arXiv subjects

Yoshiyuki Sakai

Publications and source records attributed to Yoshiyuki Sakai.

4 recordsLinked to original sources

arXiv2026

Similarity of start-up flow in porous media for large pressure gradients

We investigate the start-up flows through ordered porous media (hexagonal close-packed, face-centred cubic and body-centred sphere packs) by means of direct numerical simulations. The flows are initiated from rest and driven by a constant pressure gradient, allowing us to examine the transient development across a wide range of Hagen numbers. Dimensional analysis identifies two relevant time scales: the viscous diffusion time $τ_\mathrm{visc}$ and the inviscid time $τ_\mathrm{inv}$. While the small-time behaviour follows the viscous asymptotics of Johnson et al. [J. Fluid. Mech. 176, 379 (1987)], the subsequent emergence of nonlinear effects is universally governed by the inviscid time $τ_\mathrm{inv}$, rather than by any critical Reynolds number. At the pore scale, the transient evolution is characterised by the growth of thin vorticity layers on the sphere surfaces, their detachment into the pore space around $t \sim τ_\mathrm{inv}$, and the formation of inertial cores. Despite geometric differences, these processes occur in a remarkably similar sequence across all three packings. Vorticity magnitude exhibits laminar boundary-layer scaling with Hagen number, while in the body-centred cubic sphere pack case a transition towards turbulent-type scaling is observed. These results establish $τ_\mathrm{inv}$ as a unifying measure for the onset of nonlinearity in strongly accelerated porous media flows, with direct implications for the modelling of unsteady transport in natural and engineered systems.

physics.flu-dyn↗

arXiv2026

How is the free surface influence transported in turbulent open channel flows?

We investigate how the influence of a free surface is transported in turbulent open channel flow by analysing matched open- and closed-channel direct numerical simulations up to $Re_\mathrmτ \approx 900$ in a domain large enough to accommodate very-large-scale motions (VLSMs). The turbulent kinetic energy (TKE) budget shows that the surface influence is communicated primarily through transport terms. Near the free surface, pressure transport supplies energy towards the interface, whereas turbulent transport and dissipation are reduced; the resulting energy surplus is exported away from the surface predominantly by viscous diffusion. The near-surface budget terms do not exhibit a single universal similarity scaling: viscous diffusion is organised over the near-surface viscous scale $\ell_\mathrm{V}$, dissipation over the Kolmogorov sublayer scale $\ell_\mathrm{K}$, and pressure-related terms require the mixed velocity scale $u_\mathrm{b} u_\mathrmτ^2 /h$. The pressure-strain redistribution further reveals outer-inner coupling: although intense pressure-strain events remain small-scale, their magnitude and directional bias are organised by low-velocity VLSM streaks. The free-surface influence is therefore best understood as a coupled multi-scale process involving local kinematic constraints, Reynolds-number-dependent surface layers, and outer-layer coherent motions.

physics.flu-dyn↗

arXiv2025

How far does the influence of the free surface extend in turbulent open channel flow?

Turbulent open channel flow is known to feature a multi-layer structure near the free surface. In the present work we employ direct numerical simulations considering Reynolds numbers up to $\mathrm{Re}_τ=900$ and domain sizes large enough ($L_x=12 πh$, $L_z=4 πh$) to faithfully capture the effect of very-large-scale motions in order to test the proposed scaling laws and ultimately answer the question: How far does the influence of the free surface extend? In the region near the free surface, where fluctuation intensities of velocity and vorticity become highly anisotropic, we observe the previously documented triple-layer structure, consisting of a wall-normal velocity damping layer that scales with the channel height $h$, and two sublayers that scale with the near-surface viscous length scale $\ell_V=\mathrm{Re}_b^{-1/2}h$ and with the Kolmogorov length scale $\ell_K=\mathrm{Re}_b^{-3/4}h$, respectively. The Kolmogorov sublayer measures $δ_K \approx 20 \ell_K$ and the layer, where the wall-normal turbulence intensity decreases linearly to zero near the free surface, scales with $\ell_V$ and the corresponding near-surface viscous sublayer measures $δ_V \approx \ell_V$. Importantly, the streamwise turbulence intensity profile for $\mathrm{Re}_τ\ge 400$ suggests that the influence of the free-slip boundary penetrates essentially all the way down to the solid wall through the appearance of enhanced very-large-scale motions ($δ_{SIL}\approx h$). In contrast, the layer where the surface-normal turbulence intensity is damped to zero is restricted to the free surface ($δ_{NVD}\approx 0.3h$). As a consequence, the partitioning of the surface-influenced region has to be expanded to a four-layer structure that spans the entire channel height $h$.

physics.flu-dyn↗

arXiv2023

Direct numerical simulation of turbulent open channel flow: Streamwise turbulence intensity scaling and its relation to large-scale coherent motions

We conducted direct numerical simulations of turbulent open channel flow (OCF) and closed channel flow (CCF) of friction Reynolds numbers up to $\mathrm{Re}_τ\approx 900$ in large computational domains up to $L_x\times L_z=12πh \times 4πh$ to analyse the Reynolds number scaling of turbulence intensities. Unlike CCF, our data suggests that the streamwise turbulence intensity in OCF scales with the bulk velocity for $\mathrm{Re}_τ\gtrsim 400$. The additional streamwise kinetic energy in OCF with respect to CCF is provided by larger and more intense very-large-scale motions in the former type of flow. Therefore, compared to CCF, larger computational domains of $L_x\times L_z=12πh\times 4πh$ are required to faithfully capture very-large-scale motions in OCF -- and observe the reported scaling. OCF and CCF turbulence statistics data sets are available at https://doi.org/10.4121/88678f02-2a34-4452-8534-6361fc34d06b .

physics.flu-dyn↗