Scalar Source Localization Using Multi-Sensor Domains of Dependence in Turbulent Channel Flow

Tracking hazardous events such as wildfire smoke, coastal oil spills, or chemical releases in natural environments is complicated by turbulent dispersion and molecular diffusion. This study presents a method to localize pollutant sources rapidly and accurately using finite time-averaged measurements from a multi-sensor network, leveraging the duality between mean forward and adjoint scalar fields. The forward-adjoint duality states that measurements at the sensor (forward field) are equal to the adjoint field at the source, providing crucial spatial information about the source. Consequently, the adjoint scalar fields can be interpreted as the domain of dependence for the sensor observations. We demonstrate this framework using multiple domains of dependence in a turbulence channel flow with friction Reynolds number $Re_{\tau} = 180$. We derive a time-averaged duality relation, which allows us to bypass detailed eddy-resolving flow fields and focus on the statistical flow properties. This approach facilitates the use of forward-adjoint duality under realistic conditions with uncertainty for rapid scalar source localization. We assess scalar source identification accuracy through Monte-Carlo simulations and compare the performance across multiple sensor-source arrangements in channel flow turbulence. With 12 sensors distributed at the same streamwise location, the results show that reconstruction performance is poorest when the sources are released in the outer layer, whereas the best performance is achieved when they are released in the buffer layer.