Inertial flows over the Koch leaf
Abstract
The main hypothesis of this paper is that inertial effects known from porous-media flow can be observed even in a simple system consisting of a single channel. The strength of inertia is controlled by the Reynolds number, Re. We investigated fluid flow through a channel with a cavity in the shape of a Koch leaf. The Koch leaf of level-6 was chosen because it combines regularity, repeatability, and representativeness with a complex multiscale structure and non-trivial hydrodynamic interactions. We analyzed nonlinear effects through the so-called friction factor and show that its deviation from Darcy's law is very subtle. We further examined the influence of inertia on the flow structure, including the participation number π and the backward-flow fraction ρ−. In contrast to disordered porous media, the participation number decreases with Re, indicating that inertia concentrates kinetic energy in the main through-flow, while recirculation (backward flow) increasingly occupies the Koch leaf cavity. The tortuosity varies non-monotonically with Re, the apparent permeability decreases, and in the inertial regime the two are related by a power law with an exponent comparable to that found for natural rock. At the lowest and highest Reynolds numbers, the local kinetic energy followed a power-law distribution, P(ε)∝ε−m, over several orders of magnitude with the same exponent, m≈0.83; inertia modified only the tails of the distribution. Our research can be regarded as an investigation of transport in an extremely porous system with porosity φ≈ 1.
Related
- Chiral-symmetry breaking and degeneracy in Koch fractal geometries
- Fully resolved particle dynamics over long time scales in acoustofluidic flows: Theory and numerical simulations
- Separated flows over swept wings across transitional Reynolds numbers
- Compact low-frequency optomechanical triaxial inertial sensor
- Maintenance of a columnar vortex by inertial waves in rotational turbulence
BibTeX
@misc{naqvi2026inertial,
title = {{Inertial flows over the Koch leaf}},
author = {Sahrish B. Naqvi and Dawid Strzelczyk and Maciej Tadej and Maciej Matyka},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38493},
eprint = {2610.38493},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38493},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Inertial flows over the Koch leaf
AU - Sahrish B. Naqvi
AU - Dawid Strzelczyk
AU - Maciej Tadej
AU - Maciej Matyka
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38493
UR - https://arxiv.org/abs/2610.38493
AB - The main hypothesis of this paper is that inertial effects known from porous-media flow can be observed even in a simple system consisting of a single channel. The strength of inertia is controlled by the Reynolds number, Re. We investigated fluid flow through a channel with a cavity in the shape of a Koch leaf. The Koch leaf of level-6 was chosen because it combines regularity, repeatability, and representativeness with a complex multiscale structure and non-trivial hydrodynamic interactions. We analyzed nonlinear effects through the so-called friction factor and show that its deviation from Darcy's law is very subtle. We further examined the influence of inertia on the flow structure, including the participation number π and the backward-flow fraction ρ^−. In contrast to disordered porous media, the participation number decreases with Re, indicating that inertia concentrates kinetic energy in the main through-flow, while recirculation (backward flow) increasingly occupies the Koch leaf cavity. The tortuosity varies non-monotonically with Re, the apparent permeability decreases, and in the inertial regime the two are related by a power law with an exponent comparable to that found for natural rock. At the lowest and highest Reynolds numbers, the local kinetic energy followed a power-law distribution, P(ε)∝ε^−m, over several orders of magnitude with the same exponent, m≈0.83; inertia modified only the tails of the distribution. Our research can be regarded as an investigation of transport in an extremely porous system with porosity φ≈ 1.
ER -