Published in European Journal of Mechanics-B/Fluids, 2026
Using two-dimensional turbulent Kolmogorov flow, this paper demonstrates that tiny variations in initial conditions of Navier-Stokes equations lead to huge differences in flow symmetry and statistics.
Recommended citation: Qin, S., Xu, K. & Liao, S. (2026). "Ultra-chaotic property of Navier-Stokes turbulence." European Journal of Mechanics-B/Fluids. 119, 204540.
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Published in Physics of Fluids, 2025
This study solves a three-dimensional (3D) turbulent Kolmogorov flow by means of Clean Numerical Simulation (CNS) and compares the result obtained via Direct Numerical Simulation (DNS) to analyze the impact of numerical noise.
Recommended citation: Qin, S. & Liao, S. (2025). "Clean numerical simulation of three-dimensional turbulent Kolmogorov flow." Physics of Fluids. 37(10), 105160.
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Published in Journal of Fluid Mechanics, 2025
Revealing a new phenomenon termed the “noise-expansion cascade” to explain the origin of randomness in turbulence through clean numerical experiments.
Recommended citation: Liao, S. & Qin, S. (2025). "Noise-expansion cascade: an origin of randomness of turbulence." Journal of Fluid Mechanics. 1009, A2.
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Published in Journal of Fluid Mechanics, 2025
A deep discussion on the physical implications of artificial numerical noises in the Direct Numerical Simulation (DNS) of turbulence.
Recommended citation: Liao, S. & Qin, S. (2025). "Physical significance of artificial numerical noise in direct numerical simulation of turbulence." Journal of Fluid Mechanics. 1008, R2.
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Published in Physics of Fluids, 2025
Investigating the impact of numerical noise on surface quasi-geostrophic (SQG) turbulence by comparing DNS and CNS methods.
Recommended citation: Zhang, B., Hu, T., Qin, S., Li, J. & Liao, S. (2025). "Influence of numerical noise on surface quasi-geostrophic turbulence." Physics of Fluids. 37(3), 036624.
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Published in Physica D: Nonlinear Phenomena, 2024
An investigation into how artificial numerical noises affect the statistical and qualitative properties of chaotic dynamic systems.
Recommended citation: Qin, S. & Liao, S. (2024). "Influences of artificial numerical noise on statistics and qualitative properties of chaotic system." Physica D: Nonlinear Phenomena. 470, 134355.
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Published in Journal of Ocean Engineering and Science, 2024
A critical examination of the absolute reliability of DNS in Navier-Stokes equations even with extremely fine computational grids.
Recommended citation: Qin, S., Yang, Y., Huang, Y., Mei, X., Wang, L. & Liao, S. (2024). "Is a direct numerical simulation (DNS) of Navier-Stokes equations with small enough grid spacing and time-step definitely reliable/correct?" Journal of Ocean Engineering and Science. 9(3), 293-310.
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Published in International Journal of Bifurcation and Chaos, 2023
A study on the complex dynamics and ultra-chaos phenomena observed in the motion of walking droplets on vibrating fluid baths.
Recommended citation: Yang, Y., Qin, S. & Liao, S. (2023). "Ultra-Chaos in the Motion of Walking Droplet." International Journal of Bifurcation and Chaos. 33(16), 2350191.
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Published in Advances in Applied Mathematics and Mechanics, 2023
Proposing a self-adaptive step-size and precision algorithm to optimize Clean Numerical Simulation (CNS) for complex chaotic systems.
Recommended citation: Qin, S. & Liao, S. (2023). "A self-adaptive algorithm of the clean numerical simulation (CNS) for chaos." arXiv preprint arXiv:2302.01284.
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Published in Journal of Fluid Mechanics, 2023
Investigating the Lagrangian chaotic properties inherent within the Arnold-Beltrami-Childress (ABC) flow using a high-precision numerical method.
Recommended citation: Qin, S. & Liao, S. (2023). "A kind of Lagrangian chaotic property of the Arnold–Beltrami–Childress flow." Journal of Fluid Mechanics. 960, A15.
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Published in Chaos, Solitons & Fractals, 2022
This work illustrates that the motion of a chaotic mobile robot belongs to ultra-chaos, a higher-level disorder where small disturbances cause huge deviations even in statistics.
Recommended citation: Yang, Y., Qin, S. & Liao, S. (2023). "Ultra-chaos of a mobile robot: a higher disorder than normal-chaos." Chaos, Solitons & Fractals. 167, 113037.
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Published in Journal of Fluid Mechanics, 2022
Demonstrating the macro-scale impacts of artificial stochastic numerical disturbances on the overall development of sustained turbulence.
Recommended citation: Qin, S. & Liao, S. (2022). "Large-scale influence of numerical noises as artificial stochastic disturbances on a sustained turbulence." Journal of Fluid Mechanics. 948, A7.
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Published in Advances in Applied Mathematics and Mechanics, 2022
Discussing ultra-chaos as a fundamental objective barrier to the reproducibility of numerical and physical experiments.
Recommended citation: Liao, S. & Qin, S. (2022). "Ultra-chaos: an insurmountable objective obstacle of reproducibility and replication." Advances in Applied Mathematics and Mechanics. 14(4), 799-815.
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Published in Chaos, Solitons & Fractals, 2020
A foundational study on the pervasive influence of numerical noises during the computer simulation of spatio-temporal chaotic systems.
Recommended citation: Qin, S. & Liao, S. (2020). "Influence of numerical noises on computer-generated simulation of spatio-temporal chaos." Chaos, Solitons & Fractals. 136, 109790.
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