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Abstract High fidelity near-wall velocity measurements in wall bounded fluid flows continue to pose a challenge and the resulting limitations on available experimental data cloud our understanding of the near-wall velocity behavior in turbulent boundary layers. One of the challenges is the spatial averaging and limited spatial resolution inherent to cross-correlation-based particle image velocimetry (PIV) methods. To circumvent this difficulty, we implement an explicit no-slip boundary condition in a wavelet-based optical flow velocimetry (wOFV) method. It is found that the no-slip boundary condition on the velocity field can be implemented in wOFV by transforming the constraint to the wavelet domain through a series of algebraic linear transformations, which are formulated in terms of the known wavelet filter matrices, and then satisfying the resulting constraint on the wavelet coefficients using constrained optimization for the optical flow functional minimization. The developed method is then used to study the classical problem of a turbulent channel flow using synthetic data from a direct numerical simulation (DNS) and experimental particle image data from a zero pressure gradient, high Reynolds number turbulent boundary layer. The results obtained by successfully implementing the no-slip boundary condition are compared to velocity measurements from wOFV without the no-slip condition and to a commercial PIV code, using the velocity from the DNS as ground truth. It is found that wOFV with the no-slip condition successfully resolves the near-wall profile with enhanced accuracy compared to the other velocimetry methods, as well as other derived quantities such as wall shear and turbulent intensity, without sacrificing accuracy away from the wall, leading to state of the art measurements in the region of the turbulent boundary layer when applied to experimental particle images.
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This content will become publicly available on April 1, 2026
Inference of inertial particle dynamics from limited measurements
A data assimilation approach is coined that enables the discovery of forcing functions in Lagrangian, point-particle models from limited measurements of trajectory coordinates. Central to the proposed formulation of this inverse problem is the expression of the forcing function in terms of modal basis functions that are dependent on the relative velocity difference between a known carrier flow and the particle solution weighted with coefficients that are known within confidence intervals. The probability density function of the random forcing coefficients is inferred using a combination of the forward, particle model and its adjoint dynamics, which calculates the gradient of the cost function defined as the distance between the measured and predicted particle locations. To ensure convergence of the gradient-based optimization, multiple measurements may be required. If the measurements are noisy, samples of the forcing model within an assumed Gaussian distribution of the confidence interval of the measurement are computed using a Hamiltonian Monte Carlo method. The method is verified to correctly infer the forcing function of particles traced in the Arnold–Beltrami–Childress flow and a homogeneous isotropic turbulence. The confidence interval of the inferred forcing function with respect to a flow condition is improved if the particle is exposed more frequently to the flow condition. The forcing coefficients adapt the model to flow conditions that are outside of the limited range for which the point-particle models are typically known only empirically or within confidence intervals.
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- Award ID(s):
- 2332057
- PAR ID:
- 10587507
- Publisher / Repository:
- AIP Publishing
- Date Published:
- Journal Name:
- Physics of Fluids
- Volume:
- 37
- Issue:
- 4
- ISSN:
- 1070-6631
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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