This book covers a new approach to analyzing hydrodynamic stability. With the use of standard remedies of functional analysis, theory of boundary value problems and infinitesimal Lie algebras, it is shown in the book that large vortex mushrooms of an ideal incompressible fluid in a vertical strip behind a water hammer proves to be 2D (plane-parallel) nonlinear (for arbitrary disturbances of initial velocities) and long wave stable. It is one of the many examples provided in the book discussing hydrodynamic stability. Sample Chapter(s) Introduction Contents: Introduction Velocity Strain: Vector Objects and Operations Continuum Motion Flows of Elements Rigid Body Rotations: Angular Momentum Equilibrium Angular Friction Conservation Laws: Fluid and Gas Momentums Viscosity Heat Conductivity A Centrifuge Turbulence: Stress of Pulsations Stress–Flow Interaction Plane Channel Flow Stability: Flows as Infinitely Dimensional Rotations Ideal Analytic Stability Viscous Asymptotic Stability References Index Readership: Persons interested in fluid stability, vortices in oceans, rivers, ducts.