Hydrodynamically locked morphogenesis in karst and ice flutings

Boundary waves often form at the interface between ice and fluid flowing adjacent to it, such as ripples under river ice covers, and steps on the bed of supraglacial meltwater channels. They may also be formed by wind, such as the megadunes on the Antarctic ice sheet. Spiral troughs on the polar ice caps of Mars have been interpreted to be cyclic steps formed by katabatic wind blowing over ice. Cyclic steps are relatives of upstream-migrating antidunes. Cyclic step formation on ice is not only a mechanical but also a thermodynamic process. There have been very few studies on the formation of either cyclic steps or upstream-migrating antidunes on ice. In this study, we performed flume experiments to reproduce cyclic steps on ice by flowing water, and found that trains of steps form when the Froude number is larger than unity. The features of those steps allow them to be identified as ice-bed analogs of cyclic steps in alluvial and bedrock rivers. We performed a linear stability analysis and obtained a physical explanation of the formation of upstream-migrating antidunes, i.e., precursors of cyclic steps. We compared the results of experiments with the predictions of the analysis and found the observed steps fall in the range where the analysis predicts interfacial instability. We also found that short antidune-like undulations formed as a precursor to the appearance of well-defined steps. This fact suggests that such antidune-like undulations correspond to the instability predicted by the analysis and are precursors of cyclic steps.

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“…We introduce the assumption

\overset{B}{true} > > | {\overset{Z}{true}}_{0} (t) |

so that the

{\overset{z}{true}}^{'}

coordinate of the ice bottom location (thickness of ice) is approximated to be

- \overset{B}{true}

(

\overset{B}{true}

). This is often referred to as the “frozen‐time approximation” in linear stability analysis [ Vesipa et al , ; Camporeale , ].…”

Section: Theoretical Analysismentioning

confidence: 99%

“…They showed that the ice‐water interface can be unstable even in the case of laminar flow, so that the instability is not particular to turbulent flow. Related stability analyses pertaining to ice and karst (calcite) morphodynamics can be found in Vesipa et al [] and Camporeale [].…”

Section: Introductionmentioning

confidence: 99%

Cyclic steps on ice

et al. 2016

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“…The interactions between a fluid, such as water or air, and a deformable surface, such as rock, ice, or sand, create marvelous natural patterns. Desert dunes generated by the wind (Lancaster, ; Pye & Tsoar, ), ice and cave features shaped by thin water films (Camporeale, , ; Chen & Morris, ), and sand ripples on the sea bottom (Blondeaux et al, ) are some of the most well known. Sediment patterns are formed by a flow that is sufficiently strong to trigger grain transport.…”

Section: Introductionmentioning

confidence: 99%

Finite Amplitude of Free Alternate Bars With Suspended Load

Bertagni¹,

Camporeale²

2018

Water Resources Research

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River bars are macroscale sediment patterns, whose main geometrical features (wavelength and amplitude) depend on the mutual interactions between hydrodynamics and sediment transport. River bars develop as an instability of the plane bed to an infinitesimal perturbation, which grows in time to eventually reach a finite amplitude. We here determine, with reference to both bed and suspended loads, a closed form for the finite amplitude, through the nonlinear Center Manifold Projection technique. Results show that suspension plays a destabilizing role in bar instability, affecting both the bar wavelength (linear analysis) and the bar amplitude (weakly nonlinear analysis). This proves the importance of considering suspended load for practical purposes. The outcomes of the model are satisfactorily compared with field observations.

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“…In the cave case, the underlying process is the precipitation-dissolution of calcite content dissolved in the water film, while in the ice case the freezing-melting condition is determined by a heat flux balance at the liquid-solid interface. Although the driving mechanism is different in the two environments, a previous work has shown that a unified approach is possible [11], since at inverted conditions (θ >π/2, where θ is the angle with the horizontal) the key role in driving the morphogenesis is played by the free surface dynamics.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear and subharmonic stability analysis in film-driven morphological patterns

Bertagni

Camporeale

2017

Phys. Rev. E

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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.

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Hydrodynamically locked morphogenesis in karst and ice flutings

Cited by 15 publications

References 45 publications

Cyclic steps on ice

Cyclic steps on ice

Finite Amplitude of Free Alternate Bars With Suspended Load

Nonlinear and subharmonic stability analysis in film-driven morphological patterns

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