Seiches

A free oscillation in an enclosed or semi-enclosed body of water, similar to the oscillation of a pendulum where the oscillation continues after the initial force has stopped, is defined as a seiche (Miles 1974). Several factors cause the initial displacement of water from a level surface, and the restoring force is gravity, which tends to maintain a level surface. Once formed, the oscillations are characteristic only of the system's geometry (length and depth) and may persist for many cycles before decaying under the influence of friction or energy leakage.

A simplest model of a continental shelf seiche is a standing wave with an anti-node at the shoreline and a node at the shelf edge. The period of the seiche is given by four times the travel time from the coast to the shelf-edge. For a mean water depth h, shallow water wave theory gives (Pugh 1987):

1 4L

Here, n is the number of nodes (n = 1 is the fundamental mode and is also the most common; L is the width of the continental shelf; g is acceleration due to gravity and h is the mean water depth. In the auto-spectrum (Fig. 7.2), 3 seiche periods were identified at Fremantle: 2.8 h, 1 h and 20 min. The seiches have amplitudes between 10 and 40 cm and contained 40-70% energy relative to the main 24 h diurnal tidal oscillation. Ilich (2006) found that the maximum amplitudes of the 2.8 h and 20 min seiches to be ~45 cm and ~12 cm respectively although the 45 cm seiche amplitude could be due to the superposition of all three seiches. Width of the continental shelf off Fremantle is ~50 km whilst the mean shelf depth is ~50 m which yields from Eq. (7.1), a period of ~2.5 h which is close to the observed value of 2.8 h.

Ilich (2006) found that changes in direction of the wind stress initiate seiching (Fig. 7.3). In particular: (a) strong wind events onshore or offshore components initiate seiching at the 1 h and to a lesser extent, the 20 min seiche; (b) strong southerly (shore-parallel) events rarely cause excitation; (c) sea breeze patterns occurring for more than two days decrease spectral energy of the entire spectrum.

Continental shelf seiches are also generated by tsunamis (Pattiaratchi and Wijer-atne 2009) and are discussed in Sect. 7.4.

150 100 50 0

150 100 50 0

320 325 330

Energy plot of a spectrum of frequencies over time series WL from FBH 2001

320 325 330

Energy plot of a spectrum of frequencies over time series WL from FBH 2001

Time (day of the year)

Fig. 7.3 Time series of a wind stress; b water level; and, c time-frequency diagram for a 15 day period in November 2001 showing that onshore winds (-ve easterly) initiates seiching. (From Ilich 2006)

Time (day of the year)

Fig. 7.3 Time series of a wind stress; b water level; and, c time-frequency diagram for a 15 day period in November 2001 showing that onshore winds (-ve easterly) initiates seiching. (From Ilich 2006)

7.4 Tsunamis

The Indian Ocean region experienced its most devastating natural disaster through the action of a tsunami, resulting from an earthquake off the coast of Sumatra, on 26th of December 2004. This was followed by tsunamis in March 2005, June 2006 and July 2007 and tide gauges in Western Australia recorded sea level oscillations related to all 4 tsunamis but did not result in large scale property damage (Pattiaratchi and Wijeratne 2009).

The tide gauge data along the west coast indicated that the tsunami waves incident at Geraldton (0720), Carnarvon (0740) and Fremantle (0740). The initial waves all indicated an increase in the water level, corresponding to leading elevation waves, and the heights along the west coast ranged from 0.33 m at Fremantle to 1.650 m at Geraldton (Fig. 7.4 and Table 7.2). Examination of the residual time series, maximum wave heights, and the elapsed time between the initial and maximum waves indicated that: (1) the maximum wave heights recorded at Carnarvon, Geraldton, and Fremantle (Table 7.2), all exceeded the mean spring tidal range at these locations; (2) at Geraldton, although initial oscillations due to the tsunami waves were observed at 0720 UTC, there was a lag of

Local Time (Days in December 2004)

Fig. 7.4 Time series of residual sea level from coastal stations located along the west coast of Australia. The dashed line shows the time of the earthquake. (Note: local time is +8 h UTC)

Local Time (Days in December 2004)

Fig. 7.4 Time series of residual sea level from coastal stations located along the west coast of Australia. The dashed line shows the time of the earthquake. (Note: local time is +8 h UTC)

Table 7.2 Characteristics of the 26 December 2004 tsunami as recorded by tide gauges

Station

Initial wave

Maximum wave

Arrival time/date

Wave heighta

Elapsed time

Wave height

(UTC)

(number)

Carnarvon

07:40 26/12/04

0.38 m

15 h 20 m (25)

1.14 m

Geraldton

07:20 26/12/04

0.13 m

15 h 15 m (19)

1.65 m

Fremantle

07:40 26/12/04

0.33 m

7 h 20 m (9)

0.60 m

a Maximum wave height is listed as the trough to crest height a Maximum wave height is listed as the trough to crest height five hours before the highest water level (2.6 m relative to datum) was reached at 1210 GMT, which coincided with the tidal high water (Fig. 7.4). However, the highest waves (trough to crest) were recorded ~10 h later and were associated with a wave group (see Fig. 7.4 below). The water levels recorded at Geraldton during this event were the highest and lowest levels recorded at this station, which has been in continuous operation for more than 40 years; (3) The residual time series indicated the arrival of a group of waves with higher wave heights at Geraldton some 13-15 h after the arrival of the initial wave (Table 7.2) suggests a reflected wave from the island of Madagascar or the Mascarene ridge (Patti-aratchi and Wijeratne 2009); and, (4) the tsunami set-up seiching along the continental shelf with periods of 4 and 2.7 h at Geraldton and Fremantle, respectively (Fig. 7.4). These periods were the same as those excited by the meteorological effects (Sect. 7.3).

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