2 Wind waves in deep water may be estimated using Eqs 53 58

2) Wind waves in deep water may be estimated using Eqs. (5.3)- (5.8) as a first approximation. The wind speed is U= 15 m/s in the following a) Estimate the spectral significant wave height Hmo and the spectral peak period Tp for fully developed (upper limit) wind waves. Estimate the minimum fetch length and the minimum storm duration required for fully developed wind waves. b) The actual fetch length and storm duration are 200 km and 10 hours, respectively Estimate the actual values of Hmo and Tp

Solution

In the problem, the water body is fully developed.

(a)

Hence, H*_mo = 0.243, T*_p = 8.13 and t* = 71,500

We can use equation (5.3) to find the fetch length and storm duration.

Given,

F* = (gF)/U²

=> F = (F*U²)/g

Also,

H*_mo = 0.0016 (F*)^1/2

From this, F* = (H*_mo)²/0.0016² = 23066.015

i.e, F = (23066.015*15²)/9.81 = 529037 m = 529 km

Similarly, duration can be found out.

t= (t*U)/g

=(71500*15)/9.81

=109327.217 sec = 30.368 hr

(b)

Given, F= 200 km, t = 10 hrs

therefore, F* = (gF)/U² = 8720 (using (5.3))

H*_mo = 0.0016(F*)^1/2 = 0.0016*8720^1/2 = 0.149

H_mo = (H*_moU²)/g = (0.149*15²)/9.81 = 3.417 m

Similarly,

T*_p = 0.286 x (F*)^1/3 = 5.886

T_p =(T*_pU)/g = 9 sec