Coastal Engineering 53 (2006) 691–704 www.elsevier.com/locate/coastaleng Atoll lagoon flushing forced by waves ⁎ David P. Callaghan a, , Peter Nielsen a, Nick Cartwright b, Michael R. Gourlay a, Tom E. Baldock a a Division of Civil Engineering, The University of Queensland, Australia b School of Engineering, Griffith University, Australia Received 22 August 2005; received in revised form 22 December 2005; accepted 17 February 2006 Available online 19 April 2006 Abstract Water level and current measurements from two virtually enclosed South Pacific atolls, Manihiki and Rakahanga, support a new lagoon flushing mechanism which is driven by waves and modulated by the ocean tide for virtually enclosed atolls. This is evident because the lagoon water level remains above the ocean at all tidal phases (i.e., ruling out tidal flushing) and because the average lagoon water level rises significantly during periods with large waves. Hence, we develop a model by which the lagoons are flushed by waves pumping of ocean water into the lagoon and gravity draining water from the lagoon over the reef rim. That is, the waves on the exposed side push water into the lagoon during most of the tidal cycle while water leaves the lagoon on the protected side for most of the tidal cycle. This wave-driven through flow flushing is shown to be more efficient than alternating tidal flushing with respect to water renewal. Improved water quality should therefore be sought through enhancement of the natural wave pumping rather than by blasting deep channels which would change the system to an alternating tide-driven one. © 2006 Elsevier B.V. All rights reserved. Keywords: Atoll lagoon flushing; Hydrodynamics; Water quality; Wave pumping; Modelling; Wave set-up; Pearl farming 1. Introduction several wide reef flats which are elevated above MSL (mean sea level). Consequently, the lagoons are virtually disconnected There are two natural sources of power for flushing atoll from the ocean (Solomon, 1997). This configuration is quite lagoons: tides and waves. Their relative importance depends on different from the other atolls, also located in the northern the topography of the atoll rim as well as on the local wave and group, which have several deep reef passes that allow the ocean tide climates. If the atoll has wide reef passes, which are deep tide to drive the lagoon flushing. However, similar to Penrhyn, compared with the wave height and the tidal range, the flushing Cook Islands, the lagoon is used to grow black lipped oysters will be generated mainly by the tide and the lagoon water level for their black pearls, which is the primary source of income for will oscillate within the range of the ocean tide as shown in Fig. the Manihiki populace (McKenzie, 2004). The water quality 1b. If, on the other hand, the atoll has an almost unbroken rim of within the lagoon is therefore of great importance to the living coral growing to a few decimetres above mean sea level profitability of this industry. To increase the pearl yield from the (MSL), the flushing will be driven by the waves as shown in lagoon, the number of oysters has been increased leading to Fig. 1a. That is, the side facing the largest waves will have large several episodic large scale oyster deaths from disease directly amounts of water pushed over the reef rim while water will linked to poor water quality (Sharma et al., 2001; McKenzie, drain to the ocean on the leeward side. The tide will modulate 2004). This reduction in water quality has also increased the this process to a degree that depends on Atide /H, i.e., the ratio number of shells rejecting the seed (nucleus for pearl between the tidal amplitude and the wave height, Fig. 1a. development) or dying after being seeded. One method to The Manihiki and Rakahanga atolls (Fig. 2) are located in the overcome these problems is improving water quality by northern group of the Cook Islands. Both atolls consist of increasing lagoon flushing. This should however be done in a way which is in harmony with the natural system. This paper ⁎ Corresponding author. Tel.: +61 7 3365 3914; fax: +61 7 3365 4599. aims to provide understanding of the natural system before E-mail address: [email protected] (D.P. Callaghan). proposing methods to enhance the flushing. 0378-3839/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.coastaleng.2006.02.006 692 D.P. Callaghan et al. / Coastal Engineering 53 (2006) 691–704 Fig. 1. Two different lagoon flushing processes possible in atoll lagoons exposed to waves (with larger waves on the exposed coast compared to the leeward coast) and ocean tide. a. The wave-driven lagoon flushing process present at Manihiki and Rakahanga, illustrated by the elevated lagoon water surface level and the persistent one-way flow across the atoll. b. The tidal flushing process that occurs when deep and wide channels connect the ocean and the lagoon. Tidal flushing typically generates alternating flow patterns in the lagoon with the lagoon water surface variations contained within the ocean tide variations. The alternating flow patterns associated with tidal flushing give less water renewal than the wave-driven through flows. Panels c. and d. show the tidal ranges and relative position for the ocean and lagoon under wave-driven and tidal-driven flushing respectively. This paper demonstrates the mechanism of wave-driven models have been formulated which compare well with the field lagoon flushing occurring at Manihiki and Rakahanga atolls measurements. These models and the field measurements using observed lagoon dynamics. The processes observed were; demonstrate that as wave energy flux increases, the lagoon inflow driven by waves via the wave pump concept where the water level height above the ocean increases. This dynamic wave breaking lifts water onto the reef flats, well above the process is different to tidal flushing, where the lagoon ocean water level (Bruun and Viggoson, 1977; Nielsen et al., fluctuations are always contained within the ocean tide 1999, 2001), outflow controlled by critical flow conditions at variations. the leeward reef edge and gravity driving the flows across the This paper is arranged as follows. Section 2 describes the lagoon from the exposed to leeward coasts. Combining these field sites and measurements obtained during two field processes with the conservation of water volume, two new experiments. Sections 3 and 4 derive respectively an analytical Fig. 2. a. Location of the Cook Islands in the South Pacific Ocean; b. Manihiki and c. Rakahanga atolls of the Cook Islands. The grey shading indicates; land ( ), reef flats ( ) and lagoon ( ). Under normal wave conditions, water enters the lagoon via the reef flats only. However, during Tropical Cyclone Martin (1997), very large waves from the west overtopped the land at Tauhunu Village (western atoll coastline). The predominant wave and swell directions for both atolls are from easterly directions (Thompson, 1986). D.P. Callaghan et al. / Coastal Engineering 53 (2006) 691–704 693 and a numerical model. The wave flushing process is discussed and 40% of infragravity wave motion (periods between 25 and in Section 5 as it influences Manihiki and similar atolls. Final 250 s is recorded). To avoid aliasing when measuring at conclusions are communicated in Section 6. locations exposed to infragravity motion, five readings at 1-min intervals were taken and averaged to represent the mean water 2. Field data level at that time. During all field experiments, manual readings were taken throughout the collection period at between 10- and The ocean and lagoon water surface levels were obtained 30-min intervals between 7 am and 10 pm. This ensured that using co-located damped stilling wells similar to those water level measurements were obtained throughout the field described by Nielsen (1999) with time constants (τ)ofca100 experiment and avoided data loss due to instrument failure. s and self logging pressure transducers (in situ MiniTROLLs The stilling wells were installed to measure both ocean and advance). From Nielsen (1999) and laboratory testing, the lagoon water surface levels. To compare stilling well readings, stilling wells used act in a manner analogously to a linear filter the well tops were surveyed to a common datum established where the relation between actual and measured signals can be during the field investigation using a Topcon AT-G7 Auto written as Level. Permanent concrete structures were used to establish the arbitrary level datum. This survey was undertaken several times Bm þ ¼ ð Þ during the measurement period with survey closure errors s B m a 1 t (Muskett, 1995) ranging from 0 to 2 mm at Manihiki and from 1 where a and m are the actual and measured signals respectively. to 2 mm at Rakahanga to the common datum, which confirms The amplitude response function (FLF) for Eq. (1) is that the stilling wells did not move vertically during the measurement period and that the correct well top levels were −1 FLFðxsÞ¼ð1 þ ixssÞ ð2Þ measured with an accuracy of ±2 mm. The measuring scale is pffiffiffiffiffiffi graduated in 2 mm increments. Consequently, the accuracy of where i ¼ −1 and ω is the angular frequency. To measure the s manually read water levels is estimated at ±4 mm (i.e., response time constant, a half height test is preformed where the centimetre accuracy), excluding human errors. time ðt = Þ is measured for the water within the stilling well to 1 2 The self logging pressure transducers (PT) were logged at fall from its initial height above the filter to half that height. 20 s intervals, corrected for atmospheric variations (using an in Under this scenario, Eq.