# Question 4.4: This example illustrates how information on spring and neap ......

This example illustrates how information on spring and neap tidal information can be related to tidal constituents to derive further information to assist in a practical problem of safely docking a ship in harbour. A port is located in an estuary, upstream of a bridge whose deck base is at +20 m CD. There is a sandbar across the entrance of the estuary which has a drying height of +2 m CD. A ship wishing to enter the port has a draft of 4 m and requires a vertical clearance allowance of 10 m. The tide is semidiurnal and exhibits a quasi-resonant behaviour with the $M_{2}$ constituent amplified preferentially. The mean tide level is +7 m CD. The maximum, spring and neap tidal ranges are 14, 12 and 8 m, respectively.

a. Find the amplitudes of the tidal constituents $M_{2}$ and $S_{2}$ , and use them to explain why the $M_{2}$ constituent might be resonant.

b. What is the water level range in which the ship can dock safely?

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a. From the tidal range information we can determine that $2(M_{2} + S_{2})$ = 12 m and $2(M_{2} − S_{2})$ = 8 m. Solving these simultaneous equations for the amplitudes of the two main semidiurnal constituents gives $M_{2}$ = 5 m and $S_{2}$ = 1 m. From equilibrium tidal theory we expect the amplitude of $M_{2}$ to be approximately twice that of $S_{2}$ .

Here, it is five times larger, indicating unusual amplification which could be caused by resonant behaviour in the estuary.

b. The ship requires a total of 14 m (4 m draft + 10 m clearance above water), and to get over the sandbar it must have a water level of +6 m CD to provide 4 m draft. (4 m draft over the drying height of +2 m CD). To fit under the bridge the water level must be less than 20–10 m to provide the necessary 10 m clearance. Hence, the ship can safely enter port if the water level is between +6 m CD and +10 m CD.

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