arXiv subjects

Masaki Shimizu

Publications and source records attributed to Masaki Shimizu.

12 recordsLinked to original sources

arXiv2026

Optimization of fluid mixing by reinforcement learning using limit cycles of a dynamical system

We propose a method to overcome the difficulties encountered when applying reinforcement learning to fluid mixing processes. The proposed method has two main features: (i) it does not require detailed measurements of the flow state, and (ii) by effectively exploiting a stable limit cycle of a two-dimensional dynamical system (the Li'enard system), it can stably perform optimization without imposing explicit constraints on the control parameters. As an illustrative example, we optimize a process in which a fluid contained in a cylindrical vessel is mixed by periodically rotating the vessel. The resulting optimal vessel motion is physically reasonable: it reverses its direction of rotation before a solid-body rotation state is established. Furthermore, even when the fluid viscosity increases with time during the mixing process, the method can continuously adapt the control parameters to the changing viscosity.

physics.flu-dyn↗

arXiv2021

The ultimate state of turbulent permeable-channel flow

Direct numerical simulations have been performed for heat and momentum transfer in internally heated turbulent shear flow with constant bulk mean velocity and temperature, $u_{b}$ and $θ_{b}$, between parallel, isothermal, no-slip and permeable walls. The wall-normal transpiration velocity on the walls $y=\pm h$ is assumed to be proportional to the local pressure fluctuations, i.e. $v=\pm βp/ρ$ (Jiménez et al., J. Fluid Mech., vol. 442, 2001, pp.89-117). The temperature is supposed to be a passive scalar, and the Prandtl number is set to unity. Turbulent heat and momentum transfer in permeable-channel flow for $βu_{b}=0.5$ has been found to exhibit distinct states depending on the Reynolds number $Re_b=2h u_b/ν$. At $Re_{b}\lesssim 10^4$, the classical Blasius law of the friction coefficient and its similarity to the Stanton number, $St\approx c_{f}\sim Re_{b}^{-1/4}$, are observed, whereas at $Re_{b}\gtrsim 10^4$, the so-called ultimate scaling, $St\sim Re_b^0$ and $c_{f}\sim Re_b^0$, is found. The ultimate state is attributed to the appearance of large-scale intense spanwise rolls with the length scale of $O(h)$ arising from the Kelvin-Helmholtz type of shear-layer instability over the permeable walls. The large-scale rolls can induce large-amplitude velocity fluctuations of $O(u_b)$ as in free shear layers, so that the Taylor dissipation law $ε\sim u_{b}^{3}/h$ (or equivalently $c_{f}\sim Re_b^0$) holds. In spite of strong turbulence promotion there is no flow separation, and thus large-amplitude temperature fluctuations of $O(θ_b)$ can also be induced similarly. As a consequence, the ultimate heat transfer is achieved, i.e., a wall heat flux scales with $u_{b}θ_{b}$ (or equivalently $St\sim Re_b^0$) independent of thermal diffusivity, although the heat transfer on the walls is dominated by thermal conduction.

physics.flu-dyn↗

arXiv2021

Efficient reinforcement learning with partially observable for fluid flow control

Despite the low dimensionalities of dissipative viscous fluids, reinforcement learning (RL) requires many observables in fluid control problems. This is because the observables are assumed to follow a policy-independent Markov decision process in the RL framework. By including policy parameters as arguments of a value function, we construct a consistent algorithm with partially observable condition. Using typical examples of active flow control, we show that our algorithm is more stable and efficient than the existing RL algorithms, even under a small number of observables.

physics.flu-dyn↗

arXiv2020

Transitional channel flow: A minimal stochastic model

In line with Pomeau's conjecture about the relevance of directed percolation (DP) to turbulence onset/decay in wall-bounded flows, we propose a minimal stochastic model dedicated to the interpretation of the spatially intermittent regimes observed in channel flow before its return to laminar flow. Numerical simulations show that a regime with bands obliquely drifting in two stream-wise symmetrical directions bifurcates into an asymmetrical regime, before ultimately decaying to laminar flow. The model is expressed in terms of a probabilistic cellular automaton evolving von Neumann neighbourhoods with probabilities educed from a close examination of simulation results. It implements band propagation and the two main local processes: longitudinal splitting involving bands with the same orientation, and transversal splitting giving birth to a daughter band with orientation opposite to that of its mother. The ultimate decay stage observed to display one-dimensional DP properties in a two-dimensional geometry is interpreted as resulting from the irrelevance of lateral spreading in the single-orientation regime. The model also reproduces the bifurcation restoring the symmetry upon variation of the probability attached to transversal splitting, which opens the way to a study of the critical properties of that bifurcation, in analogy with thermodynamic phase transitions.

physics.flu-dyn↗

arXiv2020

Ultimate heat transfer in `wall-bounded' convective turbulence

Direct numerical simulations have been performed for turbulent thermal convection between horizontal no-slip, permeable walls with a distance $H$ and a constant temperature difference $ΔT$ at the Rayleigh number $Ra=3\times10^{3}-10^{10}$. On the no-slip wall surfaces $z=0$, $H$ the wall-normal (vertical) transpiration velocity is assumed to be proportional to the local pressure fluctuation, i.e. $w=-βp'/ρ, +βp'/ρ$ (Jiménez et al., J. Fluid Mech., vol. 442, 2001, pp. 89-117), and the property of the permeable wall is given by the permeability parameter $βU$ normalised with the buoyancy-induced terminal velocity $U={(gαΔTH)}^{1/2}$, where $ρ$, $g$ and $α$ are mass density, acceleration due to gravity and volumetric thermal expansivity, respectively. A zero net mass flux through the wall is instantaneously ensured, and thermal convection is driven only by buoyancy without any additional energy inputs. The critical transition of heat transfer in convective turbulence has been found between the two $Ra$ regimes for fixed $βU=3$ and fixed Prandtl number $Pr=1$. In the subcritical regime at lower $Ra$ the Nusselt number $Nu$ scales with $Ra$ as $Nu\sim Ra^{1/3}$, as commonly observed in turbulent Rayleigh-Bénard convection. In the supercritical regime at higher $Ra$, on the other hand, the ultimate scaling $Nu\sim Ra^{1/2}$ is achieved, meaning that the wall-to-wall heat flux scales with $UΔT$ independent of the thermal diffusivity, although the heat transfer on the wall is dominated by thermal conduction. The physical mechanisms of the achievement of the ultimate heat transfer are presented.

physics.flu-dyn↗

arXiv2020

Multi-scale steady solution for Rayleigh-Bénard convection

We have found a multi-scale steady solution of the Boussinesq equations for Rayleigh-Bénard convection in a three-dimensional periodic domain between horizontal plates with a constant temperature difference by using a homotopy from the wall-to-wall optimal transport solution given by Motoki et al. (J. Fluid Mech., vol. 851, 2018, R4). The connected steady solution, which turns out to be a consequence of bifurcation from a thermal conduction state at the Rayleigh number $Ra\sim10^{3}$, is tracked up to $Ra\sim10^{7}$ by using a Newton-Krylov iteration. The exact coherent thermal convection exhibits scaling $Nu\sim Ra^{0.31}$ (where $Nu$ is the Nusselt number) as well as multi-scale thermal plume and vortex structures, which are quite similar to those in the turbulent Rayleigh-Bénard convection. The mean temperature profiles and the root-mean-square of the temperature and velocity fluctuations are in good agreement with those of the turbulent states. Furthermore, the energy spectrum follows Kolmogorov's -5/3 scaling law with a consistent prefactor, and the energy transfer to smaller scales in the wavenumber space agrees with the turbulent energy transfer.

physics.flu-dyn↗

arXiv2019

Bifurcations to turbulence in transitional channel flow

In wall-bounded parallel flows, sustained turbulence can occur even while laminar flow is still stable. Channel flow is one of such flows and displays spatio-temporal fluctuating patterns of localized turbulence along its way from/to featureless turbulence. By direct numerical simulation, we study the observed inconsistency between turbulence decay according to a two-dimensional directed-percolation (2D-DP) scenario and the presence of sustained oblique localized turbulent bands (LTBs) below the DP critical point. Above Reynolds number Reg \sim 700 sustained LTBs are observed; most LTBs have the same orientation so that the spanwise symmetry of the LTB pattern is broken below Re2 \sim 1000. The frequency of transversal splitting, by which an LTB generates another one with opposite obliqueness, so that turbulence spreading becomes intrinsically two dimensional, increases in the range Reg < Re < Re2. It reaches a critical rate at Re2 beyond which symmetry is restored. 2D-DP behavior is retrieved only above Re2. A mean-field model is proposed which qualitatively accounts for the above symmetry-restoring bifurcation by considering interactions between space-averaged densities of LTBs propagating in either direction.

physics.flu-dyn↗

arXiv2019

Subcritical transition to turbulence in wall-bounded flows: the case of plane Poiseuille flow

In wall-bounded flows, the laminar regime remain linearly stable up to large values of the Reynolds number while competing with nonlinear turbulent solutions issued from finite amplitude perturbations. The transition to turbulence of plane channel flow (plane Poiseuille flow) is more specifically considered via numerical simulations. Previous conflicting observations are reconciled by noting that the two-dimensional directed percolation scenario expected for the decay of turbulence may be interrupted by a symmetry-breaking bifurcation favoring localized turbulent bands. At the other end of the transitional range, a preliminary study suggests that the laminar-turbulent pattern leaves room to a featureless regime beyond a well defined threshold to be determined with precision.

physics.flu-dyn↗

arXiv2018

Construction of low-dimensional system reproducing low-Reynolds-number turbulence by machine learning

In a dissipative system, there exists the (global) attractor which has finite fractal dimensions. The flow on the attractor can be parametrized by a finite number of parameters (Temmam 1987). Using machine learning we demonstrate how to construct precise low-dimensional governing equations which are valid in some range of Reynolds number for low-Reynolds-number turbulence in plane Couette flow.

physics.flu-dyn↗

arXiv2018

Maximal heat transfer between two parallel plates

The divergence-free time-independent velocity vector field has been determined so as to maximise heat transfer between two parallel plates of a constant temperature difference under the constraint of fixed total enstrophy. The present variational problem is the same as that first formulated by Hassanzadeh $\it et{\ }al$. (2014); however, a search range of optimal states has been extended to a three-dimensional velocity field. The scaling of the Nusselt number $Nu$ with the Péclet number $Pe$ (i.e., the square root of the non-dimensionalised enstrophy with thermal diffusion timescale), $Nu\sim Pe^{2/3}$, has been found in the three-dimensional optimal states, corresponding to the asymptotic scaling with the Rayleigh number $Ra$, $Nu\sim Ra^{1/2}$, in extremely-high-$Ra$ convective turbulence, and thus to the Taylor energy dissipation law in high-Reynolds-number turbulence. At $Pe\sim10^{0}$, a two-dimensional array of large-scale convection rolls provides maximal heat transfer. A three-dimensional optimal solution emerges from bifurcation on the two-dimensional solution branch at higher $Pe$. At $Pe\gtrsim10^{3}$, the optimised velocity fields consist of convection cells with hierarchical self-similar vortical structures, and the temperature fields exhibit a logarithmic mean profile near the walls.

physics.flu-dyn↗

arXiv2017

Optimal heat transfer enhancement in plane Couette flow

We discuss what is an optimal velocity field for more heat transfer and less energy dissipation under the constraints of the continuity equation for the velocity and the advection-diffusion equation for temperature in plane Couette flow. The excess of a wall heat flux (or equivalently total scalar dissipation) over total energy dissipation is taken as an objective functional, and by using a variational method the Euler-Lagrange equations are derived, which are solved numerically to obtain the optimal states in the sense of maximisation of the functional. At high Reynolds numbers, the optimal heat transfer is found in three-dimensional velocity field in which hierarchical self-similar quasi-streamwise vortical structures appear. The streamwise vortices are tilted in the spanwise direction so that they may produce the anticyclonic vorticity antiparallel to the mean-shear vorticity, bringing about significant three-dimensionality. The isotherms wrapped around the tilted anticyclonic vortices undergo the cross-axial shear of the mean flow, so that the spacing of the wrapped isotherms is narrower and so the temperature gradient is steeper than those around a purely streamwise (two-dimensional) vortex tube, intensifying scalar dissipation and so a wall heat flux. Moreover, the tilted anticyclonic vortices induce the flow towards the wall to push low- (or high-) temperature fluids on the hot (or cold) wall, enhancing a wall heat flux. The optimised three-dimensional velocity fields achieve a much higher wall heat flux and much lower energy dissipation than those of plane Couette turbulence.

physics.flu-dyn↗

arXiv2008

Numerical examination of plasmoid-induced reconnection model for solar flares: the relation between plasmoid velocity and reconnection rate

The plasmoid-induced-reconnection model explaining solar flares based on bursty reconnection produced by an ejecting plasmoid suggests a possible relation between the ejection velocity of a plasmoid and the rate of magnetic reconnection. In this study, we focus on the quantitative description of this relation. We performed magnetohydrodynamic (MHD) simulations of solar flares by changing the values of resistivity and the plasmoid velocity. The plasmoid velocity has been changed by applying an additional force to the plasmoid to see how the plasmoid velocity affects the reconnection rate. An important result is that the reconnection rate has a positive correlation with the plasmoid velocity, which is consistent with the plasmoid-induced-reconnection model for solar flares. We also discuss an observational result supporting this positive correlation.

astro-ph↗