Virtual sediment particles in motion

The Cappuccino Effect

Do you ever think about the swirling patterns in your cappuccino as you stir your spoon around, the brown coffee folding in past the white foam? And do you ever think about sediment transport as you do it? Just me? Ok, never mind…

I had the great privilege of hanging out in New Orleans this past week, being a sand nerd with four hundred of my fellow sand nerds at the Coastal Sediments conference. In between jazz sets at the Spotted Cat, we shared our latest ideas about coastal dynamics, built new collaborations, and rekindled old pre-pandemic friendships. My contribution this year was an attempt to bring the science behind cappuccino coffee swirls to coastal sediment transport.

Much of my research focuses on how we can identify sediment transport pathways at tidal inlets and ebb-tidal deltas. Knowing how sand moves around the Dutch coast is important to preserving its robustness against climate change. But why do we see the patterns that we see? Is there some underlying structure that can explain why sand goes where it does?

Summary of major sediment pathways at Ameland ebb-tidal delta, circa 2017 [Source: Pearson, 2022]. Why do we see these particular patterns? Is there some underlying structure to the pathways that can help us make explain it?

Our current hypothesis is that Lagrangian coherent structures (LCS) in the sediment transport velocity field might underlie the patterns that we see.

Hang on, Stuart, I can hear you saying.


Lagrangian coherent structures are often defined as something along the lines of “robust skeletons of material surfaces”, but frankly that’s also quite unhelpful. Enter the cappuccino: these swirls represent the boundaries between distinct fluid masses (i.e., coffee and milk foam). In much the same way, we can sometimes see distinctive boundaries between masses of water with different characteristics, like saltiness, temperature, or the amount of sediment suspended in them. We call these boundaries “fronts”, much like the fronts in weather systems (“there’s a cold front coming through…”).

Back in 2017, I was out in a boat collecting field measurements at Ameland Inlet when my colleague Ad Reniers said, “oh look, a front! Stick your hand in the water!” We approached a long foamy streak across the surface of the water, and as we crossed it, the temperature of the water changed noticeably. How is it that the character of the water could contrast so much over such a short distance? We had passed the boundary between two different masses of water, one heated up in the shallow Wadden Sea, and the other colder from the North Sea. This was my introduction to the world of estuarine fronts, and marked the beginning of a long fascination with these curious patterns.

Beautiful cappuccino swirls of suspended sediment at Ameland Inlet in the Netherlands. The white streaks in the centre of the inlet channels are estuarine fronts, where two or more different masses of water converge at the surface and collect floating seafoam (which is mostly algae snot, but that’s another story…) [Source: Sentinel 2].

If you spend enough time by the sea, you will notice fronts all over the place (even out the window of your airplane!). They are especially apparent if you look at estuaries and river mouths in Google Earth. In recent years, people have begun to analyze these fronts, since their presence or absence has consequences for how water, sediment, and other floating things mix near the coast. For instance, my friend Daan Kuitenbrouwer has found that these fronts can act as a barrier to oil spills and stop or delay them from reaching the shore.

Lagrangian coherent structures off the coast of Labrador made visible by floating sea ice fragments, seen as I was flying to the conference last week. The nearshore area to the left is much icier, and when it meets the ice-free open ocean, the surface currents converge, clustering and swirling the ice in streaks and filaments. Once you learn about these patterns you start seeing them everywhere!

I never had time to work on this topic during my PhD, but once I began my postdoc I turned up at Ad’s office door and we embarked on our little side project. Using the SedTRAILS model that my colleagues at Deltares and I are developing, we tried to see if these Lagrangian coherent structure or front patterns corresponded to sediment transport pathways.

We found that these LCS reveal hidden barriers to sediment transport and zones of sediment mixing, accumulation, or dispersal. This gives us a new way to explain why sand from a particular place ends up somewhere else, and how it interacts with sediment from other sources.

We are excited to develop these ideas further because we can see many potential applications to coastal management. For instance, how do these barriers to transport influence dredging operations? When and where should we place dredged sediment such that it won’t immediately return to the navigation channel? Can we feed intertidal flats by strategically timing releases? Can we avoid deposition in ecologically-sensitive areas? LCS also present many new opportunities for testing hypotheses about the patterns underlying sediment transport pathways.

Check out our conference paper below or my presentation if you are interested!

P.S. For a more detailed explanation of the math behind these beautiful patterns, check out Steve Brunton’s excellent video on Finite Time Lyapunov Exponents (from which I drew much inspiration for my own conference presentation).

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