2
$\begingroup$

I ask this question in order to qlarify a misunderstanding i have about Green's law. Green's law is a direct consequence of the principle of conservation of energy flux , which implies the amplitude of shallow water waves behaves like $$h^{-1/4}$$ where h is the local mean water depth. On the other hand, Green's law applies to tsunamis, which are manifestation of the moving "version" of the hydraulic jump phenomena. This phenomena is charecterized by loss of energy (non-conservation principle) due to turbulent flow at the transition region. So how can one make these two aspects of the same phenomena (tsunami) not at odd with each other?

$\endgroup$
3
$\begingroup$

The soliton wave of a tsunami propagating on the ocean surface does not dissipate energy (which is why it can propagate so far), and when it reaches shallow water, its behaviour is ruled by the same Saint-Venant equations (which are a linearisation of Navier-Stokes equations as pointed out by @Eddy) as normal waves with a much shorter wavelength, which in turns gives Green's law.

But what you are talking about is then a different phenomenon I believe: a tsunami moving up a narrow channel does indeed create a bore, which is essentially a moving hydraulic jump. As far as I know, the bore height does not obeys Green's law.

$\endgroup$
  • $\begingroup$ O.k thanks!! I have to admit that my knowledge of water waves theory is limited to the airy theory, the theory of hydraulic jumps, but very little of, for example, stokes theory. So i can't really understand your answer, but your answer guided me a lot - i know i need to focus at understanding the Saint-Venant equation in order to acheive better understanding. $\endgroup$ – user2554 Oct 20 '17 at 11:48
  • $\begingroup$ I second that motivation! $\endgroup$ – user154997 Oct 20 '17 at 11:51
4
$\begingroup$

Greens law is derived from the linearized shallow water equations, which do not support hydraulic jumps, and thus Greens law does not describe hydraulic jumps. A hydraulic jump is a direct consequence of the so called genuine nonlinearity of the shallow water equations.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.