Global Stability Analysis Of Opposed-jet And Thermal Convection Systems

In this dissertation,instabilities and nonlinear evolutions of three canonical flows are studied by global stability analysis and direct numerical simulation,including the opposed-jet flow,Rayleigh-Benard(RB)convection and thermal convection in a rotat-ing spherical shell.1.The bifurcation processes of two-dimensional opposed-jet flows with symmetric and slightly asymmetric inlet boundary conditions are investigated by stability analysis and numerical bifurcation analysis.When the inlet boundary conditions are symmetric,multiple symmetry-breaking bifurcations are observed and new flow patterns are identified.In addition,the case that inlet boundary conditions are slightly asymmetric is investigated.Bifurcation processes are found to be ex-tremely sensitive to the small symmetry-breaking imperfection of boundary con-ditions and much different from those in the symmetric case.Low-dimensional model equations are constructed by symmetry consideration and applied to ex-plain qualitatively the nonlinear evolutions of opposed-jet flow and the influences of slight asymmetry of boundary conditions.2.For two-dimensional cavities of finite aspect ratios,the influences of non-Oberbeck-Boussinesq(NOB)effects on flow instabilities and bifurcation characteristics of RB convection are examined.The intensity of NOB effects is measured by the dimensionless temperature differential ?.Linear stability analysis of the thermal conduction state is performed.An ?2 scaling of the leading-order corrections of critical Rayleigh number and disturbance growth rate due to NOB effects is iden-tified,which is a consequence of an intrinsic symmetry of the system.The influ-ences of weak NOB effects on critical parameters and modes are further studied by perturbation expansion of linear stability equations with respect to ?.NOB effects are found to enhance(weaken)flow stability in large(narrow)cavities.Detailed contributions of compressibility,viscosity and buoyancy actions on dis-turbance kinetic energy growth are identified by energy analysis.Viscosity action is found to be more sensitive to NOB effects.Through weakly nonlinear analysis and direct numerical simulation,the NOB influences on bifurcation character-istics of convection onset are studied for both codimension-one and-two cases.Rich bifurcation regimes are observed.3.Based on fully compressible Navier-Stokes equations,the convection onset of compressible fluids in a rapidly rotating spherical shell is studied by linear sta-bility analysis.By investigating the stability of the conduction state with respect to disturbance of given azimuthal wave number,the instability process is found to be sensitive to the Prandtl number and density stratification strength.For large Prandtl number and weak density stratification,the quasi-geostrophic Taylor columnar roll becomes unstable first,while for small Prandtl number and strong density stratification,a new compressible quasi-geostrophic mode becomes un-stable first.The inertial oscillation mode can also occur first for small Prandtl number and density stratification of a certain intensity.Although the critical Rayleigh numbers of the compressible quasi-geostrophic mode and Taylor colum-nar roll are different by several orders of magnitude,they satisfy similar scaling law with the Taylor number.The critical Rayleigh number for convection onset is found to be always positive,in contrast with the results of the anelastic model that convection can onset at negative Rayleigh number.By measuring the relative magnitude of time derivative of density perturbation in the continuity equation,it is found that the anelastic approximation fails when the Rayleigh number is small and density stratification is strong.