# Question 4.7: This example demonstrates how a cotidal chart can be used to......

This example demonstrates how a cotidal chart can be used to reveal information about the depth of the seabed. Use the phase information for $M_{2}$ in the cotidal chart below to estimate the speed of the tidal wave along the coast of Finnmark and Kola. You may assume that 1° longitude at 70° latitude is 38 km.

From your answer and assuming the tide travels as a shallow water wave, find the corresponding water depth. What is the feature at ‘A’?

Step-by-Step
The 'Blue Check Mark' means that this solution was answered by an expert.

Remember we have been asked to estimate, not calculate in fine detail.

The distance along the Finnmark to Kola coast is about 20° longitude. At 70° latitude this is approximately (38 km/degree)×20° = 760 km.

From the chart, note that the phase of the tide changes approximately from 360° (or 0°) to 150° between Finnmark and Kola. Now, 150° is 150/360 of one $M_{2}$ period (=12.42 hours). Thus, this change in phase corresponds to a time interval of (150/360) × 12.42 ≈ 6 hours. The tide wave speed is therefore approximately 760/6 km/hour or 125 km/hr.

Assuming the tide wave propagates as a shallow water wave, its speed, c, =√(gh), where h is the water depth. Knowing c and g we can estimate h, the water depth. Now, making h the subject of the wave speed equation and converting the tide speed into units of metres per second, we have

h = (125,000/(60 × 60))²/g ≈ 1205.6/9.81 ≈ 120 m.

Thus, the depth of the sea along the coast is approximately 120 m. The feature at ‘A’ is an amphidromic point.

Question: 4.1

## Calculate the tide-generating force on the Earth due to the Earth-Moon and Earth-Sun systems, given that the mass of the Earth, (m), is = 5.98 × 10^24 kg, the mass of the moon, (M), = 7.35 × 10^22 kg, the major semi-axis of the lunar orbit around the Earth, (r), is 3.84 × 10^8 m, and the mean radius ...

We may estimate the magnitude of the effect of the...
Question: 4.2

## The tidal constituents for four harbours are given in the following table. Classify the tidal regime at each harbour using the tidal ratio. Estimate the maximum tide level at each harbour. Calculate the length of the spring-neap cycle at harbours A and D. The mean water level relative to the local ...

We calculate F from the amplitudes of the constitu...
Question: 4.6

## Derive a suitable approximation for the Coriolis parameter for regional scale motions centred on a latitude of θ0. ...

We expand the Coriolis parameter in a Taylor serie...
Question: 4.4

## 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 ...

a. From the tidal range information we can determi...
Question: 4.5

## Given the following information for observed ocean tide levels (semidiurnal) at an established gauge and a new survey site, calculate the sounding datum for the new site. ...

Following the steps outlined in the section above:...
Question: 4.8

## Find the periods of free oscillations in the following cases: 1. A long narrow lake of uniform depth 15 m and length 5 km. 2. An open-ended channel of depth 20 m and length 10 km. ...

In the first case we may use the 1-dimensional ver...
Question: 4.9

## Nonlocal forcing results in an oscillation of frequency ω0 whose amplitude at the mouth of a channel is Q. If the channel is of constant depth H and of length A, determine a general expression for the amplitude of the oscillation at the head of the channel. Calculate specific values for the case ...

The governing equation is \frac{\partial²\e...
Question: 4.11

## A wave in a tsunami has a period of 30 minutes and a height, Ho, of 0.5 m at a point where the ocean has a depth of 4 km deep. Calculate the phase speed, co, and wavelength, Lo, of this wave. Calculate its phase speed, ci, wavelength, Li, and height, Hi, in a coastal water depth of 15 m accounting ...

We assume the wave is a shallow water wave so that...
Question: 4.3