By V. Sundar
Ocean Wave Mechanics: functions in Marine Structures
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Ocean wave mechanics: applications in marine structures
Ocean Wave Mechanics: purposes in Marine constructions
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Steady and unsteady II. Uniform and non-uniform III. Rotational and irrotational IV. Laminar and turbulent Ocean Wave Mechanics: Applications in Marine Structures, First Edition. V. Sundar. © V. Sundar 2016. Published by ANE Books Pvt. Ltd. and John Wiley & Sons Ltd. 26 Ocean Wave Mechanics Steady flow Fluid characteristics such as velocity u, pressure p, density r, temperature T, etc. , at (x, y, z), ∂u ∂p ∂r = 0, = 0, =0 ∂t ∂t ∂t Unsteady Flow Fluid characteristics do change with time at any point (x, y, z).
3: Definition sketch for wave motion Boundary conditions I. 1) is to be satisfied in the region d z η x where h is the water surface elevation measured from the Still Water Level, SWL. 44 Ocean Wave Mechanics II. The kinematic bottom boundary condition meaning, that the vertical velocity component at the sea bottom is zero. w= ∂φ = 0 at z = − d ∂z since z is negative downwards from SWL. III. The pressure at the free surface is zero at z = h. 4), we get h= 1 ∂φ g ∂t z = h This is the dynamic free surface boundary condition.
Let the body force per unit mass at the same point be X, Y and Z in the x, y and z directions respectively. Fig. 2: Definition sketch of coordinate system If the mass of fluid in the medium as shown in Fig. ∆z ) . p + ∂p ∆x ∆y ∆z ∂x Similarly, that in the y and z directions are (Y r∆x . ∆y. ∆z ) and ( Z r∆x . ∆y. ∆z ) where, p is the pressure intensity at point P. Since the lengths of the edges of the fluid medium are extremely small, it may be assumed that the p on the face PQRS is uniform and equal to p.