arXiv subjects

Earl Dowell

Publications and source records attributed to Earl Dowell.

6 recordsLinked to original sources

arXiv2026

Phase Reduction Analysis of Transonic Buffet

This paper develops a phase-reduced description of transonic buffet, treating buffet as a stable autonomous fluid limit cycle that is weakly perturbed by harmonic structural motion. When combined with aerodynamic work, the phase reduction model yields closed-form expressions for the equivalent aerodynamic damping and stiffness, together with a unified description of phase locking, phase slipping and aeroelastic stability of the fluid-structural system. The resulting analysis provides new insight into the mechanisms governing aeroelastic instability in oscillatory flows, including aerodynamic damping maps, singular behaviour at zero detuning, and broad regions of subcritical aeroelastic instability.

physics.flu-dyn↗

arXiv2026

Neural Differential Equations for Oscillatory Flows in Aeroelasticity Applied to Transonic Buffet

Self-excited aerodynamic flows arise across a broad range of systems and can drive nonlinear fluid-structure interactions and aeroelastic instabilities that are challenging and computationally expensive to predict. This paper presents a physics-guided neural differential equation (DE) reduced order model (ROM) combining a nonlinear fluid oscillator, a finite-memory multi-input Volterra series, and a compact neural network correction. The multi-input aerodynamic formulation is generalized to m structural modes, capturing direct and nonlinear cross-modal coupling. The model is identified from a single prescribed-motion CFD simulation with simultaneous excitation of all retained structural modes, and is then coupled with the structural equations of motion for efficient aeroelastic prediction. Applied to transonic buffet over the ONERA OAT15A airfoil, the time-marching ROM predicts aeroelastic stability, frequency lock-in, and limit cycle amplitudes in good agreement with full-order reference solutions. The ROM is used to provide substantial new insight into buffet-induced aeroelastic instabilities involving more than one structural mode.

physics.flu-dyn↗

arXiv2025

Exploratory Study of Chaotic Behavior in Walking Droplets

The interaction of 'walking droplets' and capillary waves in a weakly subcritical Faraday wave experiment has been studied as a hydrodynamic analog to Bohmian quantum mechanics (see "Hydrodynamic Quantum Analogs", J. Bush and A. Oza, Rep. Prog. Physics (2021)). We report here experimental results of walking droplets interacting with supercritical Faraday waves with dimensionless acceleration of approximately 7.7, where the onset of Faraday instability occurs at dimensionless acceleration 6.3, in flat bath topography. Our working fluid is silicone oil with a kinematic viscosity of 20 cst that is placed as a 4.2 mm horizontal liquid layer in an intermediate-aspect-ratio circular bath with a radius to Faraday wavelength ratio of 5.8. We also use different 3D-printed subsurfaces that act as slit structures with local oil depth of 0.7 mm. We confirm expected behavior for walking droplets in the supercritical Faraday regime, such as erratic trajectories, droplets clustering together due to capillary effects, and spontaneous drop creation. We note a special case of walking-droplet behavior when the bath only partially displays Faraday waves. We discuss the influence of the lateral boundaries and slits on droplet trajectory in this chaotic regime and compare the measured trajectories found here to those single and double slit experiments previously studied in the subcritical Faraday regime.

physics.flu-dyn↗

arXiv2021

Dynamic Equations of Motion for Inextensible Beams and Plates

The large deflections of cantilevered beams and plates are modeled and discussed. Traditional nonlinear elastic models (e.g., that of von Karman) employ elastic restoring forces based on the effect of stretching on bending, and these are less applicable to cantilevers. Recent experimental work indicates that elastic cantilevers are subject to nonlinear inertial and stiffness effects. We review a recently established (quasilinear and nonlocal) cantilevered beam model, and consider some natural extensions to two dimensions -- namely, inextensible plates. Our principal configuration is that of a thin, isotropic, homogeneous rectangular plate, clamped on one edge and free on the remaining three. We proceed through the geometric and elastic modeling to obtain equations of motion via Hamilton's principle for the appropriately specified energies. We enforce {\em effective} inextensibility constraints through Lagrange multipliers. Multiple plate analogs of the established 1D model are obtained, based on various assumptions. For each plate model, we present the modeling hypotheses and the resulting equations of motion. It total, we present three distinct nonlinear partial differential equation models, and, additionally, describe a class of ``higher order" models. Each model has particular advantages and drawbacks for both mathematical and engineering analyses. We conclude with an in depth discussion and comparison of the various systems and some analytical problems.

math.AP↗

arXiv2015

Minimal subspace rotation on the Stiefel manifold for stabilization and enhancement of projection-based reduced order models for the compressible Navier-Stokes equations

For a projection-based reduced order model (ROM) of a fluid flow to be stable and accurate, the dynamics of the truncated subspace must be taken into account. This paper proposes an approach for stabilizing and enhancing projection-based fluid ROMs in which truncated modes are accounted for a priori via a minimal rotation of the projection subspace. Attention is focused on the full non-linear compressible Navier-Stokes equations in specific volume form as a step toward a more general formulation for problems with generic non-linearities. Unlike traditional approaches, no empirical turbulence modeling terms are required, and consistency between the ROM and the full order model from which the ROM is derived is maintained. Mathematically, the approach is formulated as a trace minimization problem on the Stiefel manifold. The reproductive as well as predictive capabilities of the method are evaluated on several compressible flow problems, including a problem involving laminar flow over an airfoil with a high angle of attack, and a channel-driven cavity flow problem.

physics.comp-ph↗

arXiv2012

A Novel Model Order Reduction Approach for Navier-Stokes Equations at High Reynolds Number

A new approach to model order reduction of the Navier-Stokes equations at high Reynolds number is proposed. Unlike traditional approaches, this method does not rely on empirical turbulence modeling or modification of the Navier-Stokes equations. It provides spatial basis functions different from the usual proper orthogonal decomposition basis function in that, in addition to optimally representing the training data set, the new basis functions also provide stable and accurate reduced-order models. The proposed approach is illustrated with two test cases: two-dimensional flow inside a square lid-driven cavity and a two-dimensional mixing layer.

physics.flu-dyn↗