If there was any doubt left that coastal sand accumulations called ‘chevrons’ are *not* related to gigantic tsunamis (see previous thoughts on the subject here and here; Ole also has a recent blog post, and see a news release here), the May issue of Geology provides additional arguments to show that this is the case. Joanne Bourgeois of University of Washington and Robert Weiss of Texas A&M University, both experts in the sedimentology of tsunami deposits, present two lines of arguments. First they show that the orientation of the Madagascar chevrons is significantly different from what is predicted through modeling the tsunami. While the tsunami wave tends to hit the coast with an overall perpendicular orientation, due to wave refraction, the ‘chevrons’ are oriented at various angles to the coast, angles that are more consistent with predominant wind directions. Second, they look at the sediment transport conditions and suggest that even coarse sand must have been in suspension in flows deep enough to create the chevrons. However, dune-like bedforms cannot develop without sediment being transported as bedload; therefore, the bedforms must have a different origin than mega-tsunamis. The obvious alternative is parabolic dunes; these well-known bedforms show up when vegetation partially covers the dune’s tails and slows down sediment transport. The authors don’t hesitate to draw the conclusion that

The extraordinary claim of “chevron” genesis by mega-tsunamis cannot withstand simple but rigorous testing.

I am far from being a tsunami expert, but I find this subject fascinating. The issue of suspended load vs. bedload and stratified or laminated vs. graded bedding is equally important for deposition from tsunami waves and turbidity currents. It is worth spending a bit of time and blogspace to explore the kind of analysis of sediment transport conditions that this paper presents.

Although I see no reasons to disagree with the paper’s conclusions (as it could be predicted from my previous posts on the subject), at first reading I didn’t fully understand the line of reasoning about suspended load vs. bedload. So here goes my attempt to understand it.

The argument goes as follows. The Rouse number is the ratio between the settling velocity of a certain grain size and the shear velocity of the flow, multiplied by von Karman’s constant (which is ~0.4): Ro = ws/k*u_shear. For a grain of a given size, if the Rouse number is larger than 2.5, the grain’s settling velocity is much larger than the upward-directed component of the turbulence, and the grain tends to stay close to the bottom, in the bedload. [This is equivalent to saying that the settling velocity has to be larger or equal to the shear velocity, a condition also known as the suspension criterion]. If the Rouse number is less than 0.8, the flow is turbulent enough to keep the grain fully suspended. In between these values, there is a zone of transitional behavior. For the flows that might have deposited the chevrons, the Rouse number is always less than 2.5, regardless of how the other parameters like the Froude number, grain diameter, and roughness length are varied. Although the authors state that the flows must have been deeper than 8 m (because most chevrons are higher than 4 m, and the flow must be at least twice as high as the bedform), there seems to be no other constraint on tsunami behavior [note that I did not have access – yet – to the supplementary web material].

So the question is: doesn’t this reasoning apply to other types of flows as well? For example, the Mississippi River is certainly deeper than 8 m in many places — does this mean that it is able to suspend very coarse (2 mm diameter) sand? In other words, what is the difference between flow in a tsunami run-up and the Mississippi River? The answers might be obvious to many, but they are certainly not obvious to me.

One thing we can do is to create a different kind of plot: instead of plotting the Rouse number against flow depth, let’s plot velocity vs. depth. I have a better feeling for what are reasonable velocities for different kind of flows than I do for Rouse numbers. The Rouse number would form the third dimension of the plot; one can visualize that as a contour map of Rouse numbers as a function of flow depth and velocity:

The Rouse numbers shown in this plot are valid for a grain diameter of 2 mm and roughness length of 1 m (using the same equations for settling velocity and shear velocity as in Bourgeois & Weiss 2009). Anything coarser than this cannot be called sand any more. So if this grain size doesn’t stay in the bedload, there is no chance for finer sediment either. It is obvious from the plot that, for flows deeper than 8-10 m, very coarse sand will be part of the bedload unless flow velocity is larger than ~5 m/s. The Mississippi River at New Orleans has velocities on the scale 1.5 m/s, so 1-2 mm sand should definitely stay close to the bottom, and in fact it does.

We know however that tsunamis are not exactly tranquil flows like the big old Mississippi at New Orleans. The larger ones are fast and furious and Google Earth might need massive updates after they rearrange entire coastal landscapes. [Don’t get me wrong, I am not trying to diminish the power and destructive force of the Mississippi.] In other words, the Froude number of a tsunami run-up is larger than the Froude number of the Mississippi River. The Mississippi is relatively slow and deep; the tsunami is fast and relatively shallow. The Froude number is the ratio between velocity and the square root of gravity multiplied by flow depth:

Fr = u/√(g*d)

This number for the Mississippi is much less than one (these flows are called subcritical flows). On the other hand, tsunamis are waves of very large wavelengths, and they behave even in the open ocean as shallow water waves (wavelength 20 times larger than water depth). For these kinds of waves, the velocity is solely a function of water depth:

u = √(g*d)

If we assume that the tsunami run-up has a comparable velocity to that of the tsunami wave in the nearshore zone, we find that the Froude number of the run-up must be around 1. This is obviously a very back-of-the-envelope argument, but the point is that these flows must have in general relatively large Froude numbers. If we plot the lines for Fr = 1 and Fr =1.5 on the depth-velocity diagram (see above), we can see how different likely tsunami behavior is from that of large rivers. It also becomes evident that even coarse sand would not be part of the bedload in these flows, especially not in flows deep enough to build the ‘chevrons’. Which means that sandy tsunami deposits are likely to be largely unstructured or poorly structured sand sheets rather than several m thick accumulations of cross-bedded sand.

And that ends my Saturday exercise in Fluid Mechanics 101.

Reference

Bourgeois, J., & Weiss, R. (2009). “Chevrons” are not mega-tsunami deposits–A sedimentologic assessment Geology, 37 (5), 403-406 DOI: 10.1130/G25246A.1

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