Mesoscale processes in the atmosphere refer to the atmospheric processes that take place within a scale of a few to several hundred kilometres. Atmospheric phenomena like thunderstorms, inertia-gravity waves, jet streaks, fronts and many others have length scales within the range of Mesoscale dynamics. In the study of these processes, because the horizontal length scales are very large as compared to the vertical scales, often vertical acceleration is ignored. Such type of processes are termed as hydrostatic mesoscale processes. If the vertical accelerations are not ignored, then the mesoscale processes are known as nonhydrostatic mesoscale processes. This research work gives a study of the convectively forced nonhydrostatic mesoscale processes. Comparison is made between the results of both hydrostatic and nonhydrostatic mesoscale processes. To do so, a stably stratified, two-dimensional, Boussinesq, nonrotating, inviscid fluid experiencing a thermal forcing is considered under both hydrostatic and nonhydrostatic assumptions. While explicit analytic solutions are available for the hydrostatic cases under both a constant and a shear (linear in z) background profile, to understand the nonhydrostatic cases, a complete discritization of the governing linearized set of equations is carried out for the same background profiles. It has been found that the hydrostatic assumption does not depict the complete dynamics of the process. A horizontal propagation of a wave which is found to be present in the nonhydrostatic cases, is completely missing in the hydrostatic cases. Further, we show that for both, hydrostatic and nonhydrostatic, cases a sinusoidal shear background profile is nonlinearly unstable. However, because of mathematical difficulties, this work is done for a more specific convectively forced mesoscale processes. More specifically, a sinusoidal background profile is chosen and the external forcing is also treated in a more specific manner. Different from the study of flows forced by an external heating source, where the impacts of the forced wave modes with the atmosphere are studied, for various processes we need to allow the feedback of the atmosphere to the latent heating and a well known way to get such a feedback of the atmosphere is to assume that the diabatic heating is everywhere proportional to the vertical velocity. This kind of treatment of the external forcing is appropriate, for instance, for the processes like moist convection. Under such an assumption, the heating will respond to the motion of an air parcel. If the parcel rises upward, latent heat will be released and evaporative cooling will be observed if the parcel of air undergoes a downward motion. To prove the nonlinear instability for a sinusoidal background profile, first the well-posedness of the governing set of nonlinear equations is established. Then, a linear unstable mode is constructed using a method of continued fractions and then finally, following Grenier's idea, it is shown that the constructed linear unstable mode is also nonlinearly unstable. / Graduate / 0280 / 0346 / 0725 / 0373 / awais.qu@live.ca

The three-dimensional (3D) baroclinic response of Cayuga Lake to surface wind forcing was investigated using the fully nonhydrostatic MITgcm. The model was validated against observed temperature data using a hydrostatic 450 m (horizontal) grid and both qualitative and quantitative methods. The model correctly reproduces the basin-scale dynamics (e.g., seiche with horizontal mode-one period T1 = 80 h) with a basin-wide root-mean-square error of 1.9 C. Nonlinear internal surges were visualized to evolve due to (i) a wind-induced locally downwelled thermocline (wind duration Twind < T1/4), (ii) a basin-scale wind-induced upwelled thermocline (Twind > T1/4), (iii) internal hydraulic jumps (IHJs). Results from a 113 m grid and field observations were used to characterize the basin-scale internal wave field according to composite Froude number (G2), Wedderburn number (WN), and Lake number (LN). The typical Cayuga Lake response is a surge when ~ 1 < WN (LN) < ~ 2-12 and a surge with emergent nonlinear internal waves (NLIWs) when WN or LN < ~ 2, in agreement with published laboratory studies. An observed shock front was simulated to be an IHJ, occurring at mid-basin during strong winds when WN < 0.8. This is the first simulation of a mid-basin seiche-induced IHJ due to super critical conditions (G2 > 1) in a lake. The topographic-induced IHJs were also shown to form when the surges interact with a sill-contraction topographic feature. Both high-resolution hydrostatic and nonhydrostatic models were used to investigate the evolution, propagation and shoaling of NLIWs at medium lake-scale. A nonhydrostatic 22 m grid with lepticity λ ~ 1 ensures minimal numerical relative to physical dispersion, qualitatively reproducing observed dispersive NLIWs using ~ 2.3E+8 grid cells. Solitary waves evolve with almost unchanged wavelengths upon grid refinement from 40 m (λ ~ 2) to 22 m; suggesting model convergence to the correct solution. Corresponding hydrostatic grids were shown to produce a packet of narrower spurious solitary-like motions with different wavelengths, representing a balance between nonlinear steepening and numerical dispersion. Local gyre-like patterns and secondary transverse NLIW packets were visualized to result from wave-topography interaction, suggesting that NLIW propagation in long narrow lakes, where the bottom topography has irregularities is fundamentally 3D. / Thesis (Ph.D, Civil Engineering) -- Queen's University, 2012-12-14 12:45:21.727