Why does the assumption of waves amplitude being small, compared to the wavelength, (as used for surface gravity waves in water) lead to the equivalent condition: $$ {\partial v \over \partial t } >> { (v \nabla )v}$$
This seems to be one of the basic assumptions of certain classes of fluid mechanic problems.
I spend two hours in the library today reading the applicable chapters of about nine books and not in one the explanation was more detailed that to claim that $ (v \nabla )v$ must be on the order of $v^2<<1$.
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