flow when the mean water level is at or below the reef flat (Gourlay 1996a,b). In the latter situation, wave breaking occurs on the reef front and wave‐driven flow is due to swash running up and onto the reef flat.
When the depth over the reef is shallow, flows will be weak due to the friction of the reef flat, whereas if water is deep over the reef, flows will be weak because of limited wave breaking (Hearn 2011). There will thus be a water depth at which the wave‐driven flow is maximum. Tidal variations also induce variations in mean flows over a reef as tides will vary the water depth over the reef front and reef flat thereby affecting water flow. For instance, in the Puerto Morelos fringing reef lagoon off Mexico where tides are small, surface wave‐induced flow is the predominant flux with some influence from the Yucatán Current (YC) and trade winds (Coronado et al. 2007). The wave flow regime is modulated by the presence of the YC offshore. Similarly, cool, clear water flow up onto the flat of the fringing coral reef off the south coast of Molokai, Hawaii, during flood tide (Storlazzi et al. 2004). At high tide, sediment resuspension increases due to greater wave energy being available to propagate onto the reef flat. Trade‐wind driven surface currents and wave breaking at the reef front cause increasing water depth on the reef flat, enhancing the development of depth‐limited waves and sediment resuspension. As the tide ebbs, water and suspended sediment flow off the reef flat and is advected offshore and to the west by trade winds and tidally driven currents. Thus, the muddy, shallow reef flat is linked to suspended sediments on the deeper reef front where coral growth is maximal.
Each coral reef is unique, but water flow on all reefs conforms roughly to the same general pattern of water flow impinging on the reef front and flowing over the reef flat and attenuating into a lagoon or back reef. Water circulation in reef lagoons is rapid compared to adjacent oceanic waters, but reef lagoons are quiescent and usually deep enough to accumulate unconsolidated carbonate mud and sand deposits.
Water circulation in and around coral reefs thus depends greatly on reef type and geomorphology. Reefs fringing a shoreline such as the fringing reefs of Pago Bay, Guam, have a simpler hydrology than an individual oceanic reef; water flow on the Pago Bay reefs is driven mainly by wave height in the reef flat and channel (Comfort et al. 2019). Wind and wave directions that are directly across‐shore contribute to faster flow speeds throughout the bay. On the fore reef, wave height is the strongest predictor of current speed, but wind direction has a strong influence on current direction. Flow in the channel and on the reef flat is more tightly tied to environmental factors of wind and waves than flow on the fore reef. Cold pulses around the slopes of the island indicate large internal waves that result in periodically cool deeper areas of the fore reef.
3.6 Fluid Mechanics in Seagrass Meadows
Seagrasses, like their mangrove and coral reef counterparts, are ecosystem engineers capable by their very existence of reducing the velocity of currents and attenuating waves to the extent that sediment particles can deposit on surfaces and on the seabed in quiescent zones (Peterson et al. 2004). Other factors play important roles in helping to accumulate carbon in seagrass meadows, such as canopy complexity, turbidity, wave height, and water depth (Samper‐Villarreal et al. 2016). But the essence of what drives the accumulation of sediment particles and associated carbon is fluid dynamics. The movement of water among, between and around seagrass blades is the key feature of carbon capture (Koch et al. 2006).
The main source of energy required to move water is the sun that causes winds that lead to waves and thermal gradients that in turn lead to expansion, mixing, and instabilities in water gradients and thus flow. Seawater, being an incompressible fluid, moves at a flow rate that is defined by the velocity of the fluid that passes through a cross‐sectional area, A. Water flow leads to both hydrostatic and dynamic pressures which are a constant. What this means in practical terms is that the sum of the pressures helps to explain lift that occurs within, around and under seagrass canopies. Drag is another force that operates in the case of water motion and has two components: (i) viscous drag that exists due to the interaction of the seagrass surface with the water and (ii) dynamic or pressure drag that exists under high flows when flows separate from boundaries (Koch et al. 2006).
Water flow can be either smooth and regular (laminar flow) or rough and irregular (turbulent flow), depending on the velocity and temporal and spatial scale under investigation as defined by the Reynolds number:
(3.1)
where l is the length scale under observation and v is the kinematic viscosity. Re defines four flow regimes that may occur: (i) creeping flow where Re < < 1 which occurs at very slow flows and spatial scales such as those experienced by microbes, (ii) laminar flow (1 < Re < 103) which is smooth and regular, (iii) transitional flow (Re ≈ 103) which involves the production of eddies and disturbances in the flow, and (iv) fully turbulent flow (Re > > 103). These flows are scale‐dependent; flow is almost always turbulent across entire seagrass meadows, but laminar at the scale of individual seagrass leaves (Koch et al. 2006).
Flow conditions become more complex when water approaches a boundary, such as the seagrass canopy or seafloor. Water cannot penetrate such boundaries, but slips by it, a condition which leads to the development of a velocity gradient perpendicular to the boundary as the velocity at the boundary will be zero relative to the stream velocity. As water flows downstream, the velocity gradient will get larger and a slower moving layer of water will develop next to the boundary. Vertically, there is a sublayer in which the forces are largely viscous. Consequently, mass transfer in this layer is slow, dominated by diffusion, in what is called a diffusive boundary layer. Such boundary layers can become embedded within one another such that it is possible to define boundary conditions around blade epiphytes, flowers, leaves, and the canopy.
At the molecular level, a boundary layer develops on the sediment surface as well as on each leaf, shoot, or flower as water flows through a meadow. The faster the water movement, the thinner the diffusive boundary layer and thus the transfer of molecules (e.g. CO2) is faster from the boundary layer to the water column. When currents are weak, the flux of molecules may be diffusion‐limited, but after a critical velocity is reached, the transfer is no longer limited by diffusion but by the rate of assimilation capacity (i.e., biological or biochemical activity). The mass transfer of molecules also depends on other factors, such as the thickness of the periphyton layer on the seagrass leaves, reactions within the periphyton layer, and the concentration of molecules in the water adjacent to the leaf‐periphyton assemblage.
At the scale of shoots (mm to cm), a feedback mechanism operates as individual shoots are affected by other shoots and its position within the canopy (that is, edge versus centre of the entire meadow). As water velocity increases, shoots bend minimising drag, but the forces exerted on individual shoots are more complex when waves are involved, as a shoot is exposed to unsteady flows in different directions. This is confirmed by the fact that in wave‐swept environments, seagrass leaves become longer as wave exposure increases (de Boer 2007). Flow around shoots results in bending but also pressure gradients on the leeward side of the leaf such that a vertical ascending flow is generated downstream of the shoot. This water then disperses horizontally at the point where the leaves bend over with the flow; interstitial water is also flushed out at the base of the shoot due to the pressure gradients generated on the sediment surface.
At the whole‐canopy level, reduced flows occur within the canopy due to the deflection of the current over the canopy and loss of momentum within the canopy. Water speed as a result can be two to >10 times slower than outside the meadow. It is this process that allows water and sediment particles to be trapped during low tide; even short seagrass canopies can reduce water velocity. Vertically, however, water flow intensifies at the height of the sheath or stem as these parts are much less effective at reducing water velocity compared with the leaf component. Canopy flow is nevertheless
