18 Aug 2022
 | 18 Aug 2022
Status: this preprint is currently under review for the journal TC.

Smoothed Particle Hydrodynamics Implementation of the Standard Viscous-Plastic Sea-Ice Model and Validation in Simple Idealized Experiments

Oreste Marquis, Bruno Tremblay, Jean-François Lemieux, and Mohammed Islam

Abstract. The Viscous-Plastic (VP) rheology with an elliptical yield curve and normal flow rule is implemented in a Lagrangian modelling framework using the Smoothed Particle Hydrodynamics (SPH) meshfree method. Results show, from perturbation analysis of SPH sea-ice dynamic equations, that the classical SPH particle density formulation expressed as a function of sea-ice concentration and mean ice thickness, leads to incorrect plastic wave speed. We propose a new formulation for particle density that gives a plastic wave speed in line with theory. In all cases, the plastic wave in the SPH framework is dispersive and depends on the smoothing length (i.e., the spatial resolution) and on the SPH kernel employed in contrast with its finite difference method (FDM) implementation counterpart. The steady-state solution for the simple 1D ridging experiment is in agreement with the analytical solution within an error of 1 %. SPH is also able to simulate a stable upstream ice arch in an idealized domain representing the Nares Strait in low wind regime (5.3 [m · s−1]) with an ellipse aspect ratio of 2, an average thickness of 1 [m] and free-slip boundary conditions in opposition to the FDM implementation that requires higher shear strength to simulate it. In higher wind regime (7.5 [m · s−1]) no stable ice arches are simulated — unless the thickness is increased — and the ice arch formation showed no dependence on the size of particles contrary to what is observed in the discrete element framework. Finally, the SPH framework is explicit, can take full advantage of parallel processing capabilities and show potential for pan-arctic climate simulations.

Oreste Marquis et al.

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • CC1: 'Comment on tc-2022-163', Oreste Marquis, 06 Mar 2023
    • EC1: 'Reply on CC1', Jari Haapala, 09 Mar 2023
      • AC1: 'Reply on EC1', Oreste Marquis, 10 Mar 2023
        • EC2: 'Reply on AC1', Jari Haapala, 10 Mar 2023
          • AC2: 'Reply on EC2', Oreste Marquis, 17 Mar 2023
  • RC1: 'Comment on tc-2022-163', Anonymous Referee #1, 01 May 2023
    • AC3: 'Reply on RC1', Oreste Marquis, 01 May 2023
    • AC4: 'Reply on RC1', Oreste Marquis, 09 Sep 2023
  • RC2: 'Comment on tc-2022-163', Anonymous Referee #2, 22 Aug 2023
    • AC5: 'Reply on RC2', Oreste Marquis, 09 Sep 2023
  • RC3: 'Comment on tc-2022-163', Anonymous Referee #3, 25 Aug 2023
    • AC6: 'Reply on RC3', Oreste Marquis, 09 Sep 2023

Oreste Marquis et al.

Oreste Marquis et al.


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Short summary
We developed a standard viscous-plastic sea-ice model based on the numerical framework called Smoothed Particle Hydrodynamics. The model converges to the theory within an error of 1 % in an idealized ridging experiment and it is able to simulate stable ice arches. However, the method creates a dispersive plastic wave speed. The framework is efficient to simulate fractures and can take full advantage of parallelization making it a good candidate to investigate sea-ice material properties.