Fundamental 52, First Harmonic 27mins.
The large peaks are thus due to the reinforcement of the fundamental maximum every 50-odd minutes by the every alternate first harmonic swing. The agreement between the observed periods and those computed by Bottomley (1955) is sufficient to make the identification certain; further evidence is presented under Text-Fig. III.
The fundamental period is not exactly double that of the first harmonic. The gradual displacement in time of the every second swing of the first harmonic with respect to each swing of the fundamental is shown in the lower trace at the left hand end.
A change in the weather occurred in the early hours of 18.5.55, there being strong winds in certain sections of the lake, and the effects on the traces became apparent at about 08.00 hours. Higher harmonics develop and there is a general loss of regularity, but the major oscillation due to the fundamental is still observable.
The traces in Text-fig. I show an average behaviour; smaller amplitudes have been recorded (some are shown in Text-fig. IV), and much larger ones have been recorded and observed visually. On 28.12.54 the amplitudes at Kingston were larger than the four inches which the machine would record and were estimated to reach a little over five inches. At no time has the hourly fluctuation been less than half an inch as observed at Kingston during occasional observations over the last eight months.
Text-Fig. 2. From the position of the nodal planes, and the surface shapes calculated by Bottomley (1955) for the fundamental and the first harmonic motion it is apparent that particular interest attaches to readings taken at or near Bob's Cove. At this site the amplitude of the fundamental should be very small owing to the nearness of the nodal plane, and yet the first harmonic (with a ventral point near Bob's Cove) should be present with some 60% of its end amplitude.
The lower curve shows, for the first twelve hours, practically pure first harmonic tracings, and these may be used with advantage to calculate the corresponding period, 27mins. The linear descent of the curve with time represents the fall in the mean lake-level with time due to excess run-off over intake. The slope of the curve and the surface area of the lake indicate a figure of 4,530 cubic feet per second for this particular occasion.
By 12.00 hours on 18.5.55 a marked change has come over the traces and there is a very pronounced development of oscillations of very short period. The upper trace shows how these continued to increase on 19.5.55 until towards 12.00 hours on that day the swings were too large to record on the instrument. These oscillations were of period 4.28 minutes, and reached an amplitude which was in excess of eight inches. At the time of these large amplitude oscillations there was virtually no surface wave in the Cove itself and there was not the slightest difficulty in seeing the periodic rise and fall of the surface level on posts and stones in the water. The advance and retreat on the sloping beach was very striking, reaching 10 or 12 feet in some places, yet it was not noticed by a party of twenty casual visitors who spent an hour near the lakeside.
There is insufficient evidence to identify positively the particular basin of the Lake which is giving rise to this mode of oscillation. Large amplitude short period waves were recorded at Kinloch during the same day, but no positive correlation can be made between the maxima at the two sites. Regrettably there was no observation station at Queenstown at the material times, but an experienced observer who knew of the phenomenon then occurring at Bob's Cove did not see any similar effect in Queenstown Bay. It is possible that the effect is that of a longitudinal seiche of either (possibly both) the Kinloch arm and the Walter Peak arm. Rough measurements on the model used by Bottomley (1955) show that the fundamental periods for these arms are 23 minutes and 12 minutes respectively, so that it would be necessary to suppose a high harmonic to obtain the required frequency.
Direct measurement on a small dam near Dunedin has shown the existence of a fundamental period of about 35 seconds. Bob's Cove is approximately the same area as this dam, and much deeper. As the period decreases with increasing depth, and as open bays have periods roughly half of the corresponding closed bay, it may safely be deduced that the natural period of Bob's Cove is not more than 30 seconds at most, and this disposes of the suggestion that that 4.28 minutes period is that of the Cove itself.
The most likely explanation is that the effect is a transverse seiche across the Lake from Bob's Cove to the South bank. Calculation shows that the period of such an action would be 3 ½-4 ½ minutes, depending somewhat on the assumed transverse section and making liberal allowances for errors in the interpretation of Lucas's survey. In the absence of simultaneous measurements on opposite banks with more rapidly revolving drums so that phase relations could be established, further discussion is conjectural.
Text-Fig. 3. This shows portions of traces taken simultaneously at the two extremities of the Lake. Both show the general pattern due to a combination of fundamental and first harmonic seiches. At a time when the first harmonic and the fundamental are in phase to give an enhanced upward swing at Kinloch, then it must be that at Kingston the first harmonic and the fundamental are acting in opposite direction, and interfere to produce a reduced swing. The various features of these two curves can be more fully interpreted in this fashion.
Text-Fig. 4. This is part of a continuous record extending over five days taken at Kingston in December, 1954. It will be noticed that there is a pronounced long term periodicity with a period of rather more than 12 hours. Similar behaviour is shown (though not so clearly) by the traces taken at Kingston and at Kinloch in May, 1955, but is not detectable at Bob's Cove.
It is considered that the effect observed can be attributed to a temperature seiche (for examples and discussions see Honda, 1915 and 1916), that is an oscillation of the general kind so far considered but taking place at the junction
Text-Fig. 4.—The upper and lower traces torm a continuous record taken at Kingston in December, 1954. The twelve-hour periodicity is shown most clearly in the upper trace, but is fairly distinct also in the lower.
between the upper hot and the lower cold layers of the lake, the thermocline. Given sufficient data for the relative depths of the two layers and their densities, it is possible to estimate the period of oscillation. Using the data obtained by Miss V. Jolly, on the location of the thermocline, one can show that the period of 12 hours is in the possible range, but much more work, observational and computational, is necessary if the suggestion is to be verified.