Parametrically Forced Rotating and/or Stratified Confined Flows

• Other Authors: Wu, Ke (Author)
• Format: Doctoral Thesis
• Language: English
• Published: 2019
• Subjects: Mathematics; Fluid mechanics; Mechanics; Applied Mathematics; Dynamical System; Rotating Fluids; Scientific Computing; Spectral Methods; Stratified Fluids
• Online Access: http://hdl.handle.net/2286/R.I.53664

abstract: The dynamics of a fluid flow inside 2D square and 3D cubic cavities under various configurations were simulated and analyzed using a spectral code I developed. This code was validated against known studies in the 3D lid-driven cavity. It was then used to explore the various dynamical behaviors close to the onset of instability of the steady-state flow, and explain in the process the mechanism underlying an intermittent bursting previously observed. A fairly complete bifurcation picture emerged, using a combination of computational tools such as selective frequency damping, edge-state tracking and subspace restriction. The code was then used to investigate the flow in a 2D square cavity under stable temperature stratification, an idealized version of a lake with warmer water at the surface compared to the bottom. The governing equations are the Navier-Stokes equations under the Boussinesq approximation. Simulations were done over a wide range of parameters of the problem quantifying the driving velocity at the top (e.g. wind) and the strength of the stratification. Particular attention was paid to the mechanisms associated with the onset of instability of the base steady state, and the complex nontrivial dynamics occurring beyond onset, where the presence of multiple states leads to a rich spectrum of states, including homoclinic and heteroclinic chaos. A third configuration investigates the flow dynamics of a fluid in a rapidly rotating cube subjected to small amplitude modulations. The responses were quantified by the global helicity and energy measures, and various peak responses associated to resonances with intrinsic eigenmodes of the cavity and/or internal retracing beams were clearly identified for the first time. A novel approach to compute the eigenmodes is also described, making accessible a whole catalog of these with various properties and dynamics. When the small amplitude modulation does not align with the rotation axis (precession) we show that a new set of eigenmodes are primarily excited as the angular velocity increases, while triadic resonances may occur once the nonlinear regime kicks in. === Dissertation/Thesis === Doctoral Dissertation Mathematics 2019