with neutral gas (the first four papers) and the other with ionized gas (the last four papers). Regarding the work on the neutral gas, we have looked at four different aspects;</p><p>1. Is the mean energy dissipation rate, C_є, independent of Reynolds number for large Reynolds numbers? This is one of the fundamental questions in turbulence, and one believe the answer will be yes, but this is as yet not conclusive. In Paper 1 we demonstrate that the value of C_є<i> </i>is highly sensitive to the method used to measure it. This might explain the discrepancies in the values of C_є found by previous authors. We also show how one can find C_є for a spread of Reynolds numbers from a single simulation.</p><p>2. Is there a “bottleneck” in the energy spectrum between the inertial range and the dissipative range? Such a bottleneck is extremely weak - or totally absent, in wind tunnel experiments. In large numerical simulations however the bottleneck is pretty clear. In Paper 2 we show that this discrepancy is due to the physical nature of the one-dimensional energy spectra found in wind tunnels and the three dimensional energy spectra found in numerical simulations.</p><p>3. In order to achieve larger Reynolds numbers we investigate the possible errors introduced by using hyper viscosity instead of normal viscosity in Paper 3. Our conclusion is that while hyper viscosity increase the hight of the bottleneck and shortens the dissipative range, it does not otherwise have any significant effect on the energy spectrum, or the structure functions. The inertial range and the large scales are the same both with normal viscosity and hyper viscosity.</p><p>4. In decaying turbulence one can find relations under which the Navier- Stokes equations are scale invariant. Using these relations it has recently been suggested by Ditlevsen et al.[1] that the energy spectrum for decaying hydrodynamical turbulence can be described by a scaling function with only two arguments. This has previously been shown both analytically and experimentally, and in Paper 4 we also confirm this in numerical experiments.</p><p>For the ionized gas we have focused on five different aspects;</p><p>1. What does the large Reynolds number energy spectra look like? Are the kinetic and magnetic energy spectra similar? The results are as yet not conclusive because the Reynolds numbers are still too small, but it seems that what at first looked like a <i>k</i>^−3/2 inertial range is actually the bottleneck in a <i>k</i>^−5/3inertial range. Furthermore we have in Paper 5 found that the peak of the magnetic energy spectrum is <i>not</i> proportional to the resistive scale, but to the forcing scale.</p><p>2. As intermittency is still an unresolved topic we have looked at the different structure functions of the MHD dynamo. In Paper 6 the longitudinal structure functions based on the Elsasser variables are found to scale like in the model of She & Leveque[2], and the magnetic field is more intermittent than the velocity field. The Elsasser variables have been shown to have a linear scaling of the third order structure function. We do not, however, find the same linear scaling for the individual structure functions of the magnetic and the kinetic field.</p><p>3. In Paper 6 we investigate the growth rate of the magnetic field as a function of magnetic Reynolds number, and we find the critical magnetic Reynolds number as a function of magnetic Prandtl number.</p><p>4. How is the dynamo altered when one imposes an external large scale magnetic field? In Paper 7 we find that an imposed field tend to suppress the dynamo activity on all scales if the field is large enough. For an imposed magnetic field of the same size as the rms velocity field equipartition is found between magnetic and kinetic energy spectra.</p><p>5. Will there be dynamos in supersonic media? One could envisage that the supersonic shock swept up and dissipated the magnetic fields before they got time to grow. Numerical simulations in Paper 8 seem to show that as one increases the Mach number toward unity the critical magnetic Reynolds number increases, but as the Mach number grows even more the critical magnetic Reynolds number stays approximately constant.</p>

Four buoyant plumes were produced within a laboratory convectively mixed layer from a source height of about z[subscript s] = 0.15 h, where h is the height of the convectively mixed layer. The projected images of these plumes in the X-Z plane were analyzed using a densitometer (photomultiplier tube) to calculate dimensionless crosswind integrated concentration values. These values were examined at regular intervals of non-dimensionalized heights and downwind distances to calculate center-of-mass heights, approximate plume limits, and touchdown distances. The plume buoyancy values were expressed in dimensionless terms as the parameter F[subscript *]. The touchdown distances are greatest and the surface integrated crosswind concentrations are smallest for the three most buoyant plumes. The highest center-of-mass and plume limit positions are also associated with the most buoyant plumes. The surface crosswind integrated concentration values for even the least buoyant plumes are much smaller than for non-buoyant plumes from previous studies. Touchdown distances for buoyant plumes from this data set agree with data from Willis and Deardorff (1983); however, the centerline and lower plume limits are at greater heights for this study. Vertical profiles of crosswind integrated concentration values indicate that the least buoyant plume has a bimodal distribution near the stack then becomes uniform at greater distances. The vertical profiles for the three most buoyant plumes show the highest concentration values are present in the upper part of the mixed layer at most downwind distances examined in this study. This distribution of effluent is also indicated by the vertical center-of- mass heights being larger than the plume centerline calculated from the average of the lower and upper plume limits. / Graduation date: 1985

In this work we have focused on the statistical properties of turbulence. This has been done in two different settings; one with neutral gas (the first four papers) and the other with ionized gas (the last four papers). Regarding the work on the neutral gas, we have looked at four different aspects; 1. Is the mean energy dissipation rate, Cє, independent of Reynolds number for large Reynolds numbers? This is one of the fundamental questions in turbulence, and one believe the answer will be yes, but this is as yet not conclusive. In Paper 1 we demonstrate that the value of Cє is highly sensitive to the method used to measure it. This might explain the discrepancies in the values of Cє found by previous authors. We also show how one can find Cє for a spread of Reynolds numbers from a single simulation. 2. Is there a “bottleneck” in the energy spectrum between the inertial range and the dissipative range? Such a bottleneck is extremely weak - or totally absent, in wind tunnel experiments. In large numerical simulations however the bottleneck is pretty clear. In Paper 2 we show that this discrepancy is due to the physical nature of the one-dimensional energy spectra found in wind tunnels and the three dimensional energy spectra found in numerical simulations. 3. In order to achieve larger Reynolds numbers we investigate the possible errors introduced by using hyper viscosity instead of normal viscosity in Paper 3. Our conclusion is that while hyper viscosity increase the hight of the bottleneck and shortens the dissipative range, it does not otherwise have any significant effect on the energy spectrum, or the structure functions. The inertial range and the large scales are the same both with normal viscosity and hyper viscosity. 4. In decaying turbulence one can find relations under which the Navier- Stokes equations are scale invariant. Using these relations it has recently been suggested by Ditlevsen et al.[1] that the energy spectrum for decaying hydrodynamical turbulence can be described by a scaling function with only two arguments. This has previously been shown both analytically and experimentally, and in Paper 4 we also confirm this in numerical experiments. For the ionized gas we have focused on five different aspects; 1. What does the large Reynolds number energy spectra look like? Are the kinetic and magnetic energy spectra similar? The results are as yet not conclusive because the Reynolds numbers are still too small, but it seems that what at first looked like a k−3/2 inertial range is actually the bottleneck in a k−5/3 inertial range. Furthermore we have in Paper 5 found that the peak of the magnetic energy spectrum is not proportional to the resistive scale, but to the forcing scale. 2. As intermittency is still an unresolved topic we have looked at the different structure functions of the MHD dynamo. In Paper 6 the longitudinal structure functions based on the Elsasser variables are found to scale like in the model of She &amp; Leveque[2], and the magnetic field is more intermittent than the velocity field. The Elsasser variables have been shown to have a linear scaling of the third order structure function. We do not, however, find the same linear scaling for the individual structure functions of the magnetic and the kinetic field. 3. In Paper 6 we investigate the growth rate of the magnetic field as a function of magnetic Reynolds number, and we find the critical magnetic Reynolds number as a function of magnetic Prandtl number. 4. How is the dynamo altered when one imposes an external large scale magnetic field? In Paper 7 we find that an imposed field tend to suppress the dynamo activity on all scales if the field is large enough. For an imposed magnetic field of the same size as the rms velocity field equipartition is found between magnetic and kinetic energy spectra. 5. Will there be dynamos in supersonic media? One could envisage that the supersonic shock swept up and dissipated the magnetic fields before they got time to grow. Numerical simulations in Paper 8 seem to show that as one increases the Mach number toward unity the critical magnetic Reynolds number increases, but as the Mach number grows even more the critical magnetic Reynolds number stays approximately constant.

Conditional Source-term Estimation (CSE) methods are used to obtain chemical closure in turbulent combustion simulation. A Laminar Flamelet Decomposition (LFD) and then a Trajectory Generated Low-Dimensional Manifold (TGLDM) method are combined with CSE in Reynolds-Averaged Navier Stokes (RANS) simulation of non-premixed autoigniting jets. Despite the scatter observed in the experimental data, the predictions of ignition delay from both methods agree reasonably well with the measurements. The discrepancy between predictions of these two methods can be attributed to different ways of generating libraries that contain information of detailed chemical mechanism. The CSE-TGLDM method is recommended for its seemingly better performance and its ability to transition from autoignition to combustion. The effects of fuel composition and injection parameters on ignition delay are studied using the CSE-TGLDM method. The CSE-TGLDM method is then applied in Large Eddy Simulation of a non-premixed, piloted jet flame, Sandia Flame D. The adiabatic CSE-TGLDM method is extended to include radiation by introducing a variable enthalpy defect to parameterize TGLDM manifolds. The results are compared to the adiabatic computation and the experimental data. The prediction of NO formation is improved, though the predictions of temperature and major products show no significant difference from the adiabatic computation due to the weak radiation of the flame. The scalar fields are then extracted and used to predict the mean spectral radiation intensities of the flame. Finally, the application of CSE in turbulent premixed combustion is explored. A product-based progress variable is chosen for conditioning. Presumed Probability Density Function (PDF) models for the progress variable are studied. A modified version of a laminar flame-based PDF model is proposed, which best captures the distribution of the conditional variable among all PDFs under study. A priori tests are performed with the CSE and presumed PDF models. Reaction rates of turbulent premixed flames are closed and compared to the DNS data. The results are promising, suggesting that chemical closure can be achieved in premixed combustion using the CSE method.

No description available.

Thesis--Ph. D., University of Hong Kong, 1978. / Also availalbe in microfilm.

Thesis (Ph. D.)--Lehigh University, 2003. / Includes vita. Includes bibliographical references (leaves 120-126).