TY - GEN
T1 - Parametrically Forced Rotating and/or Stratified Confined Flows
UR - http://hdl.handle.net/2286/R.I.53664
A1 - Wu, Ke
A1 - Lopez, Juan
A1 - Welfert, Bruno
A1 - Tang, Wenbo
A1 - Platte, Rodrigo
A1 - Herrmann, Marcus
PB - Arizona State University
N1 - Doctoral Dissertation Mathematics 2019
N2 - {'value': 'The dynamics of a fluid flow inside 2D square and 3D cubic cavities\n\nunder various configurations were simulated and analyzed using a \n\nspectral code I developed.\n\nThis code was validated against known studies in the 3D lid-driven \n\ncavity. It was then used to explore the various dynamical behaviors \n\nclose to the onset of instability of the steady-state flow, and explain\n\nin the process the mechanism underlying an intermittent bursting\n\npreviously observed. A fairly complete bifurcation picture emerged, \n\nusing a combination of computational tools such as selective \n\nfrequency damping, edge-state tracking and subspace restriction.\n\nThe code was then used to investigate the flow in a 2D square cavity \n\nunder stable temperature stratification, an idealized version of a lake \n\nwith warmer water at the surface compared to the bottom. The governing \n\nequations are the Navier-Stokes equations under the Boussinesq approximation. \n\nSimulations were done over a wide range of parameters of the problem quantifying \n\nthe driving velocity at the top (e.g. wind) and the strength of the stratification. \n\nParticular attention was paid to the mechanisms associated with the onset of \n\ninstability of the base steady state, and the complex nontrivial dynamics\n\noccurring beyond onset, where the presence of multiple states leads to a\n\nrich spectrum of states, including homoclinic and heteroclinic chaos.\n\nA third configuration investigates the flow dynamics of a fluid in a rapidly\n\nrotating cube subjected to small amplitude modulations. The responses were \n\nquantified by the global helicity and energy measures, and various peak \n\nresponses associated to resonances with intrinsic eigenmodes of the cavity \n\nand/or internal retracing beams were clearly identified for the first time.\n\nA novel approach to compute the eigenmodes is also described, making accessible\n\na whole catalog of these with various properties and dynamics. When the small\n\namplitude modulation does not align with the rotation axis (precession) we show \n\nthat a new set of eigenmodes are primarily excited as the angular velocity \n\nincreases, while triadic resonances may occur once the nonlinear regime kicks in.', 'type': 'abstract'}
KW - Mathematics
KW - Fluid mechanics
KW - Mechanics
KW - Applied Mathematics
KW - Dynamical System
KW - Rotating Fluids
KW - Scientific Computing
KW - Spectral Methods
KW - Stratified Fluids
T2 - Parametrically Forced Rotating and/or Stratified Confined Flows
N2 - {'value': 'Dissertation/Thesis'}
ER -