Deep Water Gravity Waves: On the Simpler Aspects of by Bruce J. West (auth.)

By Bruce J. West (auth.)

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Additional resources for Deep Water Gravity Waves: On the Simpler Aspects of Nonlinear Fluctuating (Weak Interaction Theory)

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On the f l u i d v e l o c i t y and v e r t i c a l surface I f the source of the f l u c t u a t i o n s is e x t e r n a l , such as the turbu- l e n t behavior o f the a i r flow d r i v i n g the water waves, then perturbation concepts must be abandoned in describing the f u l l dynamics of the surface since i n s t a b i l i t i e s in the water wave growth are possible. The l i n e a r air-sea coupling model of P h i l l i p s 85 and Miles 86'87 between the a i r flow and the surface waves contains a resonant energy f l u x from the wind to the wave f i e l d .

For a system with one degree of 53 freedom the action can be viewed as a radius vector and the angle as a rotation angle about a closed orbit. This orbit is in the two-dimensional phase space for the system and does not correspond to the orbital motion of a f l u i d parcel in a physical water wave. For a system with two degrees of freedom the motion in the four-dimensional phase space is on the surface of a doughnut (torus), the action variables are the major and minor radii and the rotations of these radii the corresponding angle variables.

The velocicy p o t e n t i a l . A function which asso- is called a scalar f i e l d , A function which associates a vector v to each point in space-time (~,t) is c a l l e d a vector f i e l d , e . g . , the v e l o c i t y f i e l d which is the spatial gradient of the v e l o c i t y potential f i e l d . I t is not always necessary to represent the water wave system by an i n f i n i t e number of degrees of freedom. In practice a large but f i n i t e number of discrete modes may be s u f f i c i e n t to determine the evolution of the physical system to a given 28 degree of accuracy.

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