Dynamics of Vortex Structures in a Stratified Rotating Fluid (eBook)

1. The Introductory Chapter1.1  Introduction 1.2  The mathematical introduction1.2.1  The derivation of potential vortex conservation equations1.2.2  Formal solution. Integral invariants1.2.3  Contour dynamics method1.2.4  Stationary axisymmetric solution1.2.5  An approach to studying the stability of a axisymmetric two-layer vortex1.2.6  The structure of simplest types of external field1.2.7  A limiting case of discrete vortices1.2.8  Phase portraits. Choreographies1.2.9  Three-layer model equations  2. Dynamics of Discrete Vortices2.1  Two vortices in a two-layer fluid2.2  2A vortices in a two-layer fluid2.2.1  The case of arbitrary A2.2.2  Case A = 2 2.2.2.1  Two hetons with zero total linear momentum and nonzero angular momentum2.2.2.2  Two hetons with nonzero total linear momentum and zero angular momentum2.2.2.3  Two hetons with zero total linear and angular momenta2.2.2.4  Vortex structures: warm heton–cold heton, two antihetons, two “horizontal” pairs2.3   A + 1 vortices in a two-layer fluid 2.3.1  Vortex structures with zero total momentum at A ≥ 2 (free motion)2.3.2  Vortex structures with zero total momentum at A ≥ 2 (motion in an external field)2.3.2.1  Analysis of static states2.3.2.2  Stationary solutions at A = 2 2.3.2.3  Analysis of optimal perturbation frequencies at A = 22.3.2.4  Origination of chaos at A = 22.3.3  The case of nonzero total momentum at A = 22.3.3.1  Phase portraits in trilinear coordinates2.3.3.2  Analysis of steady states2.3.3.3  Classification of motions of triangular vortex structures: trajectories of absolute motion, choreographies2.3.3.4  Analysis of weakly perturbed tripolar collinear states2.3.3.5  Regular advection near stationary configurations2.3.3.6  Chaotic advection near stationary configurations2.4  Heton structures in a three-layer fluid 3  Dynamics of Finite-core Vortices3.1   Studying the linear stability of a two-layer vortex3.1.1  A vortex with a vertical axis: two circular vortex patches3.1.1.1  Heton with vertical axis3.1.1.2  “Ballistic” propagation ; law of vortex domain boundary: application to deep convection in the ocean3.1.1.3  Analogy with A-symmetric structure of discrete hetons3.1.1.4  Noncompensated two-layer vortex3.1.2  Annular two-layer vortex: four circular vortex patches3.1.2.1  Studying the stability of rings3.1.2.2  Modeling the transformations of an oceanic ring intosmaller vortex structures3.2  The impact of finite perturbations3.2.1  Heton with a tilted axis: two initially circular patches3.2.2  Stationary translation hetonic V-states 3.2.3  Heton with a vertical axis: two initially elliptic vortex patches 3.3  Interaction between two hetons3.3.1  Two hetons with vertical axes3.3.2  Heton with a vertical axis and heton with a tilted axis3.3.3  Two hetons with tilted axes, the case of zero total momentum3.3.4  Two hetons with tilted axes, the case of nonzero total momentum 3.3.5  Interaction between a warm and a cold hetons 3.4 The effect of external field on heton motion 3.5  Vortex patch dynamics in a three-layer model 3.5.1  Stability study of a three-layer vortex3.5.2  Modeling the motion of meddies3.5.2.1  Merging of two initially circular vortex patches3.5.2.2  Evolution of elliptic vortex patch3.5.2.3  On detecting lenses on oceanic surface3.5.2.4  On the effect of bottom topography on the motion of lenses3.5.2.5  Dynamics of medies in the flow over submerged hills3.5.3  Examples of interaction between three-layer vortices4  The Concluding Chapter4.1  Concluding remarks 4.2  Outlook to heton problems4.3  DiscussionAppendix A. E.J. Hopfinger. Experimental study of hetonsAppendix B.  M.A. Sokolovskiy. In memory of my TeacherIndex