A Reduced-Order Dynamical Model for the Ignition of Diver-Induced Cohesive Silt-Out on Sloping Beds
Abstract
A downward fin thrust near a cohesive seabed lofts sediment. Whether this cloud settles or organizes into a self-sustaining down-slope current determines if a diver loses visibility briefly or catastrophically. We reduce the layer-averaged balances of fluid mass, sediment mass, and momentum to a temporal slab of fixed thickness in the weakly entraining limit. This yields an autonomous planar vector field in dimensionless near-bed speed and suspended load, governed by three dimensionless groups: drag against settling, erosion strength, and near-bed concentration. The field possesses a quiescent equilibrium at the origin and, above a critical bed slope obtained in closed form as the ratio of near-bed concentration times drag-settling number to erosion-strength number, an interior saddle equilibrium. The saddle's stable manifold partitions the state space into basins of decay and unbounded growth, establishing the exact threshold between self-limiting and igniting disturbances. On a flat bed, the origin attracts globally for all admissible erosion laws. For representative silt, the ignition threshold is near a 17-degree bed angle. The closed-form structure is confirmed numerically to machine precision. A closure study demonstrates the critical slope is robust in existence but closure-dependent in value, identifying the linear erosion law as the conservative choice. The model thus isolates bed slope as the controlling parameter for ignition.
Related
- Steady-state semi-analytical solutions for assessing the shape of the freshwater–seawater interface induced by a finite-sized underground physical barrier and a pumping well in a sloping coastal aquifer
- Storm-modulated submesoscale dynamics over sloping topography in a wind-driven, non-tidal basin
- Reduced, fluorine-enriched mantle preconditions giant tin mineralization
- Ocean acidification, reduced silicate availability and declines in Ocean productivity
- Digestate improved birch (Betula pendula) growth and reduced leaf trace element contents at a red gypsum landfill
BibTeX
@misc{herho2026reducedorder,
title = {{A Reduced-Order Dynamical Model for the Ignition of Diver-Induced Cohesive Silt-Out on Sloping Beds}},
author = {Sandy Hardian Susanto Herho and Iwan Pramesti Anwar and Umar Abdurrahman and Faruq Khadami and Alfita Puspa Handayani and Karina Aprilia Sujatmiko and Dasapta Erwin Irawan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05479},
eprint = {2609.05479},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05479},
}
RIS
TY - UNPB
TI - A Reduced-Order Dynamical Model for the Ignition of Diver-Induced Cohesive Silt-Out on Sloping Beds
AU - Sandy Hardian Susanto Herho
AU - Iwan Pramesti Anwar
AU - Umar Abdurrahman
AU - Faruq Khadami
AU - Alfita Puspa Handayani
AU - Karina Aprilia Sujatmiko
AU - Dasapta Erwin Irawan
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.05479
UR - https://arxiv.org/abs/2609.05479
AB - A downward fin thrust near a cohesive seabed lofts sediment. Whether this cloud settles or organizes into a self-sustaining down-slope current determines if a diver loses visibility briefly or catastrophically. We reduce the layer-averaged balances of fluid mass, sediment mass, and momentum to a temporal slab of fixed thickness in the weakly entraining limit. This yields an autonomous planar vector field in dimensionless near-bed speed and suspended load, governed by three dimensionless groups: drag against settling, erosion strength, and near-bed concentration. The field possesses a quiescent equilibrium at the origin and, above a critical bed slope obtained in closed form as the ratio of near-bed concentration times drag-settling number to erosion-strength number, an interior saddle equilibrium. The saddle's stable manifold partitions the state space into basins of decay and unbounded growth, establishing the exact threshold between self-limiting and igniting disturbances. On a flat bed, the origin attracts globally for all admissible erosion laws. For representative silt, the ignition threshold is near a 17-degree bed angle. The closed-form structure is confirmed numerically to machine precision. A closure study demonstrates the critical slope is robust in existence but closure-dependent in value, identifying the linear erosion law as the conservative choice. The model thus isolates bed slope as the controlling parameter for ignition.
ER -