Mechanisms For Transition To Turbulence In The Bottom Boundary Layer Under A Surface Solitary Wave
Transition mechanisms to turbulence in the unsteady bottom boundary layer (BBL) driven by a soliton-like pressure gradient in an oscillating water tunnel (an approximation for the BBL under surface solitary waves) are investigated in a hydrodynamic instability context. This investigation aims to establish connections across theoretical and numerical analysis and the experimental findings of Sumer et al., 2010 ( J. Fluid Mech. vol. 646, 2010,p. 207). Transition to turbulence in the surface solitary wave-driven BBL can take place according to two different scenarios. The primary scenario is associated with the classical transition resulting from the breakdown of the exponentially growing 2-D Tollmien-Schlichting waves. The alternative scenario consists of a characteristically different path to transition resulting from the formation of localized turbulent spots. The formation of these turbulent spots, which are the manifestation of an algebraic growth of infinite streamwise disturbance, i.e., zero streamwise wave number, leads to a bypass transition to turbulence. In regards to the first scenario, a detailed map for the temporal instability is established. Both linear stability analysis and fully nonlinear two- and threedimensional simulations using high-order numerical methods have been carried out. The process of delineation of the stability regions as a function of boundary layer thickness-based Reynolds number of the temporally evolving base flow, Re[delta] consists of two parts. The first part aims to assess the lower limit of the Re[delta] range within which the standard, quasi- steady, linear stability analysis is applicable as it considers individual profiles sampled during the base flow transient evolution. Below this limit, transient linear stability analysis serves as a more accurate predictor of the stability properties of the base flow. In the second step, above the Re[delta] limit where the BBL is determined to be linearly unstable, the base flow is further classified as unconditionally stable, conditionally unstable or unconditionally unstable in terms of its sensitivity to the amplitude and the insertion time of perturbations. Two distinct modes of instability exist in this case: post- and pre- flow-reversal modes. At a moderate value of Re[delta] , both modes are first observed in the wave deceleration phase. The post flow reversal mode dominates for relatively low Re and it is the one observed in Sumer et al. (J. Fluid Mech. vol. 646, 2010,p. 207). For Re above a threshold value of the base flow in the unconditionally unstable regime, the pre-flow reversal mode, which has a larger wavelength than its post-reversal counterpart, becomes dominant. In the same regime, the threshold Re[delta] value above which instability is observed in the acceleration phase of the wave is also identified. In this case, the base flow velocity profiles lack any inflection point, suggesting that the origin of such an instability is viscous. Finally, the lower Re[delta] limit above which quasi-steady linear stability analysis is valid may be independently obtained by adapting to the surface solitary wave BBL framework an instability criterion which links the average growth rate and wave event timescale, as previously proposed in studies of the instability of the interior of progressive and solitary internal waves. This part of the study is a recap to what have been published by Sadek et al. (2015). For the second transition scenario, the linear stability analysis is reformulated in the non- modal framework where the three-dimensional nature of the base flow is considered. By doing such a reformulation, an optimum initial disturbance is identified. Such a disturbance can lead to very large short-term energy growth that can not be captured by the classical modal stability analysis. The optimum initial disturbance is first calculated for different velocity profiles following a quasi-steady approach where the individual profiles are assumed steady within the wave event. Additionally, the resulting short-term maximum energy growth is determined as a function of the streamwise ([alpha]) and spanwise ([beta]) wave number. It is shown that the maximum growth is associated with the disturbance with no streamwise dependence ([alpha] = 0). The formation of streaks is simulated when the three-dimensional DNS is perturbed with the pre-determined optimum initial disturbance. In order to trigger the transition to turbulence, a secondary instability is required. The characteristics of this secondary perturbation is chosen in accordance with the flat plate boundary layer flow. This approach can successfully simulate the bypass transition. Sample result from a representative Re[delta] case are presented in the thesis hereafter.
Computational Fluid Dynamics; Hydrodynamic Instability; Transition to Turbulence
Desjardins,Olivier; Liu,Philip Li-Fan
Civil and Environmental Engineering
Ph. D., Civil and Environmental Engineering
Doctor of Philosophy
dissertation or thesis