In treating the motion of a fluid mathematically, it is convenient to make some simplifying assumptions. The assumptions which are made will be justifiable if they save long and laborious computations in practical problems, and if the predicted results agree closely enough with experimental results for practical use. In dealing with the flow of air about an airfoil, at subsonic speeds, the fluid will be considered as a homogeneous, incompressible, inviscid fluid.

This thesis documents the design and fabrication of an experimental facility that was built to produce a turbulent plane wall jet. The target flow was two-dimensional with a uniform profile of the mean streamwise velocity and a low turbulence level at the slot exit. The design requirements for a flow conditioning apparatus that could produce this flow were determined. The apparatus was then designed and constructed, and measurements of the fluid flow were obtained using particle image velocimetry (PIV). The first series of measurements was along the slot width, the second series was along the slot centerline and the third was at 46 slot heights off the centerline. The Reynolds number, based on the slot height and jet exit velocity, of the wall jet varied from 7594 to 8121. Data for the streamwise and transverse components of velocity and the three associated Reynolds stress components were analyzed and used to determine the characteristics of the wall jet.<p> This experimental facility was able to produce a profile of the mean streamwise velocity near the slot exit that was uniform over 71% of the slot height with a streamwise turbulence that was equal to 1.45% of the mean velocity. This initial velocity was maintained to 6 slot heights. The fully developed region for the centerline and the off-centerline measurements was determined to extend from 50 to 100 slot heights and 40 to 100 slot heights, respectively. This was based on self-similarity of the mean streamwise velocity profiles when scaled using the maximum streamwise velocity and the jet half-width. The off-centerline Reynolds stress profiles achieved a greater degree of collapse than did the centerline profiles.<p> The rate of spread of the wall jet along the centerline was 0.080 in the self-similar region from 50 to 100 slot heights, and the off-centerline growth rate was 0.077 in the self-similar region from 40 to 100 slot heights. The decay rate of the maximum streamwise velocity was -0.624 within the centerline self-similar region, and -0.562 within the off-centerline self-similar region. These results for the spread and decay of the wall jet compared well with recent similar studies.<p> The two-dimensionality was initially assessed by measuring the mean streamwise velocity at 1 slot height along the entire slot width. The two-dimensionality of this wall jet was further analyzed by comparing the centerline and off-centerline profiles of the mean streamwise velocity at 2/3, 4, 50, 80, and 100 slot heights, and by comparing the growth rates and decay rates. Although this facility was able to produce a wall jet that was initially two-dimensional, the two-dimensionality was compromised downstream of the slot, most likely due to the presence of return flow and spanwise spreading. Without further measurements, it is not yet clear exactly how the lack of complete two-dimensionality affects the flow characteristics noted above.

This thesis documents the design and fabrication of an experimental facility that was built to produce a turbulent plane wall jet. The target flow was two-dimensional with a uniform profile of the mean streamwise velocity and a low turbulence level at the slot exit. The design requirements for a flow conditioning apparatus that could produce this flow were determined. The apparatus was then designed and constructed, and measurements of the fluid flow were obtained using particle image velocimetry (PIV). The first series of measurements was along the slot width, the second series was along the slot centerline and the third was at 46 slot heights off the centerline. The Reynolds number, based on the slot height and jet exit velocity, of the wall jet varied from 7594 to 8121. Data for the streamwise and transverse components of velocity and the three associated Reynolds stress components were analyzed and used to determine the characteristics of the wall jet.<p> This experimental facility was able to produce a profile of the mean streamwise velocity near the slot exit that was uniform over 71% of the slot height with a streamwise turbulence that was equal to 1.45% of the mean velocity. This initial velocity was maintained to 6 slot heights. The fully developed region for the centerline and the off-centerline measurements was determined to extend from 50 to 100 slot heights and 40 to 100 slot heights, respectively. This was based on self-similarity of the mean streamwise velocity profiles when scaled using the maximum streamwise velocity and the jet half-width. The off-centerline Reynolds stress profiles achieved a greater degree of collapse than did the centerline profiles.<p> The rate of spread of the wall jet along the centerline was 0.080 in the self-similar region from 50 to 100 slot heights, and the off-centerline growth rate was 0.077 in the self-similar region from 40 to 100 slot heights. The decay rate of the maximum streamwise velocity was -0.624 within the centerline self-similar region, and -0.562 within the off-centerline self-similar region. These results for the spread and decay of the wall jet compared well with recent similar studies.<p> The two-dimensionality was initially assessed by measuring the mean streamwise velocity at 1 slot height along the entire slot width. The two-dimensionality of this wall jet was further analyzed by comparing the centerline and off-centerline profiles of the mean streamwise velocity at 2/3, 4, 50, 80, and 100 slot heights, and by comparing the growth rates and decay rates. Although this facility was able to produce a wall jet that was initially two-dimensional, the two-dimensionality was compromised downstream of the slot, most likely due to the presence of return flow and spanwise spreading. Without further measurements, it is not yet clear exactly how the lack of complete two-dimensionality affects the flow characteristics noted above.

The weather dynamics are significantly determined by the motion of the atmosphere and the ocean. This motion is often turbulent, characterized by fluctuations of the flow velocity over wide spatial and temporal scales. This fact, besides limited observability and inaccurate models, impedes the predictability of quantities such as the velocity of winds, which are relevant for the everyday life. One is always interested in improving such predictions - by employing better models or obtaining more information about the system. The Crooks fluctuation theorem is a relation from nonequilibrium thermodynamics, which has its typical applications in nanoscale systems. It quantifies the distribution of imposed work in a process, where the system is pushed out of thermal equilibrium. This distribution is broadened due to the fluctuations of the microscopic degrees of freedom in the system. The fluctuations of the velocity field in turbulent flow suggest the derivation of an analogy of Crooks' theorem for this macroscopic system. The knowledge about the validity of such a relation is additional information, which one in reverse could use to improve predictions about the system. In this thesis both issues are addressed: the derivation of the theorem, and the improvement of predictions. We illustrate the application of Crooks' theorem to hydrodynamic flow within a model of a two-dimensional inviscid and incompressible fluid field, when pushed out of dynamical equilibrium. The flow on a rectangular domain is approximated by the two-dimensional vorticity equation with spectral truncation. In this setting, the equilibrium statistics of the flow can be described through a canonical ensemble with two conserved quantities, kinetic energy and enstrophy. To perturb the system out of equilibrium, we change the shape of the domain according to a protocol, which changes the kinetic energy but leaves the enstrophy constant. This is interpreted as doing work to the system. Evolving along a forward and its corresponding backward process, we find that the distributions of the work performed in these processes satisfy the Crooks relation with parameters derived from the canonical ensembles. We address the issue of prediction in this thesis in a concrete setting: There are examples where the distributions of a variable in the forward and the backward process collapse into one, hence Crooks' theorem relates the distribution of one variable with itself. For a finite data set drawn from such a distribution, we are interested in an estimate of this variable to exceed a certain threshold. We demonstrate that, using the knowledge about Crooks' relation, forecast schemes can be proposed which improve compared to a pure frequency estimate on the data set. The findings are illustrated in three examples, studies of parameters such as exceedance threshold and data set size are presented.

Thesis(M.S.)--Auburn University, 2006. / Abstract. Vita. Includes bibliographic references (p.100-101).

Yes / The flow in the main channel of a meandering compound channel does not occur in the ridge direction because of the effect of the upstream floodplain flows. This study proposes a model for estimating the flow direction in the depth-averaged two-dimensional domain (depth-averaged flow angles) between the entrance and the apex sections. Detailed velocity measurements were performed in the region between the meander entrance section and apex section in a large-scale meandering compound channel. The vertical size of the secondary current cell is highly related to the depth-averaged flow angle; thus, the means of the local flow angles above the secondary current cell and within the cell are separately discussed. The experimental measurements indicate that the mean local flow angle above the cell is equal to the section angle, whereas the mean local flow angle within the cell is equal to zero. The proposed model is validated using published data from five sources. Good agreement is obtained between the predictions and measurements, indicating that the proposed model can accurately estimate the depth-averaged flow direction in the meandering compound channels. Finally, the limitations and application ranges of the model are discussed. / National Key Research and Development Program of China (No. 2016YFC0402302), the National Natural Science Foundation of China (Nos. 51539007 and 51609160)

The weather dynamics are significantly determined by the motion of the atmosphere and the ocean. This motion is often turbulent, characterized by fluctuations of the flow velocity over wide spatial and temporal scales. This fact, besides limited observability and inaccurate models, impedes the predictability of quantities such as the velocity of winds, which are relevant for the everyday life. One is always interested in improving such predictions - by employing better models or obtaining more information about the system. The Crooks fluctuation theorem is a relation from nonequilibrium thermodynamics, which has its typical applications in nanoscale systems. It quantifies the distribution of imposed work in a process, where the system is pushed out of thermal equilibrium. This distribution is broadened due to the fluctuations of the microscopic degrees of freedom in the system. The fluctuations of the velocity field in turbulent flow suggest the derivation of an analogy of Crooks' theorem for this macroscopic system. The knowledge about the validity of such a relation is additional information, which one in reverse could use to improve predictions about the system. In this thesis both issues are addressed: the derivation of the theorem, and the improvement of predictions. We illustrate the application of Crooks' theorem to hydrodynamic flow within a model of a two-dimensional inviscid and incompressible fluid field, when pushed out of dynamical equilibrium. The flow on a rectangular domain is approximated by the two-dimensional vorticity equation with spectral truncation. In this setting, the equilibrium statistics of the flow can be described through a canonical ensemble with two conserved quantities, kinetic energy and enstrophy. To perturb the system out of equilibrium, we change the shape of the domain according to a protocol, which changes the kinetic energy but leaves the enstrophy constant. This is interpreted as doing work to the system. Evolving along a forward and its corresponding backward process, we find that the distributions of the work performed in these processes satisfy the Crooks relation with parameters derived from the canonical ensembles. We address the issue of prediction in this thesis in a concrete setting: There are examples where the distributions of a variable in the forward and the backward process collapse into one, hence Crooks' theorem relates the distribution of one variable with itself. For a finite data set drawn from such a distribution, we are interested in an estimate of this variable to exceed a certain threshold. We demonstrate that, using the knowledge about Crooks' relation, forecast schemes can be proposed which improve compared to a pure frequency estimate on the data set. The findings are illustrated in three examples, studies of parameters such as exceedance threshold and data set size are presented.

In the present thesis we study the compressible Navier-Stokes-Fourier sys- tem. This is a system of partial differential equations describing the evolutionary problem for an adiabatic flow of a heat conducting compressible viscous fluid in a bounded domain. Here we consider the problem in two dimensions with zero Dirichlet boundary conditions for velocity. The cold pressure term in the pressure law for the momentum equation is here considered in the form pC(ϱ) ∼ ϱ logα (1+ϱ) for some α > 0, for which we need to work on the scale of Orlicz spaces in order to obtain useful estimates and in those space we formulate the problem weakly and also establish the weak compactness of the solution. The main result of this thesis is Theorem 6.1 where we show the existence of a weak solution with no assumptions on the size of the data and on arbitrary large time intervals. 1

Cellular automata constitues original computational methods, that found its application in many disciplines. The special class of cellular automata, so called lattice gas automata were succesfull in dealing with many challenges in hydrodynamic simulations, and they bootstrap one of the most perspective CFD methods, the Lattice Boltzmann models. In the theoretical part, we follow the evolution of the lattice gas automata, explore the theory behind them, and from their microdynamics, we derive the macroscopic equations. In the practical part, we implemented two distincet types of LGCA, the pair-interaction automata and FCHC. We applied them on the flow around obstacles of various shapes. The scientifically most relevant part concerns statistical properties of the turbulent flow simmulated by LGCA, but requires further research to conclude it. Powered by TCPDF (www.tcpdf.org)

Cellular automata constitutes a unique approach to the modeling of complex systems. The major phase of their development in continuum mechanics came in the late 80s, but the closer inspection of their macroscopic limit revealed that it does not accurately correspond to hydrodynamic equations. Besides the Lattice-Boltzmann model, various other approaches to improve LGCA have emerged. The main focus of our research is on the Pair-interaction cellular automaton. In this thesis, we propose the non-deterministic variant of this automaton, and we compare it with its predecessor on the simulations of the "exploding cube", Taylor- Green vortex and fully developed turbulence. The results for the non-deterministic automaton seem quiet reasonable, but derivation of the hydrodynamic equations is necessary to conclude in what extent it solves the problem with anisotropic viscosity.