Taphonomy and time-averaging of marine shelly faunas

The stratigraphy of shell concentrations.

The study of the motion of flat bodies falling in a viscous mediumdates back at least to Newton1 and Maxwell2, and is relevant to problems in meteorology3, sedimentology4, aerospace engineering1 and chemical engineering5,6,7,8. More recent theoretical studies9,10,11,12 have emphasized the role played by deterministic chaos, although many experimental studies1,5,6,7,8,13,14 were performed before the development of such ideas. Here we report experimental observations of the dynamics of disks falling in water/glycerol mixtures. We find four distinct types of motion, which are mapped out in a ‘phase diagram’. The apparently complex behaviour can be reduced to a series of one-dimensional maps, which display a discontinuity at the crossover from periodic to chaotic motion. This discontinuity leads to an unusual intermittency transition15, not previously observed experimentally, between the two behaviours.

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Chaotic dynamics of falling disks

Sediment movement under unidirectional flows: an assessment of empirical threshold curves

Taphonomic signature as a function of environmental process: Shells and shell beds in a hurricane-influenced inlet on the Texas coast

An experimental and theoretical examination has been made of the settling, entrainment and overturning of 176 valves representing 16 common Northwest European marine bivalve species, together with a comparative study of 15 plastic models in the form of segments from cylindrical tubes.



Settling behaviour in both stagnant and moving water depends on particle mass, symmetry and concavo-convexity. Separated empty bivalve shells spin and spiral while settling and, if sufficiently elongated, also pitch. At the observed Reynolds numbers, the shells and models fall concave-up, the terminal fall velocity increasing as the square root of the unit immersed mass or weight. The drag coefficient is independent of Reynolds number but increases with surface roughness and, particularly, particle elongation. Turbulence slightly lowers the critical elongation for pitching.



A separation vortex lies captive on the upper side of each descending particle. Consequently, an empty bivalve shell traversing a suspension of sand traps grains on its upper side at a rate proportional to their volume concentration and terminal fall velocity. This process, increasing the effective shell mass, is limited only by the capacity of the shell and grain spillage due to the possible onset of pitching.



The ratio (non-dimensional) of a quantity proportional to the applied fluid force and the particle unit immersed weight consistently describes the entrainment of concave-up and convex-up particles, and also the immediate overturning of a valve on settling concave-up to the bed. These thresholds vary in relative magnitude with bed-particle friction and particle concavo-convexity. In general, convex-up particles are the most stable; the concave-up entrainment and overturning thresholds are of a substantially lower but similar magnitude. The high frequency of concave-up bivalve attitudes in turbidites is understandable largely in terms of the ability of a settling valve to increase in effective mass by grain entrapment. Convex-up attitudes in the lower parts of turbidites may record currents stronger than the overturning threshold.

J. R. L. Allen

Papers

Experiments on the settling, overturning and entrainment of bivalve shells and related models