How Do Rivermouth Waves Work?

Tony Butt

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Updated 22d ago

Estuaries are some of the most complicated and dynamic things on the planet. An estuary is the interface where a river meets the sea, and where a lot of important processes take place.

They have been studied by scientists from almost every angle possible, for example; the physics and mathematics behind the way the two water masses interact, the chemical interactions between the saltwater and freshwater, the biology of the flora and fauna that populate the interface and the geology related to the sediment transported by the river. Sometimes, new words such as ‘biogeophysical’ have to be invented when these disciplines inevitably cross over.

Forecast: Mundaka

Our Mundaka cam picking up Natxo Gonzalez on a recent massive swell.

If you are a surfer, estuaries are also some of the most interesting things in the world. Some of the most perfect, long and hollow waves exist at the mouth of rivers, thanks to sandbars created and maintained by the river, the tide and the waves. In upcoming articles I’ll be talking about specific rivermouth breaks, including the most iconic one, Mundaka. But I’m going to start by talking about the dynamics of a typical rivermouth sandbar, how it forms and what keeps it in place.

Healthy rivermouth sandbars are neither totally fixed nor totally mobile. They are in a state of dynamic equilibrium, maintaining more or less the same size and shape over the long term, but varying over the short term according to the conditions.

Various forces from different directions act on the bar to change it in the short term, but these forces balance out over time to keep it stable in the long run. During periods of small waves, the bar is built up by a combination of gentle wave action bringing sediment in from the sea, combined with river and tidal flows carrying sediment out from the land. Then, during big swells or storms the bar is eroded away, the much stronger currents and undertows from the bigger waves spreading the sediment over a broader area.

In relatively calm conditions (upper panel) the bar is built up, and in storm conditions (lower panel) the bar is eroded away.

In relatively calm conditions (upper panel) the bar is built up, and in storm conditions (lower panel) the bar is eroded away.

The way in which sediments get deposited onto the bar from the sea is similar to the way in which sandbars are formed on normal beaches. Just offshore of the breakpoint, there is a slight onshore-directed net movement of water.

As a result, any sediment scooped off the bottom outside of the breakpoint will be carried onshore. This mechanism is quite weak, but a lot of sediment can be built up during long spells of persistently small waves from the same direction.

Sediment is also deposited onto the bar from the landward side. This is usually a stronger mechanism than the one on the seaward side, the sediment being transported by the flow of the river and the outgoing tidal flow.

The effect that the tide has on the river gradually diminishes with distance upstream, until it becomes insignificant at some point, perhaps several kilometres inland. During the outgoing tide, the river and tidal flows are superimposed, resulting in a strong seaward-flowing current which scoops up sediment from the bed and deposits it onto the bar.

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To understand how the sediment from the river gets deposited on the bar, we need to introduce just two basic physical concepts: the conservation of mass and the threshold of sediment suspension.

The idea of conservation of mass is very simple. Imagine water flowing down a hosepipe, the water being supplied at a constant rate by a tap on the wall. The number of cubic centimetres of water coming out the end of that pipe every second (the volumetric flow rate) must match the number of cubic centimetres entering it from the tap every second, otherwise water would have to mysteriously appear or disappear in the pipe.

Now, if you squeeze the end of that pipe, the water will shoot out faster. This happens because the volumetric flow rate is maintained, and all those cubic centimetres of water must travel that much faster to get out through a smaller hole in the same time. The same applies if you make the opening bigger – the volume of water has a wider area to flow through, so it can spread itself out more and can afford to go slower. That, basically, is the conservation of mass. One can see it in action everywhere; in rips, wind blowing through buildings in a city, egg timers and traffic jams.

The principle of flow constriction and volumetric flow rate, using a traffic jam as a simple example.

The principle of flow constriction and volumetric flow rate, using a traffic jam as a simple example.

The other concept – sediment suspension threshold – is just as simple. Imagine water flowing along in a river where the bed is made up of some sediment. The water ‘rubbing’ on the bed produces turbulence which lifts the sediment up and suspends it in the water.

At the same time, the sediment tries to fall back down under the force of gravity. But if the turbulence is strong enough, it will keep the sediment in suspension. For the turbulence to be strong enough to do this, the water flow must be above a certain velocity. That velocity is the threshold of sediment suspension. If it goes below that threshold, the force of gravity will overcome the turbulence, and the grains will drop back down to the bed.

Related: What is Wave Refraction?

Now, if you are still with me, we can combine these two principles and apply them to an estuary. The water flowing fast over the bed, particularly on the outgoing tide, scoops the sediment off the bed and keeps it suspended in the water column.

The river continues to pick up sediment as it flows towards the sea, and the flow velocity is fast enough that the sediment doesn’t drop to the bed (the velocity is above the threshold of suspension). At the mouth of the estuary, the width of the river increases. To conserve the volumetric flow rate, the flow velocity must therefore decrease. As soon as the velocity decreases below the suspension threshold, the sediment drops to the bed. As a result, the sediment accumulates in one place, to form a bar.

Top view and side view: the sediment stays in suspension in the fast-flowing river, but falls out of the water column as soon as the flow decreases at the mouth of the estuary.

Top view and side view: the sediment stays in suspension in the fast-flowing river, but falls out of the water column as soon as the flow decreases at the mouth of the estuary.

Cover shot by Jon Aspuru