arXiv subjects

Jonathan M. O. Massey

Publications and source records attributed to Jonathan M. O. Massey.

3 recordsLinked to original sources

arXiv2026

On the Poisson-Source Basis of Logarithmic Wall-Pressure-Variance Growth

In high-Reynolds-number wall-bounded flows, the inner-scaled wall-pressure variance \ra{is often represented as a} logarithmic increase with frictional Reynolds number. We consider the two sources of the incompressible pressure--Poisson equation: a linear (rapid) term linked to mean shear and a nonlinear (slow) term composed of quadratic velocity fluctuations. This paper establishes a link between the sources and the coefficients in \rtwo{a logarithmic} inner-scaled variance \rtwo{representation}. \rone{To leading order} we \rone{posit that} the \ra{linear source provides a Reynolds-number-independent offset, while the nonlinear source contributes the logarithmic coefficient}. The illustrative dataset is direct numerical simulation (DNS) at \rtwo{frictional Reynolds number} $δ^+\approx 550$, although the principal contribution is the establishment of a mechanistic link to well-known high-$δ^+$ scalings of wall-bounded turbulence. Through consideration of the sources and the integral solution method of the Poisson equation, we find that the linear source contribution sits predominantly in the buffer layer and maps to the near-wall cycle. \rone{To leading order}, this contribution becomes $δ^+$ invariant under inner scaling, thus contributing an offset in the \rtwo{logarithmic representation}. The interfacial regions between uniform momentum zones characteristic of the inertial layer (vortical fissures) spatially localise strain and vorticity contributions and contain an increasingly large proportion of the strain and vorticity. We show that fissures act as a compact carrier for the source terms, with the nonlinear term especially prominent in these regions. By considering the inertial layer statistics, we link the changing nonlinear contribution to \rtwo{the} $\ln δ^+$ \rtwo{growth}, in agreement with previous empirical observations.

physics.flu-dyn↗

arXiv2026

Two-component inner--outer scaling model for the wall-pressure spectrum at high Reynolds number

Wall-pressure fluctuations beneath turbulent boundary layers drive noise and structural fatigue through interactions between fluid and structural modes. Conventional predictive models for the spectrum--such as the widely accepted Goody model (\textit{AIAA Journal} 42 (9), 2004, 1788--1794)--fail to capture the energetic growth in the {low-frequency range} that occurs at high Reynolds number, while at the same time over-predicting the variance. To address these shortcomings, two semi-empirical models are proposed for the wall-pressure spectrum in canonical turbulent boundary layers, pipes and channels for friction Reynolds numbers $δ^+$ ranging from 180 to 47 000. The models are based on consideration of two {spectral components} that represent the contributions to the wall pressure fluctuations from inner-scale motions and outer-scale motions. The first model expresses the pre-multiplied spectrum as the sum of two overlapping log-normal {components}: an inner-scaled term that is $δ^+$-invariant and an outer-scaled term whose amplitude broadens smoothly with $δ^+$. Calibrated against large-eddy simulations, direct numerical simulations, and recent high-$δ^+$ pipe data, it reproduces the {inner-scaled peak} and the emergence of an outer-scaled peak at large $δ^+$. The second model, developed around newly available pipe data, uses theoretical arguments to prescribe the spectral shapes of the inner and outer {components}. Embedding the $δ^+$-dependence in smooth asymptotic functions yields a formulation that varies continuously with $δ^+$ {and generalises beyond the calibration range}. Both models capture the full spectrum and {recover} the observed logarithmic growth of its variance, {providing a compact, physics-informed empirical representation} for more accurate engineering predictions of wall-pressure fluctuations.

physics.flu-dyn↗

arXiv2024

Resolvent analysis of a swimming foil

This study employs resolvent analysis to explore the dynamics and coherent structures in the boundary layer of a foil that swims via a travelling wave undulation. A modified NACA foil shape is used together with undulatory kinematics to represent fish-like bodies at realistic Reynolds numbers ($ \mathit{Re} = 10,000 $ and $ \mathit{Re} = 100,000 $) in both thrust- and drag-producing propulsion regimes. We introduce a novel coordinate transformation that enables the implementation of the data-driven resolvent analysis \citep{herrmann_data-driven_2021} to dissect the stability of the boundary layer of the swimming foil. This is the first study to implement resolvent analysis on deforming bodies with non-zero thickness and at realistic swimming Reynolds numbers. The analysis reinforces the notion that swimming kinematics drive the system's physics. In drag-producing regimes, it reveals breakdown mechanisms of the propulsive wave, while thrust-producing regimes show a uniform wave amplification across the foil's back half. The key thrust and drag mechanisms scale with the boundary-layer thickness, implying geometric self-similarity in this $\mathit{Re}$ regime. In addition, we identify a mechanism that is less strongly coupled to the body motion. We offer a comparison to a rough foil that reduces the amplification of this mechanism, demonstrating the potential of roughness to control the amplification of key mechanisms in the flow. The results provide valuable insights into the dynamics of swimming bodies and highlight avenues for developing opposition control strategies.

physics.flu-dyn↗