The numerical modeling of motions in the atmosphere's planetary boundary layer (PBL) is a challenging task. In general, the boundary layer interacts with both the overlying atmosphere and the underlying land or water surface in a complex manner. Random turbulence is also present in the PBL which precludes exact prediction by numerical models. Nonetheless, expensive three-dimensional numerical models have been developed which, with several parameterizations and assumptions, can give a good idea of the PBL structure in many situations. However, on certain occasions, there is strong mixing evident in the PBL which may enable one to describe the structure of the boundary layer in a much-simplified theoretical model. By eliminating the vertical dimension from consideration, this two-dimensional mixed-layer model can be applied to mesoscale phenomena (horizontal length scale < 100 km) at greatly-reduced costs. The equations for motion and mixed-layer height are derived for such a situation and methods appropriate to the numerical modeling of the atmospheric mixed layer are discussed. Using an energy-conserving finite-difference analog of the model equations, the model is integrated in time to simulate the motions which were associated with the atmospheric vortex street observed near Cheju-do, South Korea on 17 February 1975. Experiments were carried out which investigated the effects of lateral diffusion, horizontal resolution, and mixed-layer depth. It is concluded that, given proper representation of prognostic variables on a staggered finite-difference grid, only small, realistic values of eddy diffusivity need be utilized. It also appears evident from the numerical experiments and atmospheric observations that the vortex street will form only when the obstacle which triggers its formation protrudes above the mixed layer. Although the wind fields in the simulations sometimes lack clear, fully rotational cells well downstream of the island, the characteristic sinusoidal pattern observed in laboratory experiments and cloud photographs is explicitly resolved by the model. The simulated vortex street also compares favorably with the observed in that the dimensionless governing parameters of the simulated vortex street (the Reynolds number, Strouhal number, Lin's parameter, the spacing ratio, and the speed ratio) closely match the observed values. / Graduation date: 1981

High resolution data of moisture, temperature and wind velocity collected by aircraft during the 1975 Air Mass Transformation Experiment (ANTEX '75) provide information for detailed investigations of the phenomena occurring at the top of a cloud-topped mixed layer. Joint frequency diagrams of humidity and temperature reveal that for parts of the record the coldest temperatures occur in air near saturation while drier air or air with substantial liquid water is warmer. This suggests the possible occurrence of cloud-top entrainment instability (Deardorff, 1980). Using humidity as an indicator, the flight record is systematically searched for penetrative mixed layer elements and pockets of dry air penetrating into cloudy air (wisps). The separate phenomena are then composited to produce an "average" wisp and penetrating element. The composites show evidence of net cooling due to evaporation downstream from the penetrating element and upstream from the wisps. Sinking motion is associated with the cold temperatures. These results suggest the interaction of shear, penetrating elements and wisps, and the existence of cloud-top entrainment instability. / Graduation date: 1981

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

On-going efforts to reduce aircraft drag through transition delay focus on understanding the process of boundary-layer transition from a physics-based perspective. For swept-wings subject to transition dominated by a stationary crossflow instability, one of the remaining challenges is understanding how freestream disturbances and surface features such as surface roughness create the initial amplitudes for unstable waves. These waves grow, modify the mean flow and create conditions for secondary instabilities to occur, which in turn ultimately lead to transition. Computational methods that model the primary and secondary instability growth can accurately model disturbance evolution as long as appropriate initial conditions are supplied. Additionally, transition delay using discrete roughness arrays that exploit known sensitivities to surface roughness has been demonstrated in flight and wind tunnel testing; however, inconsistencies in performance from the two test platforms indicate further testing is required. This study uses detailed hotwire boundary-layer velocity scans to quantify the relationship between roughness height and initial disturbance amplitude. Naphthalene flow visualization provides insight into how transition changes as a result of roughness height and spacing. Micron-sized, circular roughness elements were applied near the leading edge of the ASU(67)-0315 model installed at an angle of attack of -2.9 degrees in the Klebanoff-Saric Wind Tunnel. Extensive flow quality measurements show turbulence intensities less than 0.02% over the speed range of interest. A survey of multiple roughness heights for the most unstable and control wavelengths and Reynolds numbers of 2.4 x 10⁶ 2.8 x 10⁶ and 3.2 x 10⁶ was completed for chord locations of 10%, 15% and 20%. When care was taken to measure in the region of linear stability, it was found that the disturbance amplitude varies almost linearly with roughness height. Naphthalene flow visualization indicates that moderate changes in already-low freestream turbulence levels can have a significant impact on transition behavior.

This dissertation analyzes the effect of periodic roughness elements on the stability of a flat plate boundary layer. Receptivity data is extracted from direct numerical simulations and experimental data and the results are compared to theoretical predictions. This analysis shows that flow in the immediate vicinity of roughness elements is non-linear; however, the evolution of roughness-induced perturbations is a linear phenomena. New techniques are developed to calculate receptivity information for cases where direct numerical simulations are not yet possible. Additionally, the stability behavior of the roughness wake is analyzed. New instability modes are found, and the effect of boundary layer complexity, perturbation amplitude and other factors are examined. It is shown that the wake is much less stable than optimal perturbation theory predicts, and highlights the importance of receptivity studies. The implication of these results on transition-to-turbulence is discussed, and future work is proposed. T

Thesis (Ph. D.)--Lehigh University, 2000. / Includes vita. Includes bibliographical references (leaves 179-183).

Thesis (Ph. D.)--Lehigh University, 2000. / Includes vita. Includes bibliographical references (leaves 186-192).

Thesis (Ph. D.)--University of Hawaii at Manoa, 2004. / Includes bibliographical references (leaves 193-207).

Thesis (M.S.)--Naval Postgraduate School, 2002. / Thesis advisor(s): Kenneth L. Davidson, Peter Guest. Includes bibliographical references (p. 45). Also available online.

Thesis (Doctor of Philosophy in Meteorology)--Naval Postgraduate School, June 2004. / Thesis advisor(s): Qing Wang. Includes bibliographical references (p. 113-119). Also available online.