More Like this

1. Wall-to-wall optimal transport in two dimensions

   https://doi.org/10.1017/jfm.2020.42  

   Souza, Andre N.; Tobasco, Ian; Doering, Charles R. (April 2020, Journal of Fluid Mechanics)

   Gradient ascent methods are developed to compute incompressible flows that maximize heat transport between two isothermal no-slip parallel walls. Parameterizing the magnitude of the velocity fields by a Péclet number $Pe$ proportional to their root-mean-square rate of strain, the schemes are applied to compute two-dimensional flows optimizing convective enhancement of diffusive heat transfer, i.e. the Nusselt number $Nu$ up to $$Pe\approx 10^{5}$$ . The resulting transport exhibits a change of scaling from $$Nu-1\sim Pe^{2}$$ for $Pe<10$ in the linear regime to $$Nu\sim Pe^{0.54}$$ for $$Pe>10^{3}$$ . Optimal fields are observed to be approximately separable, i.e. products of functions of the wall-parallel and wall-normal coordinates. Analysis employing a separable ansatz yields a conditional upper bound $${\lesssim}Pe^{6/11}=Pe^{0.\overline{54}}$$ as $$Pe\rightarrow \infty$$ similar to the computationally achieved scaling. Implications for heat transfer in buoyancy-driven Rayleigh–Bénard convection are discussed. 

   more » « less
2. Near-wall patch representation of wall-bounded turbulence

   https://doi.org/10.1017/jfm.2020.658  

   Carney, Sean P.; Engquist, Björn; Moser, Robert D. (November 2020, Journal of Fluid Mechanics)

   null (Ed.)

   Recent experimental and computational studies indicate that near-wall turbulent flows can be characterized by universal small-scale autonomous dynamics that is modulated by large-scale structures. We formulate numerical simulations of near-wall turbulence in a small domain localized to the boundary, whose size scales in viscous units. To mimic the environment in which the near-wall turbulence evolves, the formulation accounts for the flux of mean momentum through the upper boundary of the domain. Comparisons of the model's two-dimensional energy spectra and low-order single-point statistics with the corresponding quantities computed from direct numerical simulations indicate that it successfully captures the dynamics of the small-scale near-wall turbulence. 

   more » « less
3. On the Optimal Design of Wall‐to‐Wall Heat Transport

   https://doi.org/10.1002/cpa.21832  

   Doering, Charles R.; Tobasco, Ian (May 2019, Communications on Pure and Applied Mathematics)
4. Wall Matters: Rethinking the Effect of Wall for Wireless Sensing

   https://doi.org/10.1145/3631417  

   Xie, Binbin; Cui, Minhao; Ganesan, Deepak; Xiong, Jie (December 2023, Proceedings of the ACM on Interactive, Mobile, Wearable and Ubiquitous Technologies)

   Wireless sensing has demonstrated its potential of utilizing radio frequency (RF) signals to sense individuals and objects. Among different wireless signals, LoRa signal is particularly promising for through-wall sensing owing to its strong penetration capability. However, existing works view walls as a bad thing as they attenuate signal power and decrease the sensing coverage. In this paper, we show a counter-intuitive observation, i.e., walls can be used to increase the sensing coverage if the RF devices are placed properly with respect to walls. To fully understand the underlying principle behind this observation, we develop a through-wall sensing model to mathematically quantify the effect of walls. We further show that besides increasing the sensing coverage, we can also use the wall to help mitigate interference, which is one well-known issue in wireless sensing. We demonstrate the effect of wall through two representative applications, i.e., macro-level human walking sensing and micro-level human respiration monitoring. Comprehensive experiments show that by properly deploying the transmitter and receiver with respect to the wall, the coverage of human walking detection can be expanded by more than 160%. By leveraging the effect of wall to mitigate interference, we can sense the tiny respiration of target even in the presence of three interferers walking nearby. 

   more » « less
5. On the Optimal Design of Wall-to-Wall Heat Transport

   Doering, Charles R; Tobasco, I (January 2019, Communications on pure and applied mathematics)

   We consider the problem of optimizing heat transport through an incompress- ible fluid layer. Modeling passive scalar transport by advection-diffusion, we maximize the mean rate of total transport by a divergence-free velocity field. Subject to various boundary conditions and intensity constraints, we prove that the maximal rate of transport scales linearly in the r.m.s. kinetic energy and, up to possible logarithmic corrections, as the one-third power of the mean enstro- phy in the advective regime. This makes rigorous a previous prediction on the near optimality of convection rolls for energy-constrained transport. On the other hand, optimal designs for enstrophy-constrained transport are significantly more difficult to describe: we introduce a “branching” flow design with an unbounded number of degrees of freedom and prove it achieves nearly optimal transport. The main technical tool behind these results is a variational principle for evalu- ating the transport of candidate designs. The principle admits dual formulations for bounding transport from above and below. While the upper bound is closely related to the “background method,” the lower bound reveals a connection be- tween the optimal design problems considered herein and other apparently re- lated model problems from mathematical materials science. These connections serve to motivate designs. 

   more » « less