arXiv subjects

Jonathan Massey

Publications and source records attributed to Jonathan Massey.

3 recordsLinked to original sources

arXiv2026

Modeling the wall-normal velocity spectra in channel flow

A model is proposed for the wall-normal Reynolds stress and its one-dimensional spectrum in channel flows. The model is tested for friction Reynolds numbers from 550 to 5200. The formulation for the stress is a simple modification of the one devised for boundary layers by Kunkel & Marusic (J. Fluid Mech. 548, 2006), and holds for $y/δ< 0.75$. The model for the spectrum holds for all wall distances. It is constructed in wavenumber space, and comprises two principal contributions to the spectrum: energy-containing motions and viscous-dominated motions. It is in accord with the attached eddy model where that applies, and the viscous contribution scales on the Kolmogorov length and velocity. Its extension to boundary layers, with no change to the constants, appears promising, including at Reynolds numbers well above those of the channel data.

physics.flu-dyn↗

arXiv2026

Near-cancellation of enstrophy and strain requires shear or a balanced vortex

In the nonlinear source of the pressure Poisson equation the fluctuating enstrophy and strain nearly cancel. We ask where the cancellation is complete, which we call silent, and how the source escapes it. Pointwise the source depends only on the eigenvalues of the velocity gradient. Pure shear has none, so it is silent. It is the origin of the normalised invariant plane, whose second-invariant coordinate is the normalised source. Let $f$ be the shear fraction of the gradient and $m$ its distance from that origin. We prove that $m\le1-f\le3m$ at every point of every incompressible flow. Wherever the source nearly vanishes and the third invariant is small, the gradient is nearly pure shear. Otherwise the cancelling gradient is a balanced vortex, a swirl its own strain cancels at any strength. At a no-slip wall the silent object is exact: the wall shear-stress fluctuation, a rank-one sheet. Away from the wall we assume the same sheet, dressed with a small residual, and derive how it escapes. The escape passes through one element of the residual, the along-sheet variation of the sheet-normal velocity. Its amplitude is the geometric mean of sheet and residual, and its sign selects swirl or strain. A rank-two silent object has the same source through the same gates but balanced eigenvalues, so the assumption fixes the escape's topology, not its source. The shear fraction is thus a pointwise proxy for cancellation by shear, and a model of the source must be built on what escapes.

math.AP↗

arXiv2023

A systematic investigation into the effect of roughness on self-propelled swimming plates

This study examines the effects of surface topography on the flow and performance of a Self-Propelled Swimming (SPS) body. We consider a thin flat plate with an egg-carton roughness texture undergoing prescribed undulatory swimming kinematics at a Strouhal number of $0.3$ and tail amplitude to length ratio of $0.1$; we use plate Reynolds numbers of $\mathit{Re}=6,12,$ and $24\times 10^3$, and focus on $12,000$. As the roughness wavelength is decreased, we find that the undulation wave speed must be increased to overcome the additional drag from the roughness and maintain SPS. Correspondingly, the extra wave speed raises the power required to maintain SPS, making the swimmer less efficient. To decouple the roughness and the kinematics, we compare the rough plates to equivalent smooth cases by matching the kinematic conditions. We find that all but the longest roughness wavelengths reduce the required swimming power and the unsteady amplitude of the forces when compared to a smooth plate undergoing identical kinematics. Additionally, roughness can enhance flow enstrophy by up to 116\% compared to the smooth cases without a corresponding spike in forces; this suggests that the increased mixing is not due to increased vorticity production at the wall. Instead, the enstrophy is found to peak strongly when the roughness wavelength is approximately twice the boundary layer thickness over the $\mathit{Re}$ range, indicating the roughness induces large-scale secondary flow structures that extend to the edge of the boundary layer. This study reveals the nonlinear interaction between roughness and kinematics beyond a simple increase or decrease in drag, illustrating that roughness studies on static shapes do not transfer directly to unsteady swimmers.

physics.flu-dyn↗