Hydrodynamic-driven stability analysis of morphological patterns on stalactites and implications for cave paleoflow reconstructions

Travertine crystal growth ripples record the hydraulic history of ancient Rome's Anio Novus aqueduct

Travertine crystal growth ripples are used to reconstruct the early hydraulic history of the Anio Novus aqueduct of ancient Rome. These crystalline morphologies deposited within the aqueduct channel record the hydraulic history of gravity-driven turbulent flow at the time of Roman operation. The wavelength, amplitude, and steepness of these travertine crystal growth ripples indicate that large-scale sustained aqueduct flows scaled directly with the thickness of the aqueous viscous sublayer. Resulting critical shear Reynolds numbers are comparable with those reconstructed from heat/mass transfer crystalline ripples formed in other natural and engineered environments. This includes sediment transport in rivers, lakes, and oceans, chemical precipitation and dissolution in caves, and melting and freezing in ice. Where flow depth and perimeter could be reconstructed from the distribution and stratigraphy of the travertine within the Anio Novus aqueduct, flow velocity and rate have been quantified by deriving roughness-flow relationships that are independent of water temperature. More generally, under conditions of near-constant water temperature and kinematic viscosity within the Anio Novus aqueduct channel, the travertine crystal growth ripple wavelengths increased with decreasing flow velocity, indicating that systematic changes took place in flow rate during travertine deposition. This study establishes that travertine crystal growth ripples such as those preserved in the Anio Novus provide a sensitive record of past hydraulic conditions, which can be similarly reconstructed from travertine deposited in other ancient water conveyance and storage systems around the world.

Drops on the Underside of a Slightly Inclined Wet Substrate Move Too Fast to Grow

Pendant drops suspended on the underside of a wet substrate are known to accumulate fluid from the surrounding thin liquid film, a process that often results in dripping. The growth of such drops is hastened by their ability to translate over an otherwise uniform horizontal film. Here we show that this scenario is surprisingly reversed when the substrate is slightly tilted (≈2°); drops become too fast to grow and shrink over the course of their motion. Combining experiments and numerical simulations, we rationalize the transition between the conventional growth regime and the previously unknown decay regime we report. Using an analytical treatment of the Landau-Levich meniscus that connects the drop to the film, we quantitatively predict the drop dynamics in the two flow regimes and the value of the critical inclination angle where the transition between them occurs.

Streamwise Dissolution Patterns Created by a Flowing Water Film

The dissolution of rocks by rainfall commonly generates streamwise parallel channels, yet the occurrence of these natural patterns remains to be understood. Here, we report the emergence in the laboratory of a streamwise dissolution pattern at the surface of an initially flat soluble material, inclined and subjected to a thin runoff water flow. Nearly parallel grooves about 1 mm wide and directed along the main slope spontaneously form. Their width and depth increase continuously with time until their crests emerge and channelize the flow. Our observations may constitute the early stage of the patterns observed in the field.

The second century CE Roman watermills of Barbegal: Unraveling the enigma of one of the oldest industrial complexes

The second century CE Roman watermill complex of Barbegal, France, is regarded as one of the first industrial complexes in human history. The 16 water wheels are no longer extant as all woodwork has decayed. However, carbonate deposits precipitated from water during operation of the mills forming casts on the woodwork. These casts are preserved in fragments and provide unique insights into the frequency of use and maintenance of the mills, and even into the structure of the water wheel chambers. Stable isotope time series of carbonate deposits reveal that the mill activity was regularly interrupted for several months. This strongly suggests that the mill complex was not used for a steady supply of flour to a major population center, as previously thought, but likely served to produce nonperishable hardtack for the nearby harbors.

Nonlinear and subharmonic stability analysis in film-driven morphological patterns

The interaction of a gravity-driven water film with an evolving solid substrate (calcite or ice) results in the formation of fascinating wavy patterns similar both in caves and in ice-falls. Due to their remarkable similarity, we adopt a unified approach in the study of pattern formation of longitudinally oriented organ-pipe-like structures, called flutings. Since the morphogenesis of cave patterns can evolve for millennia, they have an additional value as silent repositories of past climates. Fluting formation is studied with the aid of gradient expansion and center manifold projection. In particular, through gradient expansion, a Benney-type equation accounting for the movable boundary is obtained. The coupling with a wall evolution equation provides a morphodynamic model for fluting formation, explored through linear and nonlinear analyses. In this way, closed relationships for the selected wave number and for the finite amplitude are achieved. However, as finite-amplitude monochromatic waves may be destabilized by nonlinear interactions with other modes, we verify, through center manifold projection, the stability of the fundamental to subharmonic disturbances. Conclusively, we perform numerical simulations of the fully nonlinear equations to validate the theory results.

Do dissolving objects converge to a universal shape?

Surprisingly, macroscopic objects such as melting ice cubes and growing stalactites approach nonintuitive geometric ideals. Here we investigate the shape of dissolving cylinders in a large volume of water. The cylinders are oriented vertically and consist of amorphous glucose or poly(ethylene glycol). The dissolution causes density differences in the surrounding fluid, which induce gravity-driven convection downward along the object. The resulting concentration gradient shapes the cylinder according to fast dissolution at the tip and slow dissolution at the base. The contour of the object approaches a power law of the form z ∝ R(2), where z is the vertical distance from the tip and R is the corresponding radius. We suggest that this paraboloidal shape is the geometric attractor for the dissolution of noncrystalline objects in the presence of gravity.

Thin-film-induced morphological instabilities over calcite surfaces

Precipitation of calcium carbonate from water films generates fascinating calcite morphologies that have attracted scientific interest over past centuries. Nowadays, speleothems are no longer known only for their beauty but they are also recognized to be precious records of past climatic conditions, and research aims to unveil and understand the mechanisms responsible for their morphological evolution. In this paper, we focus on crenulations, a widely observed ripple-like instability of the the calcite-water interface that develops orthogonally to the film flow. We expand a previous work providing new insights about the chemical and physical mechanisms that drive the formation of crenulations. In particular, we demonstrate the marginal role played by carbon dioxide transport in generating crenulation patterns, which are indeed induced by the hydrodynamic response of the free surface of the water film. Furthermore, we investigate the role of different environmental parameters, such as temperature, concentration of dissolved ions and wall slope. We also assess the convective/absolute nature of the crenulation instability. Finally, the possibility of using crenulation wavelength as a proxy of past flows is briefly discussed from a theoretical point of view.