arXiv subjects

Silas Alben

Publications and source records attributed to Silas Alben.

At least 19 recordsLinked to original sources

arXiv2026

Comparison of inviscid and viscous vortex shedding from translating and rotating plates

We compare an inviscid vortex sheet model with continuous leading-edge shedding with direct Navier-Stokes simulations over a wide range of unsteady plate motions at moderate Reynolds number ($\mathrm{Re} \approx 1000$). Approximately $70$ distinct kinematic configurations are examined, spanning both body-dominated and flow-dominated regimes. In body-dominated motions, where the fluid dynamics are primarily driven by prescribed plate accelerations, the inviscid model accurately reproduces normal force histories and the qualitative structure of the induced vorticity field. In flow-dominated configurations, with quasi-periodic vortex shedding, agreement with force predictions is good but reduced at low angles of attack, reflecting the greater sensitivity of vortex shedding dynamics to physical and computational parameters. The ability of the present formulation to accommodate stable, continuous leading-edge vortex shedding enables uniform comparisons across diverse motions and clarifies the regimes in which inviscid vortex sheet models can be used reliably for force prediction and physical interpretation.

physics.flu-dyn↗

arXiv2025

Enhancing wall-to-wall heat transport with unsteady flow perturbations

We determine unsteady flow perturbations that are optimal for enhancing the rate of heat transfer between hot and cold walls (i.e. the Nusselt number Nu), under the constraint of fixed flow power (Pe$^2$, where Pe is the P\'{e}clet number). The unsteady flows are perturbations of previously computed optimal steady flows and are given by eigenmodes of the Hessian matrix of Nu, the matrix of second derivatives with respect to amplitudes of flow mode coefficients. Positive eigenvalues of the Hessian correspond to increases in Nu by unsteady flows, and occur at Pe $\geq 10^{3.5}$ and within a band of flow periods $\tau \sim$ Pe$^{-1}$. For $\tau$Pe $\leq 10^{0.5}$, the optimal flows are chains of vortices that move along the walls or along eddies enclosed by flow branches near the walls. At larger $\tau$Pe the vorticity distributions are often more complex and extend farther from the walls. The heat flux is enhanced at locations on the walls near the unsteady vorticity. We construct an iterative time-spectral solver for the unsteady temperature field and find increases in Nu of up to 7% at moderate-to-large perturbation amplitudes.

physics.flu-dyn↗

arXiv2025

Wavy optimal flows for heat transfer in channels

We compute incompressible two-dimensional fluid flows that maximize the rate of heat transfer from the walls of a straight channel given a specified flow input power $Pe^{2}$, where $Pe$ is the P\'{e}clet number. We use the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm together with an adjoint method to compute gradients. The optimal flows are approximately unidirectional up to a critical $Pe \approx 2^{12}$. Above this value the flows assume wavy patterns characterized by finger-like protrusions emanating from both the top and bottom walls of the channel. The rate of heat transfer for these wavy flows is 3% to 30% greater than that of the previously identified unidirectional optima for $2^{13} \leq Pe \leq 2^{17}$. The wavy flows have a much smaller flux through the channel than the unidirectional flows, with regions of slow-moving fluid at nearly homogeneous temperature interspersed with serpentine regions of fast-moving fluid. Consequently, the area of the interface between hot and cold fluid is increased.

physics.flu-dyn↗

arXiv2025

Falling plates with leading-edge vortex shedding

We develop a new numerical method for thin plates falling in inviscid fluid that allows for leading-edge vortex shedding. The inclusion of leading-edge shedding restores physical dynamics to vortex-sheet models of falling bodies, and for the first time large-amplitude fluttering and tumbling are observed in inviscid simulations. Leading-edge shedding is achieved by introducing a novel quadrature rule and smoothing procedure for the Birkhoff-Rott equations. The smoothing error is controlled by a novel fencing procedure. We find a transition point between fluttering and tumbling that is consistent with previous viscous simulations and experiments, and other falling motions such as looping, autorotation are also observed as the plate density increases. The dipole street wakes behind the fluttering plates resemble those in experiments. We consider plates bent into V shapes and study the effects of density and bending angle on the qualitative falling dynamics. At small densities, increasing the bending angle stabilizes the falling motion into fluttering, while at large densities, decreasing the bending angle stabilizes the falling motion into autorotation. In the autorotation regime, the magnitude of angular velocity increases as time cubed before it reaches a terminal angular velocity, and in the fluttering regime, the fluttering frequency scales as the $-1/2$ power of $R_1$, the plate density.

physics.flu-dyn↗

arXiv2024

How vortices enhance heat transfer from an oscillating plate

Oscillations of a heated solid surface in an oncoming fluid flow can increase heat transfer from the solid to the fluid. Previous studies have investigated the resulting heat transfer enhancement for the case of a circular cylinder undergoing translational or rotational motions. Another common geometry, the flat plate, has not been studied as thoroughly. The flat plate sheds larger and stronger vortices that are sensitive to the plate's direction of oscillation. To study the effect of these vortices on heat transfer enhancement, we compute the heat transfer from a flat plate with different orientations and oscillation directions in an oncoming flow with Reynolds number 100. We consider plates with fixed temperature and fixed heat flux, and find large heat transfer enhancement in both cases. We investigate the effects of the plate orientation angle and the plate oscillation direction, velocity, amplitude, and frequency, and find that the plate oscillation velocity and direction have the strongest effects on global heat transfer. The other parameters mainly affect the local heat transfer distributions through shed vorticity distributions. We also discuss the input power needed for the oscillating plate system and the resulting Pareto optimal cases.

physics.flu-dyn↗

arXiv2024

Sail dynamics during tacking maneuvers

We study the dynamics of sail membranes during a tacking maneuver, when the sail angle of attack is reversed in order to sail upwind. In successful tacking the sail flips to the mirror-image shape, while in unsuccessful tacking the sail remains stuck in a metastable state close to the initial shape. We investigate whether the sail flips, and if so, how long it takes and the subsequent dynamics, over a parameter space that describes the sail membrane properties and the kinematics of tacking. We find that the "steady" parameters -- stretching rigidity, pretension, and final angle of attack -- mostly determine whether a membrane flips or not. Flipping is more likely with larger values of the stretching rigidity, pretension, and final angle of attack. The dynamical parameters -- membrane mass density, concavity of angle-of-attack transition kinematics, and time-length of the tacking maneuver -- mainly affect how long flipping takes. With large membrane mass the membrane can maintain the momentum from the tacking motion long enough to reach the flipped state, but it may also take longer to converge to a steady shape. Concave-down angle-of-attack profiles and small tack times are generally associated with shorter flip times but a few exceptions exist, because these kinematics can also give a larger acceleration to the fluid-sail system that persists for longer times. We also investigate slack sails and find that they are more difficult to flip.

physics.flu-dyn↗

arXiv2024

Enhancing heat transfer in a channel with unsteady flow perturbations

We compute unsteady perturbations that optimally increase the heat transfer (Nu) of optimal steady unidirectional channel flows, for a given average rate of power consumption Pe$^2$. The perturbations are expanded in a basis of modes, and the heat transfer enhancement corresponds to eigenvalues of the Hessian matrix of second derivatives of the Nusselt number with respect to the mode coefficients. Enhanced heat transfer, i.e. positive eigenvalues, occur in a range of temporal periods $\tau$ that scale as Pe$^{-1}$. At small to moderate $\tau$Pe values the corresponding flows are chains of eddies near the walls that move as traveling waves at the steady background flow speed. At large $\tau$Pe the flows have eddies of multiple scales ranging up to the domain size. We use an unsteady solver to simulate these flows with perturbation sizes ranging from small to large, and find increases in Nu of up to 56% at Pe = 2$^{19}$. Large Nu can be obtained by eddies with small spatial/temporal scales and by eddies with a range of spatial scales and large temporal scales.

physics.flu-dyn↗

arXiv2023

Spanwise variations in membrane flutter dynamics

We study the large-amplitude flutter of rectangular membranes in 3-D inviscid flows. The membranes' deformations vary significantly in both the chordwise and spanwise directions. Many previous studies used 2D flow models and neglected spanwise variations, so here we focus on cases with significant spanwise nonuniformity. We determine when such cases occur and how the dynamics vary over the parameter space of membrane mass and pretension for two sets of boundary conditions and two values of both the Poisson ratio and the membrane aspect ratio. With spanwise symmetric and asymmetric initial perturbations, the motions differ for long times but eventually reach the same steady state in most cases. At large times, spanwise symmetric and asymmetric oscillations are seen, with the latter more common. Oscillations are often in the form of "side-to-side" and other standing wave motions along the span, as well as traveling wave motions, particularly with free side-edges. Motions are generally nonperiodic and more spatially complex with a large membrane mass, and sometimes periodic at small-to-moderate membrane mass. A large Poisson ratio gives somewhat smoother spatial and temporal features in the dynamics at a given pretension. Increasing the aspect ratio makes the deflection more uniform along the span. With different chordwise and spanwise pretensions we find motions that are qualitatively similar to cases with isotropic pretensions between the anisotropic values.

physics.flu-dyn↗

arXiv2023

Optimal wall shapes and flows for steady planar convection

We compute steady planar incompressible flows and wall shapes that maximize the rate of heat transfer (Nu) between and hot and cold walls, for a given rate of viscous dissipation by the flow (Pe$^2$). In the case of no flow, we show theoretically that the optimal walls are flat and horizontal, at the minimum separation distance. We use a decoupled approximation to show that flat walls remain optimal up to a critical nonzero flow magnitude. Beyond this value, our computed optimal flows and wall shapes converge to a set of forms that are invariant except for a Pe$^{-1/3}$ scaling of horizontal lengths. The corresponding rate of heat transfer Nu $\sim$ Pe$^{2/3}$. We show that these scalings result from flows at the interface between the diffusion-dominated and convection-dominated regimes. We also show that the separation distance of the walls remains at its minimum value at large Pe.

physics.flu-dyn↗

arXiv2023

Transition to branching flows in optimal planar convection

We study steady flows that are optimal for heat transfer in a two-dimensional periodic domain. The flows maximize heat transfer under the constraints of incompressibility and a given energy budget (i.e. mean viscous power dissipation). Using an unconstrained optimization approach, we compute optima starting from 30--50 random initializations across several decades of Pe, the energy budget parameter. At Pe between 10$^{4.5}$ and 10$^{4.75}$, convective rolls with U-shaped branching near the walls emerge. They exceed the heat transfer of the simple convective roll optimum at Pe between 10$^{5}$ and 10$^{5.25}$. At larger Pe, multiple layers of branching occur in the optima, and become increasingly elongated and asymmetrical. Compared to the simple convective roll, the branching flows have lower maximum speeds and thinner boundary layers, but nearly the same maximum power density.

physics.flu-dyn↗

arXiv2022

Membrane flutter in three-dimensional inviscid flow

We develop a model and numerical method to study the large-amplitude flutter of rectangular membranes (of zero bending rigidity) that shed a trailing vortex-sheet wake in a three-dimensional (3D) inviscid fluid flow. We apply small initial perturbations and track their decay or growth to large-amplitude steady state motions. For 12 combinations of boundary conditions at the membrane edges we compute the stability thresholds and the subsequent large-amplitude dynamics across the three-parameter space of membrane mass density, pretension, and stretching rigidity. With free side edges we find good agreement with previous 2D results that used different discretization methods. We find that the 3D dynamics in the 12 cases naturally form four groups based on the conditions at the leading and trailing edges. The deflection amplitudes and oscillation frequencies have scalings similar to those in the 2D case. The conditions at the side edges, though generally less important, may have small or large qualitative effects on the membrane dynamics -- e.g. steady versus unsteady, periodic versus chaotic, or the variety of spanwise curvature distributions -- depending on the group and the physical parameter values.

physics.flu-dyn↗

arXiv2022

Efficient sliding locomotion of three-link bodies with inertia

Many previous studies of sliding locomotion have assumed that body inertia is negligible. Here we optimize the kinematics of a three-link body for efficient locomotion and include among the kinematic parameters the temporal period of locomotion, or equivalently, the body inertia. The optimal inertia is non-negligible when the coefficient of friction for sliding transverse to the body axis is small. Inertia is also significant in a few cases with relatively large coefficients of friction for transverse and backward sliding, and here the optimal motions are less sensitive to the inertia parameter. The optimal motions seem to converge as the number of frequencies used is increased from one to four. For some of the optimal motions with significant inertia we find dramatic reductions in efficiency when the inertia parameter is decreased to zero. For the motions that are optimal with zero inertia, the efficiency decreases more gradually when we raise the inertia to moderate and large values.

physics.bio-ph↗

arXiv2022

Efficient bending and lifting patterns in snake locomotion

We optimize three-dimensional snake kinematics for locomotor efficiency. We assume a general space-curve representation of the snake backbone with small-to-moderate lifting off the ground and negligible body inertia. The cost of locomotion includes work against friction and internal viscous dissipation. When restricted to planar kinematics, our population-based optimization method finds the same types of optima as a previous Newton-based method. A few types of optimal motions prevail. We find an s-shaped body with alternating lifting of the middle and ends for small-to-moderate transverse friction. For large transverse friction, curling and sliding motions are typical with small viscous dissipation, replaced by large-amplitude bending with large viscous dissipation. With small viscous dissipation we find local optima that resemble sidewinding motions across friction coefficient space. They are always suboptimal to alternating lifting motions, with average input power 10--100\% higher.

physics.bio-ph↗

arXiv2021

Packing of elastic rings with friction

We study the deformations of elastic filaments confined within slowly-shrinking circular boundaries, under contact forces with friction. We perform computations with a spring-lattice model that deforms like a thin inextensible filament of uniform bending stiffness. Early in the deformation, two lobes of the filament make contact. If the friction coefficient is small enough, one lobe slides inside the other; otherwise, the lobes move together or one lobe bifurcates the other. There follows a sequence of deformations that is a mixture of spiraling and bifurcations, primarily the former with small friction and the latter with large friction. With zero friction, a simple model predicts that the maximum curvature and the total elastic energy scale as the wall radius to the -3/2 and -2 powers respectively. With nonzero friction, the elastic energy follows a similar scaling but with a prefactor up to 8 times larger, due to delayering and bending with a range of small curvatures. For friction coefficients as large as 1, the deformations are qualitatively similar with and without friction at the outer wall. Above 1, the wall friction case becomes dominated by buckling near the wall.

cond-mat.soft↗

arXiv2021

Dynamics of flags over wide ranges of mass and bending stiffness

There have been many studies of the instability of a flexible plate or flag to flapping motions, and of large-amplitude flapping. Here we use inviscid simulations and a linearized model to study more generally how key quantities -- mode number (or wavenumber), frequency, and amplitude -- depend on the two dimensionless parameters, flag mass and bending stiffness. In the limit of small flag mass, flags perform traveling wave motions that move at nearly the speed of the oncoming flow. The flag mode number scales as the -1/4 power of bending stiffness. The flapping frequency has the same scaling, with an additional slight increase with flag mass in the small-mass regime. The flapping amplitude scales approximately as flag mass to the 1/2 power. For large flag mass, the dominant mode number is low (0 or 1), the flapping frequency tends to zero, and the amplitude saturates in the neighborhood of its upper limit (the flag length). In a linearized model, the fastest growing modes have somewhat different power law scalings for wavenumber and frequency. We discuss how the numerical scalings are consistent with a weakly nonlinear model.

physics.flu-dyn↗

arXiv2021

Dynamics of tethered membranes in inviscid flow

We investigate the dynamics of membranes that are held by freely-rotating tethers in fluid flows. The tethered boundary condition allows periodic and chaotic oscillatory motions for certain parameter values. We characterize the oscillations in terms of deflection amplitudes, dominant periods, and numbers of deflection extrema along the membranes across the parameter space of membrane mass density, stretching modulus, pretension, and tether length. We determine the region of instability and the small-amplitude behavior by solving a nonlinear eigenvalue problem. We also consider an infinite periodic membrane model, which yields a regular eigenvalue problem, analytical results, and asymptotic scaling laws. We find qualitative similarities among all three models in terms of the oscillation frequencies and membrane shapes at small and large values of membrane mass, pretension, and tether length/stiffness.

physics.flu-dyn↗

arXiv2020

Efficient sliding locomotion of three-link bodies

We study the efficiency of sliding locomotion for three-link bodies in the presence of dry (Coulomb) friction. Friction coefficient space can be partitioned into several regions, each with distinct types of efficient kinematics. These include kinematics resembling lateral undulation with very anisotropic friction, small-amplitude reciprocal kinematics, very large amplitude kinematics near isotropic friction, and kinematics that are very asymmetric about the flat state. In the two-parameter shape space, zero net rotation for elliptical trajectories occurs mainly with bilateral or antipodal symmetry. These symmetric subspaces have about the same peak efficiency as the full space but with much smaller dimension. Adding modes with two or three times the basic frequency greatly increases the numbers of local optimal for efficiency, but only modestly increases the peak efficiency. Random ensembles with higher frequencies have efficiency distributions that peak near a certain nonzero value and decay rapidly up to the maximum efficiency. A stochastic optimization algorithm is developed to compute optima with higher frequencies. These are simple closed curves, sharpened versions of the elliptical optima in most cases, and achieve much higher efficiencies mainly for small normal friction. With a linear resistance law, the optimal trajectories are similar in much of friction coefficient space, and relative efficiencies are much lower except with very large normal friction.

physics.bio-ph↗

arXiv2020

Eigenmode analysis of membrane stability in inviscid flow

We study the instability of a thin membrane (of zero bending rigidity) to out-of-plane deflections, when the membrane is immersed in an inviscid fluid flow and sheds a trailing vortex-sheet wake. We solve the nonlinear eigenvalue problem iteratively with large ensembles of initial guesses, for three canonical boundary conditions---both ends fixed, one end fixed and one free, and both free. Over several orders of magnitude of membrane mass density, we find instability by divergence or flutter (particularly at large mass density, or with one or both ends free). The most unstable eigenmodes generally become "wavier" at smaller mass density and smaller tension, but with regions of nonmonotonic behavior. We find good quantitative agreement with unsteady time-stepping simulations at small amplitude, but only qualitative similarities with the eventual steady-state large-amplitude motions.

physics.flu-dyn↗