# An Introduction to Hydrodynamics and Water Waves by Bernard LeMehaute PDF

By Bernard LeMehaute

ISBN-10: 3642855679

ISBN-13: 9783642855672

ISBN-10: 3642855695

ISBN-13: 9783642855696

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Extra info for An Introduction to Hydrodynamics and Water Waves

Example text

For a fluid particle moving westward the centrifugal force is not sufficient to balance the component of gravity force. Therefore, the fluid particle is deflected toward the Pole. In the northern hemisphere, the deflection is to the right, and in the southern hemisphere, the deflection is to the left. 3 In the case where a component of motion is perpendicular to the earth's axis, a similar effect is observed. Angular momentum is conserved. Therefore, if the particle goes downward, towards the center of the earth, it will be rotating faster than an earth fixed particle at the same location and therefore it will deflect eastward.

The concept of irrotationality is essentially mathematical [(8u/8y) - (8vj8x) = 0 in the case of two-dimensional motion]. The difficulty arises when one tries to establish some simple practical rules for assessing the validity of this assumption. Indeed, rotation is often caused by viscous forces, but a rotational solution also exists for a perfect fluid, and irrotational flows exist in a viscous fluid. For example, let us consider a reservoir, where the flow velocity is practically zero, and a connected duct.

2 Sometimes a partial effect of the convective acceleration is taken into account by the use of an approximate solution given by a number of terms of a series. (Example: gravity wave theories to the second order, third order, etc. 3 Another method to take account of a partial effect of the convective acceleration is by the assumption of irrotationality when the friction effects are negligible as seen previously. 4 Sometimes only some terms of the convective acceleration may be neglected. The case of a two-dimensional boundary layer on a flat plate is given here as an example (Fig.