In a funnel-shaped estuary, especially if it faces the direction of the tidal wave in the sea, the tide in going up the channel increases in velocity, and the momentum of the water causes it to rise higher and higher as the width decreases. At the upper end of the Bristol Channel the range of the tide is double the range in the sea outside the channel. The Bay of Fundy is another place where a similar phenomenon occurs. When a river or estuary is shallow and the range of the tide is great, so that its rise is rapid, the flood tide in some cases advances in the form of a wave or “bore,” causing a sudden rise in the water-level and a sudden reversal of the flow of the stream. A bore is most pronounced at spring tides. That of the Severn is well known.
In the case of a tide running along a coast or up an estuary, the water of the flood tide, after it has ceased to rise, continues for a short time, owing to its momentum, to flow in the same direction as before. The same thing happens when the ebb tide ceases to fall. The tide also acquires special velocity, just as a river does, round any projecting headland.
The rise and fall of the tide are least rapid near the turns of the tide. If the time from the beginning to the end of the flow be divided into six equal parts, the proportional rise of the water will be approximately as follows. And similarly with the fall during the ebb.
| Time | 1 | 2 | 3 | 4 | 5 | 6 |
| Rise of water | ·067 | ·25 | ·5 | ·75 | ·933 | 1 |
Tidal waters are frequently charged, more or less, with silt, obtained from the shore or from shallows near it, either by currents or tidal waves sweeping along it, or by the action of ordinary waves. Tidal waters flowing up and down the lower portions of rivers render them to an enormous degree more capable of carrying navigation and, especially if they become enlarged and form estuaries, more capable of being altered by training works.
A tide-gauge is constructed on the same principle as a self-registering stream-gauge. The rise and fall of the water are reduced, by mechanism, to a convenient range, and are recorded on a band carried on a drum, which is caused to revolve by clockwork. Another kind, which depends on the use of an inverted syphon filled with air and a syphon of mercury, is described in Min. Proc. Inst. C.E., vol. clxiv.
Fig. 66.
2. Tidal Rivers.—Let A B ([fig. 66]) be the surface of the lower part or mouth of a river, supposed to be of uniform width, and let B be the mean sea-level. As the tide rises to D the water of the river is headed up and assumes the line A D. When the tide falls to F there is a draw, the river surface taking the line A F. If the rise of the tide B H is so great that the discharge of the river cannot keep pace with it, so as to fill up the whole space between A and H to the level of H, there will be a flow of sea water from H to some point M, and of river water from A to M. The point M will be lower than A and H. If the tide now turns and the water-level H begins to fall, there will still be a flow along H M. For a brief period it will be due to momentum, but it will continue until, by the rise of the water-level at M and the fall at H, the surface has assumed the form indicated by the dotted line A N J. While this is happening, the point corresponding to M—where the concave curve of the upland water meets the convex curve of the tidal water—rises higher and shifts seaward. The character of the two curves remains the same, but they become flatter and the surface N J nearly level.
Thus the time of high tide at M is later than at H. It is later for each point passed in going up the river from H towards A. Eventually a point A is reached where there is no tide, that is, no rise or fall. Far below this point, between A and B, there is a point above which there is no upward current but only a slackening of the downstream flow. At H a diagram showing the rise and fall of the tide is symmetrical, at N the rises and falls are less than at H, and the periods of their occurrence later. In going up the river the duration of the flood tide decreases and that of the ebb tide increases. The flood tide attains its greatest velocity soon after its commencement, the ebb tide towards its close. The distances to which the tidal influence extend are of course greater the greater the range of the tide and the flatter the slope of the river. The discharge of the river of course varies. The greater the discharge the more the rise of the river tends to keep pace with that of the tide and the less the distance to which the tidal influence extends. On a longitudinal section of the river, the high-water line will be shown as A N H. This is merely done for convenience. It is never high water at all points simultaneously. To show the actual state of affairs at various stages of the tide, series of lines must be drawn as in [fig. 67], where the firm lines show the flood, and the dotted lines the ebb tide.