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So I am calculating phase velocity of a wave for Froude number scaling for model testing of a boat. I got data from Lloyd's Rules saying for the specific sea area I did $H_s=3.6\text{ m}$ and $T_z=6.8\text{ s}$.

Assuming a regular, progressive wave (this is where I might be wrong) and using the deep water relationship of $\lambda = \dfrac{gT^3}{2\pi}=712.5\text{ m}$.

Wave celerity $v=\dfrac{\lambda}{T}=\dfrac{712.5}{6.8}=104.7\text{ m/s} = 377\text{ km/s}$? Am I doing this right? Are ocean waves supposed to be that fast?

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  • $\begingroup$ I assume that's meant to be 377 km/h, not km/s, right? If so, please edit your question to correct that typo. $\endgroup$
    – Wasabi ♦
    Nov 30, 2018 at 20:14

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I'm not sure where did you brought the 'deep water relationship' in here. If you're dealing with usual water wave (gravity, surface, linear, and close to sinusoidal wave form), then the relationship you'd need to use will be dispersion relationship.

$\omega^2 = gk\tanh(kh)$

As you're assuming deep water, it becomes: $\omega^2 = gk$

Which leads to almost exactly same equation you came up with, but one less power of T:

$\lambda = \dfrac{gT^2}{2\pi} = 72m$

and phase velocity of 10.61 meter/second.

(Actually, your original calculation, with $T^3$ was incorrect. That should have give you wave length of 491 meter, instead of 712 meter)

Additional comments:

  1. YES. Wave can be very fast, if it is extra long wave like tsunami, like 400 kph. But the wave you gave as example, (T = 6.8 s) can't be too fast.

  2. What you did was not really worth of value for model test if you're not specifically interested in surge-direction slamming. You'll need to match the length scale first, and calculate the corresponding dimensions (in case of wave, fit the height and length first according to length ratio, and then fit time and modify your wave maker actuator) Refer page 21 of linked document. http://www.ivt.ntnu.no/imt/courses/tmr7/lecture/Scaling_Laws.pdf

  3. As you came up with zero up-crossing period for the wave, I believe you have wave spectrum instead of single wave. The input for wave maker will be pretty much different if you need to generate wave spectrum instead of regular wave.

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