arXiv subjects

Yoshiki Hiruta

Publications and source records attributed to Yoshiki Hiruta.

7 recordsLinked to original sources

arXiv2026

Phase-symmetry breaking as a mechanism for subcritical transition in shell models of turbulence

Subcritical transition to turbulence, in which the laminar state is linearly stable yet finite-amplitude perturbations develop into turbulence, is ubiquitous but lacks a simple analytical framework. We demonstrate such a framework using a shell model of turbulence, in which external forcing breaks the phase symmetry of the governing equations. This symmetry breaking suppresses the linear instability of the laminar state, while the energy cascade and spectrum of the developed turbulent state are preserved. A complementary single-triad model admits an exact elliptic neutral stability curve, revealing that the stabilization depends only on the breaking strength and not on the nonlinear coupling coefficients. Since the phase symmetry of the shell model corresponds to Galilean invariance in the Navier--Stokes equations, this mechanism may offer a new perspective on subcritical transition in fluid systems.

physics.flu-dyn↗

arXiv2026

Most probable path and invariant sets in noise-induced transition to turbulence

Turbulence transition often arises from a subcritical transition between bistable states characterized by invariant sets of deterministic dynamical systems, and such transitions can be triggered by system noise as rare events. In this study, we employ the Onsager-Machlup (OM) formulation of stochastic dynamics to examine the Hamilton equations governing the most probable transition paths (MPPs). We introduce an effective potential function, termed the OM potential, which depends on the noise strength. Focusing on the Dauchot-Manneville model as a minimal system with an edge state, we comprehensively analyze the MPP between laminar and turbulent states for different transition times. We find that the MPPs cross the separatrix at nearly the same point regardless of the transition time, and the obtained OM action values suggest that the transition to turbulence occurs more frequently than the transition to the laminar state. Moreover, we numerically demonstrate that the noise-induced transition paths follow the OM potential landscape and its bifurcation diagram, indicating that the qualitative behavior of the MPPs is determined by the OM potential. Our methodology formulated in general dynamical systems provides a theoretical basis for predicting noise-induced transitions among invariant sets of the dynamics.

physics.flu-dyn↗

arXiv2025

Emergence of edge state in suspension of self-propelled particles

We numerically study a model convection system of a suspension of self-propelled particles, motivated by recent experimental findings of localized and bistable bioconvection pattern, being distinct from classical Rayleigh--Bénard convection. Linear stability analysis of the model system reveals that the trivial noncovection state is stabilized by an increase of self-propelled speed in the vertical direction. Through numerical simulations, we found a nonlinear convection state even when the nonconvection state is stable. Applying ideas and tools developed in wall-bounded flows, we numerically identified an edge state, which is an unstable solution on a basin boundary in the model dynamical systems.

physics.flu-dyn↗

arXiv2024

Localization and bistability of bioconvection in a doubly periodic domain

A suspension of swimming microorganisms often generates a large-scale convective pattern known as bioconvection. In contrast to the thermal Rayleigh-Benard system, recent experimental studies report an emergence of steady localized convection patterns and bistability near the onset of instability in bioconvection systems. In this study, to understand the underlying mechanisms and identify the roles of particle self-propulsion in pattern formation, we theoretically and numerically investigate a model bioconvection system in a two-dimensional periodic boundary domain. In doing so, we extend a standard bioconvection model by introducing the equilibrium density profile as an independent parameter, for which the particle self-propulsion is treated as an independent dimensional parameter. Since the large-scale vertical structure dominates in this system, we are able to simplify the model by truncating the higher vertical modes. With this truncated model, we analytically derived the neutrally stable curve and found that the particle motility stabilizes the system. We then numerically analyzed the bifurcation diagram and found the bistable structure at the onset of instability. These findings, localization and bistability, are consistent with experimental observations. We further examined the global structure of the bistable dynamical system and found that the non-trivial unstable steady solution behaves as an edge state that separates the basins of attractors. These results highlight the importance of particle self-propulsion in bioconvection, and more generally our methodology based on the dynamical systems theory is useful in understanding complex flow patterns in nature.

physics.flu-dyn↗

arXiv2023

Reciprocal microswimming in fluctuating and confined environments

From bacteria and sperm cells to artificial microrobots, self-propelled microscopic objects at low Reynolds numbers often perceive fluctuating mechanical and chemical stimuli and contact exterior wall boundaries both in nature and the laboratory. In this study, we theoretically investigate the fundamental features of microswimmers by focusing on their reciprocal deformation. Although the scallop theorem prohibits the net locomotion of reciprocal microswimmers, by analyzing a two-sphere swimmer model, we show that in a fluctuating and geometrically confined environment, reciprocal deformations can afford a statistically average displacement. After designing the shape gait, a reciprocal swimmer can migrate in any direction, even in the statistical sense, while the statistical average of passive rigid particles statistically diffuses in a particular direction in the presence of external boundaries. To elucidate this symmetry breakdown, by introducing an impulse response function, we derive a general formula for predicting the nonzero net displacement of a reciprocal swimmer. Using this theory, we determine the relation between the shape gait and net locomotion as well as the net diffusion constant increase and decrease owing to a reciprocal deformation. Based on these findings and a theoretical formulation, we provide a fundamental basis for environment-coupled statistical locomotion. Thus, this study is valuable for understanding biophysical phenomena in fluctuating environments, designing artificial microrobots, and conducting laboratory experiments.

cond-mat.soft↗

arXiv2018

Subcritical laminar-turbulence transition with wide domains in simple two-dimensional Navier-Stokes flow without walls

We have confirmed numerically that a subcritical laminar-turbulence transition that belongs to directed percolation (DP) universality class occurs in a purely two-dimensional (2D) simple Navier-Stokes (NS) flow without any walls. The flow is called (extended) Kolmogorov flow which is governed by 2D NS equation in a doubly periodic box with a linear drag and a finite flow rate in the direction in which Galilean invariance is broken. We examine the mechanism of DP class transition focusing on the role of the additional control parameters: the drag coefficient and the flow rate. The drag kills coherent active structures of the system size. The flow rate interferes the growth of weak disturbances. These two effects control two essential and intrinsic elements of an absorbing state phase transition, i.e., the existence of an absorbing state and the locality of active dynamical structures. We also discuss what physically corresponds to the additional parameters in general flow.

physics.flu-dyn↗

arXiv2017

Intermittent direction reversals of moving spatially-localized turbulence observed in two-dimensional Kolmogorov flow

We have found that in two-dimensional Kolmogorov flow a single spatially-localized turbulence (SLT) exists stably and travels with a constant speed on average switching the moving direction randomly and intermittently for moderate values of control parameters: Reynolds number and the flow rate. We define the coarse-grained position and velocity of an SLT and separate the motion of the SLT from its internal turbulent dynamics by introducing a co-moving frame. The switching process of an SLT represented by the coarse-grained velocity seems to be a random telegraph signal. Focusing on the asymmetry of the internal turbulence we introduce two coarse-grained variables characterizing the internal dynamics. These quantities follow the switching process reasonably. This suggests that the twin attracting invariant sets each of which corresponds to a one-way traveling SLT are embedded in the attractor of the moving SLT and the connection of the two sets is too complicated to be represented by a few degrees of freedom but the motion of an SLT is controlled by the internal turbulent dynamics.

physics.flu-dyn↗