I seem to have spent a lot of time around boils over the past few months.
The most obvious features of a tide race are its waves and eddy lines. These are the things that we tend to spend time teaching people to deal with: breaking in/out, crosses and surfing. But as tide races get more energetic, some other features start to become prominent - whirlpools and boils. Whilst whirlpools tend to form somewhat predictably as eddy lines widen, boils turn up all over the place. And how you deal with them can often be the difference between successful and unsuccessful moves.
Boily eddy by the south pier of the bridge at the Falls of Lora. Negotiating the boils is the key to getting onto the wave.
Boils seem to be ubiquitous features on tidal flows - from small energetic ones like in the photo above to large and more gentle upwellings in lazier flows.
But what causes boils in the first place? It's fairly obvious that they're caused by water moving upwards - but why does that happen? I remember being told years ago that water was simply pushed upwards by underwater obstructions. I'm sure this happens in some places, but it doesn't explain boily eddies or trains of boils forming in certain parts of channels, nor how boils occur in deep water where you might expect such a disturbance not to propagate to the surface.
It turns out that this question isn't one that's been fully studied - especially not for the sort of fast flows that occur in races. But the scientific literature has some good explanations for at least some of the boils that we see, and it hints at what might be happening more broadly. And it may be more complicated than you imagine....
Kolk boils
Near the seabed, even under a fast-moving flow, the water is almost stationary. The speed rapidly increases with distance from the bottom across what's known as the 'boundary layer'. This rapid change in water speed creates unstable, turbulent conditions, with fast-moving water moving down closer to the seabed and slow moving water popping into the faster water at random positions.
Imagine what happens if some slow moving water pops up into the faster water above - the fast water will smear it along into an elongated 'hump' of slow water [1]:
As a result 'streaks' of slow moving water form, aligned with the flow.
The rapid change in speed has a second effect - and it's one that's ubiquitous in fluid mechanics - the formation of vortices. Imagine holding a pencil between your palms and moving your hands relative to each other - the pencil rotates. In the same way, layers of fluid moving at different speeds tend to cause packets of fluid to start rotating. The image below shows vortices forming at the interface of 2 fluids, one coloured with a dark dye, that are moving at different speeds [2]:
What happens when these two effects - streaks of slow fluid and vortex creation - occur together? The vortex still forms at the boundary between slow and fast flows, but to do this it has to arch over the streak of slow flow. And, of course, the top of it tends to get swept downstream by the faster flow [3]:
These rotating tubes of fluid are known as 'horseshoe' or 'hairpin' vortices for obvious reasons, or by the Dutch term 'kolks'. The image below shows hairpin vortices forming in a boundary layer over a plate, as seen from above [2]:
Notice that because of the rotation direction of the horseshoe vortex, fluid in the centre of the vortex is moving upwards. Like many vortices, the horseshoe vortex is a fairly stable structure, so it tends to retain its swirling motion as it gets lifted from the seabed and moved off downstream. Eventually some, but not all, horseshoe vortices reach the sea surface, where the water moving upward from the centre of the horseshoe appears on the surface as a boil [3]:
Often, the horseshoe vortices are formed at downstream-facing steps in the seabed - so counterintuively, many boils have their origins in holes in the seabed rather than protrusions. However, horseshoe vortices can form even on a smooth seabed, although it is likely that boils formed in the absence of seabed irregularities are weaker [4].
It's been suggested that the diameter of these boils is about half the water depth and that they'll tend to appear in downstream lines with a distance between each boil equal to about twice the depth [3].
Boils due to secondary flows
A second mechanism for boil formation is secondary flows. Channels of moving water often have some form of helical flow rotating around the downstream direction. Rivers often have a single rotation around the stream, especially at bends in the river. In wider channels, cells of rotating flows moving in opposite directions can form [5]:
Note that the cell widths are about the same as the depth, and areas of upwelling boils occur at distances downstream separated by about twice the depth. Closer examination of this sort of flow reveals that it may actually be less regular than the diagram above, with circulations driven by horseshoe vortices forming at the boundaries between the cells, pushing fluid upwards [6].
Other boils
Vortices are ubiquitous in nature, occurring wherever layers of water flowing at different speed contact. Although it doesn't seem to have been studied by scientists, I suspect that all sorts of vortex phenomena result in boils.
One example that paddlers are probably more familiar with than academics is the eddy line. Given that eddy lines are areas where flow speed changes over a short space, it's no wonder that they're associated with vortex generation - and many sea kayakers will be well aware that boils often occur at and near eddy lines.
The image below [7] shows streamlines of an eddy from above, and across a series of cross-sections of the flow at the lines indicated in red:
The diagram isn't the simplest thing to understand - but hopefully the outline of an eddy will be familiar! The sections show a vortex with its axis running downstream, and rotation clockwise as viewed from downstream, forming near the bottom of the channel at the upstream end of the eddy. The vortex rises in the flow as you look further down the eddy line, hitting the surface and disappearing around the last section line. The streamlines in the sections indicate a lot of vertical flow near the eddyline, so it's wouldn't be surprising to see boils form where the water is being forced upwards, and where this vortex meets the surface.
The top image shows how much the water level moves up and down over time. Notice that there are significant variations in the region around the eddy line, likely due to periodic upwelling and boils.
References/images
1: "Streaks in turbulence" Chernyshenko, S.I. web page. See also: Chernyshenko, S. I., and M. F. Baig. "The mechanism of streak formation in near-wall turbulence." Journal of Fluid Mechanics 544 (2005): 99-131.
2: Van Dyke, Milton, An album of fluid motion. Vol. 176. Stanford: Parabolic Press, 1982.
3: Rashidi, Mehdi. "Burst–interface interactions in free surface turbulent flows." Physics of Fluids 9.11 (1997): 3485-3501.
4: Nakagawa, Hiroji, and Iehisa Nezu, eds. 1993. Turbulence in Open Channel Flows. 1st edition. CRC Press.
5: Imamoto, H., and T. Ishigaki. "Visualization of longitudinal eddies in an open channel flow." Flow Visualization IV: Proceedings of the Fourth International Symposium on Flow Visualization. Washington, DC: Hemisphere, 1986.
6: Adrian, Ronald J., and Ivan Marusic. "Coherent structures in flow over hydraulic engineering surfaces." Journal of Hydraulic Research 50.5 (2012): 451-464.
7: Jeon, Jeongsook, Ji Yong Lee, and Seokkoo Kang. "Experimental investigation of three‐dimensional flow structure and turbulent flow mechanisms around a nonsubmerged spur dike with a low length‐to‐depth ratio." Water Resources Research 54.5 (2018): 3530-3556.