arXiv subjects

Susumu Goto

Publications and source records attributed to Susumu Goto.

At least 19 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↗

arXiv2026

Relative velocity between a particle and turbulence

The relative velocity between a particle and the surrounding fluid is a key quantity that determines the various phenomena of particle-laden turbulence, such as particle clustering and turbulence modulation due to particles. We theoretically derive the expression for the relative velocity of a particle laden in turbulence by extending the argument of Balachandar (2009). This derivation provides a simplified form of the analytical model of Berk and Coletti (2024), and it makes the underlying physical assumptions explicit. Using direct numerical simulation data of turbulence in a periodic cube and turbulent channel flow, we demonstrate the validity of the derived expression, and show that it also holds for non-spherical particles and droplets.

physics.flu-dyn↗

arXiv2026

Physical mechanism of turbulence attenuation by polymers from a timescale perspective

To elucidate the physical mechanism of turbulence attenuation by polymers at each scale, we conduct direct numerical simulations of homogeneous isotropic turbulence in dilute polymer solutions. We model polymers as FENE dumbbells and simulate them using Brownian dynamics. By visualising the hierarchical structures of coherent vortices, we demonstrate that as the Weissenberg number increases, polymers progressively suppress vortices from smaller to larger scales, attenuating their turbulent energy. While inspired by Lumley's theory, we propose a novel timescale-based framework for analysing this attenuation process using the scale decomposition. We define a scale-dependent Weissenberg number, $\mathrm{Wi}_{\mathrm{sd}}(k)$, as the ratio of the polymer relaxation time to the turnover time of multiscale vortices at each wave-number. We reveal that when expressed in terms of $\mathrm{Wi}_{\mathrm{sd}}(k)$, the energy attenuation rate at each scale collapses onto a single curve that rises at $\mathrm{Wi}_{\mathrm{sd}}(k) \gtrsim 1$, proving that $\mathrm{Wi}_{\mathrm{sd}}(k)$ successfully describes both the onset and the degree of turbulence attenuation at any given scale $k^{-1}$. Furthermore, the scale decomposition uncovers that polymers preferentially align with the turbulent stretching direction at the scale satisfying $\mathrm{Wi}_{\mathrm{sd}}(k) \approx 1$. Based on these results, we establish a physical picture of the polymer--turbulence interaction and explicitly link it to the statistics in turbulence attenuated by polymers.

physics.flu-dyn↗

arXiv2026

Lagrangian velocity statistics of homogeneous isotropic turbulence in dilute polymer solutions

We conduct direct numerical simulations of homogeneous isotropic turbulence in dilute polymer solutions to investigate the Lagrangian velocity statistics. We show how polymers modulate the power spectral density of the Lagrangian velocity and the Lagrangian integral timescale by varying the Reynolds number, forcing method, and polymer relaxation time. As the polymer relaxation time increases, the attenuation of the power spectral density extends successively from high to low frequencies, and the Lagrangian integral timescale increases. To clarify the mechanism underlying the modulation of the Lagrangian velocity statistics, we decompose the Lagrangian velocity into the contributions from vortices at different length scales. Using this scale-decomposition analysis, we demonstrate that the observed modulation of the Lagrangian velocity statistics results from polymer-induced suppression of vortices that proceeds from smaller to larger scales.

physics.flu-dyn↗

arXiv2026

Multifractal sets of coherent and incoherent vortices in turbulence

We numerically verify multifractal theory (Frisch and Parisi 1985) for turbulence using simulation data at a high Reynolds number. First, we propose a simple method to directly estimate the multifractal dimension $D(h)$ of vortical structures with a given Hölder exponent $h$. Thus measured $D(h)$ is in good agreement with indirectly measured experimental data. Then, we demonstrate that these structures for $h\ll1/3$ form the hierarchy of coherent eddies, while those for $h\gg1/3$ are featureless.

physics.flu-dyn↗

arXiv2025

Attenuation mechanism of wall-bounded turbulence by heavy finite-size particles

To elucidate the attenuation mechanism of wall-bounded turbulence due to heavy small particles, we conduct direct numerical simulations (DNS) of turbulent channel flow laden with finite-size solid particles. When particles cannot follow the swirling motions of wall-attached vortices, vortex rings are created around the particles. These particle-induced vortices lead to additional energy dissipation, reducing the turbulent energy production from the mean flow. This mechanism results in the attenuation of turbulent kinetic energy, which is more significant when the Stokes number of particles is larger or particle size is smaller under the condition that the volume fraction of particles is fixed. Moreover, we propose the method to quantitatively predict the degree of turbulence attenuation without using DNS data by estimating the additional energy dissipation rate in terms of particle properties.

physics.flu-dyn↗

arXiv2025

Can Frontier LLMs Replace Annotators in Biomedical Text Mining? Analyzing Challenges and Exploring Solutions

Multiple previous studies have reported suboptimal performance of LLMs in biomedical text mining. By analyzing failure patterns in these evaluations, we identified three primary challenges for LLMs in biomedical corpora: (1) LLMs fail to learn implicit dataset-specific nuances from supervised data, (2) The common formatting requirements of discriminative tasks limit the reasoning capabilities of LLMs particularly for LLMs that lack test-time compute, and (3) LLMs struggle to adhere to annotation guidelines and match exact schemas, which hinders their ability to understand detailed annotation requirements which is essential in biomedical annotation workflow. We experimented with prompt engineering techniques targeted to the above issues, and developed a pipeline that dynamically extracts instructions from annotation guidelines. Our results show that frontier LLMs can approach or surpass the performance of SOTA BERT-based models with minimal reliance on manually annotated data and without fine-tuning. Furthermore, we performed model distillation on a closed-source LLM, demonstrating that a BERT model trained exclusively on synthetic data annotated by LLMs can also achieve a practical performance. Based on these findings, we explored the feasibility of partially replacing manual annotation with LLMs in production scenarios for biomedical text mining.

cs.CL↗

arXiv2025

Relationship between the power spectral density of the Lagrangian velocity and the hierarchy of coherent vortices in turbulence

We conduct direct numerical simulations of developed turbulence in a periodic cube to investigate the formation mechanism of the power spectral density of the Lagrangian velocity. We compare the power spectral density of the Lagrangian velocity of turbulent flows with different forcing methods and Reynolds numbers. This systematic comparison demonstrates that universal behavior is observed in a narrow high-frequency regime, whereas non-universality originating from the forcing method broadly appears in a low-frequency regime. To reveal the formation mechanism of the spectra in terms of the hierarchy of coherent structures in turbulence, we propose a scale-decomposition method for the Lagrangian velocity, which enables us to evaluate the contribution of vortices at different scales. This scale-decomposition analysis directly demonstrates that the largest-scale flows driven by the external force can contaminate the Kolmogorov scaling of the Lagrangian velocity spectra formed by small-scale vortices in the inertial range, thus leading to the narrow Lagrangian inertial range. Furthermore, we provide evidence that this remarkable effect by the largest-scale flows is specific to the Lagrange velocity by demonstrating that the power spectral density of the Eulerian velocity is less sensitive to the forcing method.

physics.flu-dyn↗

arXiv2024

Data-driven nonlinear turbulent flow scaling with Buckingham Pi variables

Nonlinear machine learning for turbulent flows can exhibit robust performance even outside the range of training data. This is achieved when machine-learning models can accommodate scale-invariant characteristics of turbulent flow structures. This study presents a data-driven approach to reveal scale-invariant vortical structures across Reynolds numbers that provide insights for supporting nonlinear machine-learning-based studies of turbulent flows. To uncover conditions for which nonlinear models are likely to perform well, we use a Buckingham Pi-based sparse nonlinear scaling to find the influence of the Pi groups on the turbulent flow data. We consider nonlinear scalings of the invariants of the velocity gradient tensor for an example of three-dimensional decaying isotropic turbulence. The present scaling not only enables the identification of vortical structures that are interpolatory and extrapolatory for the given flow field data but also captures non-equilibrium effects of the energy cascade. As a demonstration, the present findings are applied to machine-learning-based super-resolution analysis of three-dimensional isotropic turbulence. We show that machine-learning models reconstruct vortical structures well in the interpolatory space with reduced performance in the extrapolatory space revealed by the nonlinearly scaled invariants. The present approach enables us to depart from labeling turbulent flow data with a single parameter of Reynolds number and comprehensively examine the flow field to support training and testing of nonlinear machine-learning techniques.

physics.flu-dyn↗

arXiv2023

Space-local Navier--Stokes turbulence

We investigate the physical-space locality of interactions in three-dimensional incompressible turbulent flow. To that, we modify the nonlinear terms of the vorticity equation such that the vorticity field is advected and stretched by the locally induced velocity. This space-local velocity field is defined by the truncated Biot--Savart law, where only the neighboring vorticity field in a sphere of radius $R$ is integrated. We conduct direct numerical simulations of the space-local system to investigate its statistics in the inertial range. We observe a standard $E(k) \propto k^{-5/3}$ scaling of the energy spectrum associated with an energy cascade for scales smaller than the space-local domain size $k \gg R^{-1}$. This result is consistent with the assumption Kolmogorov's 1941 paper made for the space-locality of the nonlinear interactions. The enstrophy amplification is suppressed for larger scales $k \ll R^{-1}$, and for these scales, the system exhibits a scaling consistent with a conservative enstrophy cascade.

physics.flu-dyn↗

arXiv2023

Characterizing Data Assimilation in Navier-Stokes Turbulence with Transverse Lyapunov Exponents

Data assimilation (DA) reconstructing small-scale turbulent structures is crucial for forecasting and understanding turbulence. This study proposes a theoretical framework for DA based on ideas from chaos synchronization, in particular, the transverse Lyapunov exponents (TLEs). The analysis with TLEs characterizes a critical length scale, below which the turbulent dynamics is synchronized to the larger-scale turbulent dynamics, indicating successful DA. An underlying link between TLEs and the maximal Lyapunov exponent suggests that the critical length scale depends on the Reynolds number. Furthermore, we discuss new directions of DA algorithms based on the proposed framework.

physics.flu-dyn↗

arXiv2023

Minimal model of quasi-cyclic behaviour in turbulence driven by Taylor--Green forcing

We attempt to formulate the simplest possible model mimicking turbulent dynamics, such as quasi-cyclic behaviour (QCB), using only three variables. To this end, we first conduct direct numerical simulations of three-dimensional flow driven by the steady Taylor--Green forcing to find a similarity between a stable periodic orbit (SPO) at a small Reynolds number ($Re$) and turbulent QCB at higher $Re$. A close examination of the SPO allows the heuristic formulation of a three-equation model, representing the evolution of Fourier modes in three distinct scales. The model reproduces the continuous bifurcation from SPO to turbulence with QCB when $Re$ is varied. We also demonstrate that, by changing model parameters, the proposed model exhibits a discontinuous transition from steady to chaotic solutions without going through an SPO.

physics.flu-dyn↗

arXiv2022

Attenuation of turbulence in a periodic cube by finite-size spherical solid particles

To investigate the attenuation of turbulence in a periodic cube due to the addition of spherical solid particles, we conduct direct numerical simulations using an immersed boundary method with resolving flow around each particle. Numerical results with systematically changing particle diameters and Stokes numbers for a fixed volume fraction $Λ$ show that the additional energy dissipation rate in the wake of particles determines the degree of the attenuation of turbulent kinetic energy. On the basis of this observation, we propose the formulae describing the condition and degree of the attenuation of turbulence intensity. We conclude that particles with the size proportional to $λ/\sqrtγ$, where $λ$ and $γ$ are the Taylor length and the mass density ratio between particles and fluid, most significantly reduce the intensity of developed turbulence under the condition that $γ$ and $Λ$ are fixed.

physics.flu-dyn↗

arXiv2022

Correlation function and linear response function of homogeneous isotropic turbulence in the Eulerian and Lagrangian coordinates

We study the correlation function and mean linear response function of the velocity Fourier mode of statistically steady-state, homogeneous and isotropic turbulence in the Eulerian and Lagrangian coordinates through direct numerical simulation (DNS). As the Lagrangian velocity, we here adopt Kraichnan's Lagrangian history framework where Lagrangian particles are labelled with current positions and their velocity are measured at some time before. This Lagrangian velocity is numerically calculated with a method known as passive vector method. Our first goal is to study relation between the correlation function and the mean linear response function in the Eulerian and Lagrangian coordinates. Such a relation is known to be important in analysing the closed set of equations for the two functions, which are obtained by direct-interaction-approximation type closures. We demonstrate numerically that the fluctuation-dissipation theorem (proportionality between the two functions) does not hold. The relation is further investigated with general analytical expressions of the mean linear response function under stochastic settings, which are known as the fluctuation-response relations in non-equilibrium statistical mechanics. Our second goal is to identify characteristic times associated with the two functions and to compare the times between the Eulerian and Lagrangian coordinates. Our DNS result supports the common view that the Eulerian characteristic times have the sweeping-time scaling ($\propto k^{-1}$, where $k$ is the wavenumber) for both functions and the Lagrangian characteristic times in the inertial range have the Kolmogorov-time scaling ($\propto k^{-2/3}$) for both functions.

physics.flu-dyn↗

arXiv2021

Mathematical reformulation of the Kolmogorov-Richardson energy cascade in terms of vortex stretching

In this paper, with the aid of direct numerical simulations (DNS) of forced turbulence in a periodic domain, we mathematically reformulate the Kolmogorov-Richardson energy cascade in terms of vortex stretching. By using the description, we prove that if the Navier-Stokes flow satisfies a new regularity criterion in terms of the enstrophy production rate, then the flow does not blow up. Our DNS results seem to support this regularity criterion. Next, we mathematically construct the hierarchy of tubular vortices, which is statistically self-similar in the inertial range. Under the assumptions of the scale-locally of the vortex stretching/compressing (i.e. energy cascade) process and the statistical independence between vortices that are not directly stretched or compressed, we can derive the $-5/3$ power law of the energy spectrum of statistically stationary turbulence without directly using the Kolmogorov hypotheses.

physics.flu-dyn↗

arXiv2021

Self-similar hierarchy of coherent tubular vortices in turbulence

Energy transfers from larger to smaller scales in turbulence. This energy cascade is a process of the creation of smaller-scale coherent vortices by larger ones. In our recent study (Yoneda, Goto and Tsuruhashi 2021), we reformulated the energy cascade in terms of this stretching process and derived the $-5/3$ law of the energy spectrum under physically reasonable assumptions. In the present study, we provide a quantitative verification of these assumptions by using direct numerical simulations. We decompose developed turbulence in a periodic cube into scales by using the band-pass filter and identify the axes of coherent tubular vortices by the low-pressure method. Even when the turbulent kinetic energy and its dissipation rate temporally fluctuate about their temporal means, the total length of the vortices at each scale varies little with time. This result is consistent with our assumption of the temporal stationarity on the vorticity decomposition. The present numerical analysis also shows that the hierarchy of vortex axes is self-similar in a wide range of scales, i.e. in the inertial range and a lower part of the dissipation range and that the volume fraction occupied by the tubular vortices at each scale is independent of the scale.

physics.flu-dyn↗

arXiv2020

Transfer learning for nonlinear dynamics and its application to fluid turbulence

We introduce transfer learning for nonlinear dynamics, which enables efficient predictions of chaotic dynamics by utilizing a small amount of data. For the Lorenz chaos, by optimizing the transfer rate, we accomplish more accurate inference than the conventional method by an order of magnitude. Moreover, a surprisingly small amount of learning is enough to infer the energy dissipation rate of the Navier-Stokes turbulence because we can, thanks to the small-scale universality of turbulence, transfer a large amount of the knowledge learned from turbulence data at lower Reynolds number.

physics.flu-dyn↗

arXiv2017

Insights from Single-File Diffusion into Cooperativity in Higher Dimensions

Diffusion in colloidal suspensions can be very slow due to the cage effect, which confines each particle within a short radius on one hand, and involves large-scale cooperative motions on the other. In search of insight into this cooperativity, here the authors develop a formalism to calculate the displacement correlation in colloidal systems, mainly in the two-dimensional case. To clarify the idea for it, studies are reviewed on cooperativity among the particles in the one-dimensional case, i.e. the single-file diffusion (SFD). As an improvement over the celebrated formula by Alexander and Pincus on the mean-square displacement (MSD) in SFD, it is shown that the displacement correlation in SFD can be calculated from Lagrangian correlation of the particle interval in the one-dimensional case, and also that the formula can be extended to higher dimensions. The improved formula becomes exact for large systems. By combining the formula with a nonlinear theory for correlation, a correction to the asymptotic law for the MSD in SFD is obtained. In the two-dimensional case, the linear theory gives description of vortical cooperative motion.

cond-mat.soft↗