Equations of motion for post-mortem sinking of cephalopod shells

Abstract

We have modified our equations of motion for sinking Nautilusshells to a more general form suitable for application to fossil cephalopods. The new equations incorporate the effects of hydrodynamic stability and loss of buoyancy due either to the unrestricted entry of water into the shell during sinking, or to entry by diffusion across the wall of the siphuncular tube. With our new equations it is possible to calculate sinking velocity and pressure across the shell wall as a function of depth for shells of any size and shape. Our system provides a means of analyzing several aspects of the post-mortem history of cephalopod shells including vertical preservation. In the latter case, our equations enable us to find water depth from the geometry of a vertically preserved shell. We calculate the maximum water depth of the Hauptmuschelkalk beds (Triassic, south-central Germany) to have been about 3 m. Our method is unique in providing a way of obtaining numerical values for maximum water depth of ancient sediments and sedimentary environments. These equations also offer the possibility of examining the paleoecology and paleobiology of the living animals, especially with respect to swimming ability and vertical migration.