Numerical simulations of incompressible, two-dimensional, monochromatically and bichromatically forced laminar free shear layers are performed on the basis of a vorticity-velocity formulation of the complete Navier-Stokes equations employing central finite differences. Spatially periodic shear layers developing in time (temporal model) are compared with shear layers developing in the stream-wise direction (spatial model). The regimes of linear growth and saturation of the fundamental are quantitatively scrutinized, the saturation of the subharmonic and vortex merging are investigated, and the effects of a forcing phase-shift between fundamental and subharmonic. For the spatial model the appearance of an unforced subharmonic was also examined. It was found that contrary to temporal shear layers a significant control of vortex merging by means of a forcing phase-shift and vortex shredding are not possible in spatial shear layers due to strong dispersion.

A two-scale approach for the turbulent mixing of momentum in an unstable stratified boundary layer is proposed in an attempt to eliminate existing inconsistencies between parameterized mixing of heat and momentum. The parameterization of the large eddy stress is suitable for simple boundary layer models where computational efficiency is important. We test the proposed formulation in a simple boundary layer model and compare predicted momentum profiles with Lidar mean momentum profiles from FIFE 1989. We examine the sensitivity of the proposed mixing scheme to baroclinicity. While the proposed two-scale approach is able to better predict observed conditions of well mixed momentum profiles, the complexity of momentum transport in baroclinic conditions is not well approximated. / Graduation date: 1994

The influence of irregular terrain on the evolution of the daytime planetary boundary layer (PBL) and meso-β scale dry circulations is studied using two three-dimensional hydrostatic σ-coordinate models with different approaches for the PBL parameterizations; the 4-layer model uses the mixed-layer (bulk-layer) approach, while the 7-layer model adopts the eddy-diffusivity (multi-layer) approach. Numerical experiments are carried out under the conditions of a dry, sunny summer day with moderate prevailing westerly winds blowing over gently sloping idealized hills in a domain of 150 km on a side. The results from the two models are compared and their performances are evaluated. The behaviors of the mean PBL depth and inversion strength are analytically described using a simple one-point mixed-layer model. Counterclockwise rotation of the mean PBL winds with time observed in both model results can be explained only when the non-zero momentum flux at the PBL top is taken into account. However, stresses associated with entrainment at the PBL top are not sufficient to pull the cold air out of the valleys so as to result in breakup of the early morning stable layer, as is suggested in a previous study. The regions of weak winds that persist in the morning PBL are attributed largely to the baroclinic effect of horizontal variations of potential temperature θ in the PBL, while the effect of surface drag is quite small in these areas. Significant differences in the flow patterns near the surface in two results suggest the importance of the local pressure gradient force associated with terrain irregularities. The effect of horizontal θ advection is also significant in helping reduce the PBL θ anomalies and promote breakup of the stable layer. The well-mixed assumption generally applies quite well to the development of the θ profiles, while for momentum it seems valid only during the peak of convective mixing and the eddy-diffusivity approach is probably preferable for a better description of the low-level flows. The fields of the PBL top height obtained using different procedures in the two models are found to correspond fairly well to each other. Mass-flux convergence associated with terrain irregularities and resulting changes in the wind fields are shown to play a key role in the midday PBL height patterns. The development of the PBL structure as revealed by the θ cross sections obtained from either model corresponds favorably to that indicated by idealized cross sections previously constructed from observed data. The formation of a region of mass-flux convergence and accompanying updrafts near the surface on the leeward side of a mountain, processes which are likely to be important in terrain-induced cloud initiations, seem to be simulated. / Graduation date: 1985

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No description available.

Simple models of transpiration, e.g., the Penman-Monteith equation, treat atmospheric conditions as driving variables. In fact, transpiration modifies temperature and humidity throughout the convective boundary layer, creating feedbacks that stabilize the water use of vegetation. This thesis concentrates on the new empirical relationships proposed by Monteith (1995), for developing simple models of feedback, and then applies these relationships to data from the Oregon Cascades. Monteith showed that there is strong laboratory evidence to support a linear relationship between leaf transpiration rate and leaf conductance. If this relationship holds for vegetation in the field, simple models to explain the diurnal variation of canopy conductance can be developed. When this model was applied to data from a Douglas fir forest, canopy conductance changed in response to transpiration rate, rather than to saturation deficit, as has been previously assumed. Monteith also reanalyzed data from McNaughton and Spriggs (1989) which explored the dependence of the Priestley-Taylor coefficient alpha on surface parameters. He showed that there is a linear relationship between alpha and surface conductance. By combining this "demand function" with the physiological "supply function" described earlier, the PMPT model is developed in which evaporation rate depends on physical feedbacks in the convective boundary layer and physiological feedbacks within plants. The thesis will focus on the results of the research done using this model. The PMPT model will then be compared with other simple models of transpiration in order to determine its applicability. / Graduation date: 1997

Three new computational procedures are presented for the simulation of incompressible wall-bounded turbulent flows. First, an integral method based on the strip integral method has been developed for the solution of three-dimensional turbulent boundary-layer flows. The integral equations written in a general form using non-orthogonal streamline coordinates include the turbulent shear stress at the upper limit of an inner strip inside the boundary-layer. The shear stress components are modeled using the Boussinesq assumption, and the eddy viscosity is defined explicitly as in differential methods. The turbulence modeling is not hidden in opaque empirical correlations as in conventional integral methods. A practical four-parameter velocity profile has been established based on the Johnston Law of the Wall using a triangular model for the crosswise velocity. Two strips are used to solve for the four unknowns: skin friction coefficient, wall crossflow angle, boundary-layer thickness, and location of maximum crosswise velocity. The location of maximum crosswise velocity proves to be a natural and adequate parameter in the formulation, but it is numerically sensitive and has a strong influence on the wall crossflow angle. Good results were obtained when compared to predictions of other integral or differential methods. Secondly, two computational procedures solving the Reynolds Averaged Navier-Stokes equations for 20 and 3D flows respectively have also been developed using a new treatment of the near-wall region. The flow is solved down to the wall with a slip velocity based on Clauser's idea of a pseudolaminar velocity profile. The present idea is different from the wall-function methods and does not require a multi-layer eddy viscosity model. The solution of the equations of motion is obtained by the Finite Element Method using the wall shear stress as a boundary condition along solid surfaces, and using the Clauser outer region model for the eddy viscosity. The wall shear stress distribution is updated by solving integral equations obtained from the enforcement of conservation of mass and momentum over an inner strip in the near-wall region. The Navier-Stokes solution provides the necessary information to the inner strip integral formulation in order to evaluate the skin friction coefficient for 2D flows, or the skin friction coefficient and the wall crossflow angle for 3D flows. The procedures converge to the numerically "exact" solution in a few iterations depending on the accuracy of the initial guess for the wall shear stress. A small number of nodes is required in the boundary-layer to represent adequately the physics of the flow, which proves especially useful for 3D calculations. Excellent results were obtained for the 2D simulations with a simple eddy viscosity model. 3D calculations gave good results for the turbulent boundary-layer flows considered here. The present methods were validated using well-known experiments chosen for the STANFORD conferences and EUROVISC workshop. The 2D numerical predictions are compared with the experimental measurements obtained by Wieghardt-Tillmann, Samuel-Joubert, and Schubauer-Klebanoff. For the 3D analyses, the numerical predictions obtained by the strip-integral method and the Finite Element Navier-Stokes Integral Equation procedure are validated using the Van den Berg-Elsenaar and Müller-Krause experiments. / Ph. D.

published_or_final_version / Mechanical Engineering / Doctoral / Doctor of Philosophy

Two-dimensional flow in a viscous incompressible fluid, generated by a circular cylinder executing large-amplitude rectilinear oscillations in a plane perpendicular to its axis and parallel to one of the sides of a surrounding rectangular box filled with incompressible fluid is studied numerically. The circular cylinder moves back and forth through its own wake, resulting in an extremely complex flow field. For ease of implementing boundary conditions, a numerically generated body-fitted coordinate system is used. At each time step, the physical domain is doubly-connected, and a cut is introduced in order to map it into a rectangular computational domain. A body-fitted grid is generated by solving a pair of Laplace equations with a simple grid spacing control method which preserves the essential one-to-one property of the mapping. A finite difference/pseudo-spectral technique is used in this work to solve the Navier-Stokes equations in velocity-vorticity formulation. The time integration of the vorticity transport equation is handled by a fully explicit three-level Adams-Bashforth method. The two Poisson equations for the velocity components are 11-banded and block-diagonal in form, and are solved by a preconditioned biconjugate gradient routine. An integral constraint on the vorticity field is used to determine the boundary vorticity that simultaneously satisfies the no-slip and no-penetration conditions. The surface vorticity is uniquely determined by a general solution procedure developed in this study which is valid for flows over multiple solid bodies. With this approach, the physical process of vorticity generation on the solid boundary is properly simulated and the principle of vorticity conservation is satisfied. Results for various test cases and the complex vortex shedding phenomena generated by an oscillating circular cylinder are presented and discussed.

Boundary-layer flows near leading edges of generally curved obstacles have been studied for a long time. Apart from having many practical applications, the theory and approaches prevailing in this area stimulate development of a variety of computational tools and form a ground for testing them. The specific aim of this work is to study two-dimensional laminar boundary layer flows near the leading edges of airfoils and other elongated bodies, and to explore geometries for which boundary layer separation can be avoided. This class of problems is relevant to optimal design of wings, aircraft and projectile noses, laminar flow control methods and adaptive wing technology. One of the findings of this work suggests that local modifications to parabolic wing noses can yield up to 11% increase in the unseparated angle of attack. Another result obtained here is the set of shortest possible generalised elliptic noses of long symmetric bodies which allow unseparated flow. Methods adopted in this work are based on the combined use of numerically solved Prandtl equations written in Gortler variables, and inviscid solutions obtained semi-analytically by the conformal mapping method. The resulting technique being reliable, fast and computationally inexpensive, can complement or test the results obtained using a comprehensive CFD approach. / Thesis (Ph.D.)--School of Mathematical Sciences, 2002.