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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