Optimization of a Moving Sensor Trajectory for Observing a Point Scalar Source in Turbulent Flow

We propose a strategy for optimizing a sensor trajectory in order to estimate the time dependence of a localized scalar source in turbulent channel flow. The approach leverages the view of the adjoint scalar field as the sensitivity of measurement to a possible source. A cost functional is constructed so that the optimal sensor trajectory maintains a high sensitivity and low temporal variation in the measured signal, for a given source location. This naturally leads to the adjoint-of-adjoint equation based on which the sensor trajectory is iteratively optimized. It is shown that the estimation performance based on the measurement obtained by a sensor moving along the optimal trajectory is drastically improved from that achieved with a stationary sensor. It is also shown that the ratio of the fluctuation and the mean of the sensitivity for a given sensor trajectory can be used as a diagnostic tool to evaluate the resultant performance. Based on this finding, we propose a new cost functional which only includes the ratio without any adjustable parameters, and demonstrate its effectiveness in predicting the time dependence of scalar release from the source.