# Model-Based Estimation of Vortex Shedding in Unsteady Cylinder Wakes

## TL;DR

This paper develops a harmonic decomposition-based model and two estimation methods, LE and LTE, to accurately estimate vortex shedding in cylinder wakes from single sensor data at different Reynolds numbers.

## Contribution

It introduces LTE, a novel nonlinear estimation method that outperforms LE in reconstructing vortex shedding dynamics from limited sensor data.

## Key findings

- LTE outperforms LE in flow field reconstruction.
- Higher harmonic motions are subordinate to the fundamental frequency.
- The model effectively captures vortex shedding dynamics at specified Reynolds numbers.

## Abstract

This paper considers single-sensor estimation of vortex shedding in cylinder wakes at $Re=100$ in simulations and at $Re=1036$ in experiments. A model based on harmonic decomposition is developed to capture the periodic dynamics of vortex shedding. Two model-based methods are proposed to estimate time-resolved flow fields. First, Linear Estimation (LE) which implements a Kalman Filter to estimate the flow. Second, Linear-Trigonometric Estimation (LTE), which utilizes the same Kalman Filter together with a nonlinear relationship between harmonics of the vortex shedding frequency. LTE shows good performance and outperforms LE regarding the reconstruction of vortex shedding. Physically this suggests that, at the Reynolds numbers considered, the higher harmonic motions in the cylinder wake are slave to the fundamental frequency.