Seiching in Cockburn Sound by Emma Molloy Department of Environmental Engineering University of Western Australia November, 2001 Abstract A seiche is the oscillating response of an enclosed or semi-enclosed water body to external forcing, in order to return the system to equilibrium. The disturbances that cause seiches can be a variety of atmospheric and water-based mechanisms, including wind, air pressure, waves and tsunamis. In semi-enclosed micro-tidal water bodies such as Cockburn Sound, the prime mechanisms driving seiches are changes in wind speed and direction (Luettich et al, 2000). Cockburn Sound is a north-south oriented oval-shaped harbour system located 35 km south of Perth, Western Australia. It is enclosed on all sides by land, with a large opening on the north-east side. This opening facilitates water exchange to the north of Cockburn Sound. However, to the west there are reefs restricting flow. Therefore, the seiches oscillate between Mangles Bay in the south of Cockburn Sound and Fremantle. This is considered to be a semi-enclosed (“open”) system. Cockburn Sound houses a large variety of industry, as well as marine and bird life, and is used by the public for recreation. The seiches in Cockburn Sound have an impact on all of these areas. The primary effect of seiches is in influencing the mixing and flushing of the system, especially of contaminants released by the industries. Water level data were collected from Mangles Bay at the southern end of Cockburn Sound during May 2001. Water level data were also available from previous studies in this area. Meteorological data, including wind speed and direction and atmospheric pressure, were obtained from the Bureau of Meteorology. Spectral plots of the water level data from all the locations indicated peak at 2.8 – 3 hours, assumed to be due to seiches. The water level and meteorological data were closely examined to determine the mechanisms responsible for causing seiches and changing the seiches that were already present. The general patterns that were observed are that: • The wind direction changing is the primary cause of seiches in Cockburn Sound. • Various factors, such as the wind speed, atmospheric pressure, and total water level, will influence the magnitude of the seiches generated. • A change in wind speed of a least 2 m/s may also change the water level oscillations. • During spring and summer, when there is a diurnal wind pattern, the seiches vary diurnally in amplitude. They may also be influenced by the diurnal variation in total water level associated with tides. Data from other locations in the Perth area indicated that the seiches generated propagate up the coast from Mangles Bay at least to Two Rocks Marina, and up the Swan River to at least Barrack Street Jetty. The celerity of the seiche was calculated to be 9.5 m/s. The seiche was expected to have a node at Fremantle. However, this was not observed. Further work needs to be done in this area to determine the mode and limits of the seiche that travels along the west coast of Western Australia. Also, other forcing mechanisms that may have an influence on the seiches in this area should be studied. Table of Contents Literature Review and Background Information 1 1 Introduction to Seiches 1 1.1 What Are Seiches? 1 1.2 How Seiches Form 2 1.3 The Theoretical Study of Seiches 4 1.4 The Effects of Seiches 7 1.5 Observing Seiches 8 2 Introduction to Cockburn Sound 11 2.1 Forcing Mechanisms in Cockburn Sound 12 2.1.1 Remote Mechanisms 12 2.1.2 Local Mechanisms 13 2.2 The Local Climate 15 2.3 Other Important Influences 15 2.4 The Importance of Understanding Seiches in This Area 17 3 Methodology 19 3.1 Field Work – Data Collection 19 3.2 Data Transformation 23 3.3 Data Analysis 25 4 Results and Discussion 29 4.1 Spectral Analysis 29 4.2 Time Series Analysis 37 4.3 Correlations Between Data Sets 43 4.4 James Point 2000 Seiches 45 4.5 Mangles Bay 2001 Seiches 47 4.6 Wind Direction Changing from South to North 51 4.7 Wind Direction Changing from North to South 55 4.8 Wind Direction Changing between East and West 57 4.9 Wind Speed Changes 59 4.10 Estimating the Friction in this System 63 4.11 1995 Data Seiches 65 4.12 Cross-Spectral Analysis 69 5 Conclusions 73 6 Recommendations for Further Work 75 References 77 Literature Review and Background Information 1 Introduction to Seiches 1.1 What Are Seiches? A seiche is the oscillating response of an enclosed or semi-enclosed water body to external forcing. A free seiche occurs when there is an initial force that disturbs the water level in a system. When the initial force stops, the water level changes in the opposite direction to that imposed by the initial force, in an attempt to return the system to equilibrium. However, the inertia of the water carries the system past equilibrium. The water level then continues to oscillate about the equilibrium level at a period characteristic of the system (Sorensen, 1978). This “natural period” depends on the length and depth of the basin (Sorensen, 1978). The magnitude of the initial force only influences the magnitude of the oscillations (Sorensen, 1978). Free seiches decay exponentially due to friction, if the forcing is not repeated (Sorensen, 1978). A forced seiche occurs when the forcing event is cyclic, but with a period different to the natural period of the system (Sorensen, 1978). This causes the water level to oscillate at periods that are closer to the period of the forcing than to the natural period of the system. There is resistance to oscillation at these periods, so work must be done to maintain a forced seiche (Wilson, 1972). The oscillation of a seiche is a special case of a standing wave, which may be considered as the addition of two identical waves travelling in opposite directions. The interactions of these waves result in nodes and antinodes. Nodes are points where there is no vertical movement of the water surface, but there is maximum horizontal movement. Nodes occur at openings to basins (van Rijn, 1994). Antinodes are points where there is maximal vertical movement of the water surface, but there is no horizontal movement. Anti-nodes occur at points where the seiche is reflected off a surface (van Rijn, 1994). For example, anti-nodes are present at the closed end of a basin. Seiches can occur in various wavelengths for each water body. This results in different numbers and locations of nodes and antinodes (figure 1). Page 1 Literature Review and Background Information Figure 1.1: Different modes of oscillation of seiches in a rectangular basin of uniform depth. (a) uninodal; (b) binodal; (c) trinodal; (d) quadrinodal; (e) quinquinodal; (f) sextinodal; (g) septuanodal; (h) plan view (from Wilson, 1972). 1.2 How Seiches Form Seiches can only form in systems where the standing wave can reflect off of something at each end. A typical example of this is a closed basin such as a lake. Seiches can also occur in semi-enclosed systems such as harbours that are mostly enclosed, with an opening at one end. A semi-enclosed system may have an abrupt change in bathymetry that the seiche is reflected off. The causes of seiches are various. In both lake and harbour systems, seiches can be caused by: 1. The passage of small barometric fluctuations, associated with the general system of isobars, with a period close to the natural seiche period of the system. Page 2 Literature Review and Background Information 2. A rapid change in air pressure due to a squall. 3. The impacts of wind gusts on the water surface. 4. A lapse in strong onshore winds, causing pent-up water at the shore to be released. 5. Heavy rain, snow or hail over a portion of the water body. 6. Flood discharge from a river at one end of the system. 7. Tilting or movement of the lake or sea bed resulting from seismic movement of the earth due to earthquakes. (Chrystal, 1908-1909) For both coastal and lake seiches, meteorological causes are the most important (Wilson, 1972). However, coastal seiches have other causes as well. The first of these is long-period ocean waves. A harbour will respond to long-period waves that have the same period as the natural resonance of the harbour (Wilson, 1972). However, seiches are also proposed to respond to long waves of very low height, which are hard to detect (Wilson, 1972). This response is not well understood. Long-period ocean waves can be generated in three ways. The first is a combination of variable wind stress and atmospheric pressure fluctuations. It is theoretically possible for long-period waves to be generated by moving pressure disturbances. However, the identification of waves generated this way is difficult due to the various wave spectra close to the shore, including surf beat and seiches. (Wilson, 1972). Long-period ocean waves can also be generated by surf beat. These long-period waves are predominantly in shallow water, moving shoreward. They are produced by the radiation stress resulting from ordinary waves breaking on the beach. Seiches also occur during periods of high swell. These seiches may be caused by long-period waves induced by the swell, which cannot otherwise be seen. (Wilson, 1972). The third way in which long-period ocean waves are generated is by seismic disturbances of the ocean bed (Wilson, 1972). These long-period waves are known as tsunamis.