Nonlinear and subharmonic stability analysis in film-driven morphological patterns

Matteo Bernard Bertagni and Carlo Camporeale
Phys. Rev. E 96, 053115 – Published 27 November 2017

Abstract

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.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Received 18 January 2017
  • Revised 24 May 2017

DOI:https://doi.org/10.1103/PhysRevE.96.053115

©2017 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
  1. Physical Systems
Fluid DynamicsInterdisciplinary PhysicsNonlinear Dynamics

Authors & Affiliations

Matteo Bernard Bertagni* and Carlo Camporeale

  • Politecnico di Torino, DIATI, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy

  • *matteo.bertagni@polito.it
  • carlo.camporeale@polito.it

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 96, Iss. 5 — November 2017

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review E

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×