THE STRUCTURE OF VELOCITY & DENSITY INTERFACES IN WEAKLY TURBULENT STRATIFIED SHEAR FLOW

By ABIGAIL SMITH

CONTENTS MATHEMATICAL BACKGROUND DYNAMICAL SYSTEMS VECTOR ?ELDS AND DYNAMICAL SYSTEMS CRITICAL POINTS IN PHASE SPACE HIGHER-ORDER AUTONOMOUS SYSTEMS DIRAC DELTA FUNCTION SPECIAL FUNCTIONS GREEN’S FUNCTION BOUNDARY AND INITIAL VALUE PROBLEMS ASYMPTOTIC BEHAVIOR AND STABILITY ASYMPTOTIC EXPANSIONS ASYMPTOTIC BEHAVIOR OF AUTONOMOUS SYSTEMS STABILITY OF AUTONOMOUS SYSTEMS MORE ON STABILITY BIFURCATIONS INSTABILITY AND BIFURCATIONS SADDLE-NODE BIFURCATION TRANSCRITICAL AND PITCHFORK BIFURCATIONS HOPF BIFURCATION SADDLE-NODE BIFURCATION OF A PERIODIC ORBIT GLOBAL BIFURCATION ATTRACTORS CHAOTIC MOTION AND SYMBOLIC DYNAMICS HOMOCLINIC TANGLES AND SMALE’S HORSESHOE MAP POINCAR´E RETURN MAP LYAPUNOV’S EXPONENTS AND ENTROPY ATTRACTING SETS AND ATTRACTORS FRACTALS LOCAL STRUCTURE OF FRACTALS OPERATIONS WITH FRACTALS FRACTAL ATTRACTORS IN DYNAMICAL SYSTEMS PERTURBATIONS REGULAR PERTURBATION THEORY SINGULAR PERTURBATION THEORY ELEMENTS OF TENSOR ANALYSIS TRANSFORMATIONS OF COORDINATE SYSTEMS COVARIANT AND CONTRAVARIANT DERIVATIVES CHRISTO?EL SYMBOLS AND CURVATURE TENSOR INTEGRAL FORMULAS NAVIER–STOKES EQUATIONS FOR NONEQUILIBRIUM GAS MIXTURE CONTINUITY, MOMENTUM AND ENERGY EQUATIONS CLOSING RELATIONS AND TRANSPORT COE?CIENTS BOUNDARY CONDITIONS DEDUCING NAVIER–STOKES EQUATION EXISTENCE AND UNIQUENESS OF SOLUTIONS OF THE NAVIER–STOKES EQUATION RELATIVISTIC NAVIER–STOKES EQUATION EXERCISES BIBLIOGRAPHY MODELS FOR HYDRODYNAMIC INSTABILITIES STABILITY CONCEPTS INVISCID AND HIGH-REYNOLDS-NUMBER ?OW BASIC DE?NITIONS RAYLEIGH–TAYLOR INSTABILITY POTENTIAL ?OW PLANE BOUNDARIES SPHERICAL BOUNDARIES NONLINEAR PERTURBATION THEORY INHOMOGENEOUS ?UIDS VISCOUS ?UIDS KELVIN–HELMHOLTZ INSTABILITY INSTABILITY OF ANNULAR INCOMPRESSIBLE JET ROTATING JETS SUPERSONIC VISCOUS JET SUPERSONIC VISCOUS JET WITH GAUSSIAN SOUND VELOCITY DISTRIBUTION RELATIVISTIC JET MODELS FOR TURBULENCE SYMMETRIES AND CONSERVATION LAWS EULER AND NAVIER–STOKES EQUATIONS SYMMETRIES CONSERVATION LAWS ANOMALOUS SCALING EXPONENTS MULTIFRACTAL MODELS RANDOM VARIABLES AND CORRELATION FUNCTIONS RICHARDSON–KOLMOGOROV CONCEPT OF TURBULENCE SCALING OF THE STRUCTURE FUNCTIONS DISSIPATIVE AND DYNAMICAL SCALING FUSION RULES IN TURBULENCE SYSTEMS CALCULATION OF SCALING EXPONENTS BASIC FORMULAS BIFURCATIONS FOR THE KURAMOTO–SIVASHINSKY EQUATION SYMMETRY: TRANSLATIONS, RE?ECTIONS, AND O(2)-EQUIVARIANCE KURAMOTO–SIVASHINSKY EQUATION STRANGE ATTRACTORS AND TURBULENCE THE TAYLOR–COUETTE EXPERIMENT DYNAMICAL SYSTEMS WITH ONE OBSERVABLE LIMIT CAPACITY AND DIMENSION DIMENSION AND ENTROPY GLOBAL ATTRACTOR FOR NAVIER–STOKES EQUATION THE LADDER INEQUALITY ESTIMATES LENGTH SCALES IN THE TWO-DIMENSIONAL CASE THREE-DIMENSIONAL REGULARITY THE ATTRACTOR DIMENSION HIERARCHICAL SHELL MODELS GLEDZER–OHKITANI–YAMADA SHELL MODEL (N, ?)-SABRA SHELL MODELS NAVIER–STOKES EQUATIONS IN THE COMMON WAVELETS REPRESENTATION ENTROPY PRINCIPLE MAXIMUM ENTROPY AND PROBABILITY DERIVATION OF THE MOTION EQUATIONS THE HIERARCHICAL DYNAMICAL SYSTEM FOKKER–PLANCK EQUATION APPENDIX: INEQUALITIES 310 EXERCISES MODELING OF FLOW OVER BLUNTED BODIES ONSAGER’S THEORY GENERAL CONCEPT OF A MULTI-COMPONENT GAS MIXTURE THERMODYNAMIC POTENTIALS, FORCES AND ?OWS CLOSING RELATIONS GOVERNING EQUATIONS FOR HYPERSONIC VISCOUS GAS ?OW CONDITIONS ON THE SURFACE OF DISCONTINUITY GOVERNING PARAMETERS TRANSFORMATION OF INITIAL EQUATIONS FLOW REGIMES FOR HYPERSONIC VISCOUS GAS ?OW VISCOUS SHOCK LAYER VORTEX INTERSECTION, NONSTRONG AND STRONG INJECTION BOUNDARY LAYER, NONSTRONG AND STRONG INJECTION BOUNDARY LAYER AND STRONG STRUCTION SHOCK WAVE STRUCTURE OUTER SUBLAYER MIDDLE SUBLAYER INNER SUBLAYER MAIN EQUATIONS GENERALIZED RANKINE–HUGONIOT CONDITIONS AT THE SHOCK WAVE MODELS FOR SHOCK SUBLAYERS INVISCID SHOCK AND BOUNDARY LAYERS INJECTION GAS LAYER VISCOUS BOUNDARY AND MIXING GAS LAYERS VISCOUS BOUNDARY LAYER WITH STRONG SUCTION FLOW AT VISCOUS BOUNDARY LAYER FLOW AT INJECTION GAS LAYER GENERAL STAGNATION POINT WINGS AT INCIDENCE AT SLIPPING ANGLES FLOW OVER SWIRLING AXISYMMETRIC BODIES NONUNIFORM ?OW AT INVISCID SHOCK LAYER NONUNIFORM ?OW OF THE FAR-WAKE TYPE UPSTREAM SWIRLING ?OW OVER AXISYMMETRIC BODIES