Heinonen R A, Biferale L, Celani A, Vergassola M
Dept. Physics and INFN, University of Rome "Tor Vergata", Via della Ricerca Scientifica 1, 00133 Rome, Italy.
Quantitative Life Sciences, The Abdus Salam International Centre for Theoretical Physics, 34151 Trieste, Italy.
Phys Rev Fluids. 2025 Apr;10(4). doi: 10.1103/physrevfluids.10.044601. Epub 2025 Apr 9.
In turbulent flows, tracking the source of a passive scalar cue requires exploiting the limited information that can be gleaned from rare, randomized encounters with the cue. When crafting a search policy, the most challenging and important decision is what to do in the absence of an encounter. In this work, we perform high-fidelity direct numerical simulations of a turbulent flow with a stationary source of tracer particles, and obtain quasi-optimal policies (in the sense of minimal average search time) with respect to the empirical encounter statistics [1-3]. We study the trajectories under such policies and compare the results to those of the infotaxis heuristic. In the presence of a strong mean wind, the optimal motion in the absence of an encounter is zigzagging (akin to the well-known insect behavior "casting") followed by a return to the starting location. The zigzag motion generates characteristic scaling of the rms displacement envelope. By passing to the limit where the probability of detection vanishes, we connect these results to the classical linear search problem and derive an estimate of the tail of the arrival time pdf as a stretched exponential for some , in agreement with Monte Carlo results. We also discuss what happens as the wind speed becomes smaller.
在湍流中,追踪被动标量线索的来源需要利用从与该线索的罕见、随机相遇中收集到的有限信息。在制定搜索策略时,最具挑战性和重要的决策是在没有相遇时该怎么做。在这项工作中,我们对带有示踪粒子固定源的湍流进行了高保真直接数值模拟,并根据经验相遇统计数据获得了准最优策略(从平均搜索时间最短的意义上来说)[1 - 3]。我们研究了在这些策略下的轨迹,并将结果与信息趋化启发式方法的结果进行比较。在存在强平均风的情况下,没有相遇时的最优运动是曲折前进(类似于众所周知的昆虫行为“投撒”),然后返回起始位置。这种曲折运动会产生均方根位移包络的特征标度。通过过渡到检测概率消失的极限情况,我们将这些结果与经典线性搜索问题联系起来,并推导出到达时间概率密度函数尾部的估计值,对于某些情况,其为拉伸指数形式,这与蒙特卡罗结果一致。我们还讨论了风速变小时会发生什么情况。