"Simplified wind-to-wave transformation methods are oftenbased on a
"rectangular" wind which starts suddenly, blows for a given time with
a constant speed, for then suddenly to cease away. One of the few
historical storms which evidently behaved in this way, was the storm
on the Lake of Gnnesareth, Reference .
Select a relevant wind-speed. Estimate the evolution of the sea-state and find the maximum. Calculate the wave height of the largest individual wave."
To convert the wind force to wave heights we need to know the fetch length, that is, the distance from land in the direction against the wind. The lake is about 20 km long and about half as wide, and the boat was evidently situated somewhere in the middle of the lake. We may therefore assume the fetch length to have been about 6 km.
|Table 5.2.16: Calibration of Greek Wind Terms
against the Beaufort Scale.
When wind-speed and fetch length are given, there exists a maximum sea-state which will be obtained after a certain saturation time. With reference to Figure 3.4.6, the sea-state will behave in different ways, depending on how far the storm duration is shorter, equal or larger than this saturation time. The change in the nautic conditions will, however, be most dramatc if those times are equal. In this case the local sea-state follows the trace A-B-C in Figure 3.4.6, where the local maximum is obtained at B. At this point the wind ceases, the local wave-spectrum is just filled up and the wave begin to decay immediately, and in the same rate as they increased. A time profile of the sea-state may then be traced by means of the charts given in Appendix A at the end of the book. This is shown in Figure 5.2.3 with some explanation.
To calculate the maximum sea-state more accurately, we may then call up the auto-course. The input is given directly in the key-code, and with some reference to the Tables 5.2.12 to 15, the consultation may go as follows: (Some additional comments are given in parentheses.)
Operator: Auto-course version 2.2. It's the central, may I have the Post number please? Client: 34 (Requires the post for wind-drive waves.) Operator: Post 34 for wind-driven waves. Give service number, please. Client: #4 (Print the post introduction.) Operator: The introduction has been printed. The report contains 9 lines. Post 34 for wind-driven waves. Give service number, please. Client: 1 (Requires the Beaufort scale.) Operator: Beaufort's wind scale. Give Beaufort number, please. Client: 9# (Beaufort number 9.) Operator: 9. Beaufort 9: Strong gale. Wind speed 41, to 47, knots. that is, 20.9, to 24.5, metres per second. Recommended wind speed is, 23. metres per second. Client: #6 (Print all data concerning Beaufort 9.) Operator: The results have been printed. The report contains 14 lines. Beaufort's wind scale. Give Beaufort number, please. Client: 9# (Return to the post entrance.) Operator: Post 34 for wind-driven waves. Give service number, please. Client: 3 (Asks for sea-state by given fetch.) Operator: Input to: Sea-state by given fetch. Confirm the values by 00, or give a new value. Wind speed in metres per second: 23. Client: 00. (Accepts the wind speed.) Operator: Fetch length in kilo-metres, zero. Client: 6*0# (Fetch length is 6 kilometres.) Operator: 6 Client: 00 (Confirms the fetch length.) Operator: Thank you. To continue the calculations, Push: 1. Client: 1 (Continues the calculation.) Operator: Three blocks with results from: Sea-State by Given Fetch. Client: #6 (Prints the complete result table.) Operator: All results have been printed. The report conatins 31 lines. Client: #4 (Prints the result comments.) Operator: The comment has been printed. The report contains 33 lines.
WIND DRIVEN WAVES. Wind-driven waves are discussed in Article 3.4. A differential equation for the wave spectrum moments is derived in Section 3.4.4. The calculations are carried ou for the one-parameter wave spectrum (3.4.49) under the action of a constant wind. Derivations are carried out in Sections 3.4.5, and, 3.4.6. The sea is initially calm. Wind speed, fetch length and duration are chosen according to input specifications. Beaufort 9: Strong gale. Wind speed 41 to 47 knots, that is, 20.9 to 24.5 metres per second. Recommended wind speed is: 23. metres per second. "High waves. Dense streaks of foam along the direction of the wind. Sea beings to roll. Visibility affected." Sea-State by Given Fetch. (Block 1:) Storm conditions. Wind speed, v, 23.0 m/s. Retch length, X, 6.0 km Required time of blowing, t, (3.4.55) 0.46668 hours. That is, 28.0005 minutes. (Block 2:) Sea-state. Significant wave height, Hs, (3.4.63) 1.51569 metres. Wave period, Tz, (3.4.64) 4.11623 seconds. Increase of Hs with fetch, (3.4.82) 0.10121 m/km. Increase of Hs with time, (3.4.83) 1.65571 m/hour. (Block 3:) Dimensionless variables. Sea-state variable, y, (3.4.57) 0.39516. Fetch length, xi, (3.4.54) 1.33520e-02. Time required, tau, (3.4.58) 4.29084e-02. Space gradient, dy/d xi, (3.4.56) 5.92856. Time gradient, d y / d tau, (3.4.46) 2.34275. The estimated time required to develop this sea-state, may be somewhat short. Effects of sea-depth are not considered. - - - - -
(iv) Extreme Wave-Height.
In the sea-state condition chosen, that is A-B-C in Figure 3.4.6, the significant wave height Hs is nearly linearly increasing at the storm maximum, followed by a linear fall with the same rate. The highest wave-crest in this case may be estimated from (4.3.121) with s=1 and Ao=Hs/V8. The largest wave height may be taken as 1.8 times the largest wave crest. The effective number of wave cycles ntau in this storm, is given in (4.3.109) and may be calculated numerically by the help of (4.3.119).
These formulae are not coded explicitly in the auto-course. We may, however, get hold of the basic values for Hs, Tz and dHs/dt from the current result table, and evaluate xc from the formulae by the calculator. To have some kind of documentation, we may shift to keyboard and alphanumeric input, switch on the printer and give commands with ample redundant text. We may also save some work by using the Macro 4 and Macro 5 prepared in Section 5.2.4(iv) above.
The conversation may then continue as shown below. As usual, the letter sequences trapped by the verbal compiler are indicated by bold-face types. Acoustically the conversation will be heard as it is written, with the actors represented by different voices. The text in the report will also be similar, but the numbers will have more decimals.
Client: 2. (go to next block in the result table.) Operator: Block 1: Storm conditions. Client: 2 (Go to next block in the result table.) Operator: Block 2: Sea-state. Client: #01. (Set the permanent printer on.) Operator: The printer is on. Client: #08. (Change to keyboard and alpha-numeric input.) Operator: Use the keyboard, please. Client: Get the results and save the values needed. 0 to get first line. Operator: Significant wave height, Hs, from equation (3.4.63). 1.52 metres. Client: Enter Hs into memory 7. Operator: Entered into memory 7. Client: 0 to get next line. Operator: Wave period Tz from equation (3.4.64). 4.12 seconds. Client: Enter Tz into memory 8. Operator: Entered into memory 8. Client: 0 to get next line. Operator: Increase of Hs with fetch, dHs/dx, from (3.4.82). 0.10. m/km. Client: 0 to get next line. Operator: Increase of Hs with time, dHs/dt, from (3.4.83). 1.66. m/hour. Client: Enter into memory 9. Operator: Entered into memory 9. Client: Whe have now saved the data needed, and may key from macro 4. Operator: New instrument is macro 4. Macro-4: Macro-4: Extreme wave height in a storm 8.0. Operator: 8. Macro-4: Square root Operator: Square root gives: 2.828. Macro-4: Inverse. Operator: Inverse gives: 0.354. Macro-4: Recall Hs from memory 7 and multiply. Operator: Multiplication with memory 7 gives: 0.5359. Macro-4: Enter A-0 into memory 1. Operator: Entered into memory 1. Macro-4: 0.5 Operator: 0.5 Macro-4: Recall Hs from memory 7 and multiply. Operator: Multiplication with memory 7 gives: 0.758. Macro-4: Recall Tz from memory 8 and divide. Operator: Division with memory 8 gives: 0.184. Macro-4: Recall dHs/dt per hour from memory 9 Operator: Recalled from memory 9: 1.656. Macro-4: 3600 Operator: 3600. Macro-4: Divide to get dHs/dt per second. Operator: Division gives: 4.599e-04. Macro-4: Divide to get n-tau. Operator: Division gives: 400.3. Macro-4: Enter n-tau into memory 2. Operator: Entered into memory 2. Macro-4: s is 1.0 Operator: 1.0 Macro-4: Enter s into memory 3. Operator: Entered into memory 3. Macro-4: Key macro 5 to calculate x-c. Operator: New instrument is macro 5. Macro-5: Macro-5: x-c from equation (4.3.121). 1.0 Operator: 1. Macro-5: Recall s from memory 3 and add. Operator: Addition of memory 3 gives: 2. Macro-5: Recall s from memory 3 and divide. Operator: Division with memory 3 gives: 2. Macro-5: Take the gamma function. Operator: Gamma function gives: 1. Macro-5: Recall n-tau from memory 2 and multiply. Operator: Multiplication with memory 2 gives: 400.3. Macro-5: 2.0 Operator: 2. Macro-5: Multiply. Operator: Multiplication gives: 800.6. Macro-5: Take the natural log. Operator: Natural log is 6.685. Macro-5: Duplicate this number. Operator: Entered: 6.685. Macro-5: Take the natural log again. Operator: Natural log is 1.9. Macro-5: Recall s from memory 3 and divide. Operator: Division with memory 3 gives: 1.9. Macro-5: Subtract the second term from the first. Operator: Subtraction gives: 4.785. Macro-5: Take the square root. Operator: Square root gives: 2.188. Macro-5: Recall A-0 from memory 1 and multiply. Operator: Multiplication gives: 1.172. Macro-5: Enter x-c into memory 4. Operator: Entered into memory 4. Macro-5: Return to the current instrument. Operator: New instrument is macro 4. Macro-4: Get from wave-crest, x-c, to wave-height, H-max. 1.8 Operator: 1.8 Macro-4: Recall x-c from memory 4 and multiply. Operator: Multiplication with memory 4 gives: 2.11. Macro-4: Enter H-max into memory 5. Operator: Entered into memory 5. Macro-5: Recall the current instrument. Operator: Use the keyboard please. Client: Recall H-max from Memory 5. Operator: Recalled from memory 5: 2.11. Client: Please, say this with multiple decimals. Operator: I repeat: 2. point. 1. 1. 0. 0. 8. 6. Client: Thank you. This is the largest wave-height, in metres, encountered on the lake of Gennesaret, during that storm. Operator: The printer is off. Client: Recall the print information. Operator: Number of lines printed is 134. Client: Good-bye. Operator: It's the Central. Good-bye, and thank you for calling the Auto-Course.