By Bernard LeMehaute

ISBN-10: 3642855679

ISBN-13: 9783642855672

ISBN-10: 3642855695

ISBN-13: 9783642855696

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Additional info for An Introduction to Hydrodynamics and Water Waves

Example text

H(O,CI>)U E sm Cl>] a } + ao [h(O,)U sJ = 0 where a is the mean earth radius, '7 the free surface elevation around the still water level, UE is the component of the current velocity in the direction of increasing 0, us is the component of velocity in the direction of increasing Cl>, 0 is the longitude, Cl> is the latitude, h(O,CI>) is the water depth. 1 The Newton Equation Inertia Forces To cause the motion of a constant mass M, or, more generally, to change the state of an existing motion, it is necessary to apply to this mass a force F, which causes an acceleration dV/dt such that F = M(dV/dt).

Figure 4-12 Determine the maximum value of u and w and the location where they are maximum. Some simplifying assumptions will be accepted for these calculations. Determine the expression for the local inertia and the convective inertia, their maximum values, and the ratio of the maximum value of convective inertia to the maximum value of the local inertia. Present a criterion permitting the evaluation when the convective inertia is negligible. 8 Demonstrate that (V2 -du = -ou + 2(w'7 - vO + -o ox ot dt 2 ) and find similar expressions for dvjdt and dw/dt.

They are valid when the distribution of velocity in a cross section can be assumed to be a constant; then the gravity waves are called long waves. 1 Translatory Gravity Waves [h a¢ J U=- ax a(hu) dx dt u+~ aq -dxdt ax or ~V = - az¢ ax 2 a(hu) dx dt (3-3) ax On the other hand, the volume at the time t is h dx, and at the time t + dt, since the free surface level changes the volume is [h + (ahjat) dt] dx. 2 Irrotational Flow If the density p is a constant, the continuity relationship has been seen to be (aujax) + (avjay) + (awjaz) = 0.

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An Introduction to Hydrodynamics and Water Waves by Bernard LeMehaute

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