Learning to traverse convective flows at moderate to high Rayleigh numbers

2026/04/16 by Ao Xu, Hua-Lin Wu, Ben-Rui Xu +1
Physics and Astronomy · Computer Science · Engineering · #Micro and Nano Robotics #Distributed Control Multi-Agent Systems #Particle Dynamics in Fluid Flows

paper · pdf · doi:10.1017/jfm.2026.11802

Abstract

We study the navigation of a self-propelled inertial particle in two-dimensional Rayleigh–Bénard convection at Prandtl number italic probability equals 0.71 <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:mrow> <mml:mtext mathvariant="italic" class="MJX-tex-mathit">Pr</mml:mtext> </mml:mrow> <mml:mo>=</mml:mo> <mml:mn>0.71</mml:mn> </mml:math> Pr=0.71 and cell aspect ratio upper Gamma equals 4 <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:mi>Γ</mml:mi> <mml:mo>=</mml:mo> <mml:mn>4</mml:mn> </mml:math> \varGamma =4 for Rayleigh numbers upper R a <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:mi>R</mml:mi> <mml:mi>a</mml:mi> </mml:math> Ra ranging from 10 Superscript 7 <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>7</mml:mn> </mml:msup> </mml:math> 10⁷ to 10 Superscript 11 <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mn>11</mml:mn> </mml:mrow> </mml:msup> </mml:math> 10¹¹ . A reinforcement-learning (RL) controller selects the propulsive acceleration, subject to an upper bound script upper A Subscript italic max <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:msub> <mml:mrow> <mml:mi mathvariant="script" class="MJX-tex-caligraphic">A</mml:mi> </mml:mrow> <mml:mrow> <mml:mrow> <mml:mtext mathvariant="italic" class="MJX-tex-mathit">max</mml:mtext> </mml:mrow> </mml:mrow> </mml:msub> </mml:math> A_max , to achieve a prescribed horizontal displacement. We find that the success rate increases abruptly with script upper A Subscript italic max <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:msub> <mml:mrow> <mml:mi mathvariant="script" class="MJX-tex-caligraphic">A</mml:mi> </mml:mrow> <mml:mrow> <mml:mrow> <mml:mtext mathvariant="italic" class="MJX-tex-mathit">max</mml:mtext> </mml:mrow> </mml:mrow> </mml:msub> </mml:math> A_max at moderate upper R a <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content">

Citations

• Machine Learning for Fluid Mechanics
• Efficient collective swimming by harnessing vortices through deep reinforcement learning
• Lagrangian Coherent Structures
• The hydrodynamics of swimming microorganisms
• Small-Scale Properties of Turbulent Rayleigh-Bénard Convection

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