An Introduction to Hydrodynamics and Water Waves

acceleration approximation axis Bernoulli equation bottom boundary conditions boundary layer calculation coefficient considered constant continuity equation coordinates cross section defined deformation density determined direction discharge dy dz energy equal example expressed external forces Figure flow pattern fluid particle free surface friction forces given gravity wave head loss Hence horizontal hydraulic jump inertia forces integral irrotational laminar flow linear long wave long wave theory mass transport mathematical mean motion mean value mean velocity method momentum equation momentum theorem Navier–Stokes equations neglected nonlinear obtained order of approximation pipe plane porous medium pressure distribution pressure forces respect to space Reynolds number rotational scale model shear stress similitude sinh solution spectrum steady flow stream function streamlines theoretically turbulent flow two-dimensional uniform flow unsteady vector velocity components velocity distribution velocity potential function vertical void coefficient water depth water waves wave height wave motion zero