We study the cross-stream inertial migration of a torque-free neutrally buoyant spheroid, of an arbitrary aspect ratio $\kappa$, in wall-bounded plane Poiseuille flow for small particle Reynolds numbers ($Re_p\ll 1$) and confinement ratios ($\lambda \ll 1$), with the channel Reynolds number, $Re_c = Re_p/\lambda ^2$, assumed to be arbitrary; here $\lambda =L/H$, where $L$ is the semi-major axis of the spheroid and $H$ denotes the separation between the channel walls. In the Stokes limit ($Re_p =0)$, and for $\lambda \ll 1$, a spheroid rotates along any of an infinite number of Jeffery orbits parameterized by an orbit constant $C$, while translating with a time-dependent speed along a given ambient streamline. Weak inertial effects stabilize either the spinning ($C=0$) or tumbling orbit ($C=\infty$), or both, depending on $\kappa$. The asymptotic separation of the Jeffery rotation and orbital drift time scales, from that associated with cross-stream migration, implies that migration occurs due to a Jeffery-averaged lift velocity. Although the magnitude of this averaged lift velocity depends on $\kappa$ and $C$, the shape of the lift profiles are identical to those for a sphere, regardless of $Re_c$. In particular, the equilibrium positions for a spheroid remain identical to the classical Segre–Silberberg ones for a sphere, starting off at a distance of about $0.6(H/2)$ from the channel centreline for small $Re_c$, and migrating wallward with increasing $Re_c$. For spheroids with $\kappa \sim O(1)$, the Jeffery-averaged analysis is valid for $Re_p\ll 1$; for extreme aspect ratio spheroids, the regime of validity becomes more restrictive being given by $Re_p \kappa /\ln \kappa \ll 1$ and $Re_p/\kappa \ll 1$ for $\kappa \rightarrow \infty$ (slender fibres) and $\kappa \rightarrow 0$ (flat disks), respectively.

We carry out direct numerical simulation (DNS) of turbulent flow in rough pipes. Two types of irregular roughness are investigated, namely a grit-blasted and a graphite surface. A wide range of Reynolds numbers is tested, from the laminar up to the fully rough regime, attempting to replicate Nikuradse's pioneering study. Despite the large relative roughness, outer-layer similarity is achieved at high Reynolds number as hypothesised by Townsend, with deviations from the smooth wall case of 4 % for the grit-blasted surface and 13 % for the graphite surface. This makes it possible to define a roughness function and the equivalent sand-grain roughness. The results are compared with those obtained in plane channels, with small differences pointing to the residual influence of the duct cross-sectional shape in the presence of relatively large roughness. The computed friction factors behave similar to those Nikuradse's chart, with differences in terms of the friction factor in the laminar region and of the critical Reynolds number, which are partly absorbed by using the hydraulic radius as reference length scale. The distributions of the velocity fluctuations intensities point to a isotropisation of turbulence in the near-wall region resulting from the roughness, with influence of the roughness geometry. Comparison of the computed equivalent sand-grain roughness height suggest that existing correlations suffer from poor predictive power, at least for surfaces with large relative roughness.

The power exchange between fluid and structure plays a significant role in the force production and flight efficiency of flapping wings in insects and artificial flyers. This work numerically investigates the performance of flapping wings by using a high-fidelity fluid–structure interaction solver. Simulations are conducted by varying the hinge flexibility (measured by the Cauchy number, $Ch$, i.e. the ratio between aerodynamic and torsional elastic forces) and the wing shape (quantified by the radius of the first moment of area, $\bar {r}_1$). Results show that the lift production is optimal at $0.05 < Ch \leq 0.2$ and larger $\bar {r}_1$ where the minimum angle of attack is around $45^\circ$ at midstroke. The power economy is maximised for wings with lower $\bar {r}_1$ near $Ch=0.2$. Power analysis indicates that the optimal performance measured by the power economy is obtained for those cases where two important power synchronisations occur: anti-synchronisation of the pitching elastic power and the pitching aerodynamic and inertial powers and nearly in-phase synchronisation of the flapping aerodynamic power and the total input power of the system. While analysis of the kinematics for the different wing shapes and hinge stiffnesses reveals that the optimal performance occurs when the timing of pitch and stroke reversals are matched, thus supporting the effective transfer of input power from flapping to passive pitching and into the fluid. These results suggest that careful optimisation between wing shapes and hinge properties can allow insects and robots to exploit the passive dynamics to improve flight performance.

The atomisation of a suspension containing liquid and dispersed particles is prevalent in many applications. Previous studies of droplet breakup mainly focused on homogeneous fluids, and the heterogeneous effect of particles on the breakup progress is unclear. In this study, the breakup of particle-laden droplets in airflow is investigated experimentally. Combining synchronised high-speed images from the side view and the 45$^\circ$ view, we compare the morphology of particle-laden droplets with that of homogeneous fluids in different breakup modes. The results show that the higher effective viscosity of particle-laden droplets affects the initial deformation, and the heterogeneous effect of particles appears in the later breakup stage. To evaluate the heterogeneous effect of particles quantitatively, we eliminate the effect of the higher effective viscosity of particle-laden droplets by comparing cases corresponding to the same inviscid Weber number. The quantitative comparison reveals that the heterogeneous effect of particles accelerates the fragmentation of the liquid film and promotes localised rapid piercing. A correlation length that depends on the particle diameter and the volume fraction is proposed to characterise the length scale of the concentration fluctuation under the combined effect of the initial flattening and later stretching during the droplet breakup process. Based on this correlation length, the fragment size distributions are analysed, and the scaling results agree well with the experimental data.

We investigate the spatial distribution and dynamics of the vortices in rotating Rayleigh–Bénard convection in a reduced Rayleigh number range $1.3\le Ra/Ra_{c}\le 83.1$. Under slow rotations ($Ra\approx 80\,Ra_{c}$), the vortices are distributed randomly, which is manifested by the size distribution of the Voronoi cells of the vortex centres being a standard $\varGamma$ distribution. The vortices exhibit Brownian-type horizontal motion in the parameter range $Ra\gtrsim 10\,Ra_{c}$. The probability density functions of the vortex displacements are, however, non-Gaussian at short time scales. At modest rotating rates ($4\,Ra_{c}\le Ra\lesssim 10\,Ra_{c}$), the centrifugal force leads to radial vortex motions, i.e. warm cyclones (cold anticyclones) moving towards (outwards from) the rotation axis. The horizontal scale of the vortices decreases with decreasing $Ra/Ra_c$, and the size distribution of their Voronoi cells deviates from the $\varGamma$ distribution. In the rapidly rotating regime ($1.6\,Ra_{c}\le Ra\le 4\,Ra_{c}$), the vortices are densely distributed. The hydrodynamic interaction of neighbouring vortices results in the formation of vortex clusters. Within clusters, cyclones exhibit inverse-centrifugal motion as they submit to the outward motion of the strong anticyclones, and the radial velocity of the anticyclones is enhanced. The radial mobility of isolated vortices, scaled by their vorticity strength, is shown to be a simple power function of the Froude number. For all flow regimes studied, we show that the number of vortices with a lifespan greater than $t$ decreases exponentially as $\exp ({-t/{\tau }})$ for large time, where $\tau$ represents the characteristic lifetime of long-lived vortices.

Microvortex generators are passive control devices smaller than the boundary layer thickness that energise the boundary layer to prevent flow separation with limited induced drag. In this work, we use direct numerical simulations (DNS) to investigate the effect of the Reynolds number in a supersonic turbulent boundary layer over a microramp vortex generator. Three friction Reynolds numbers are considered, up to $Re_\tau = 2000$, for fixed free stream Mach number $M_\infty =2$ and fixed relative height of the ramp with respect to the boundary layer thickness. The high-fidelity data set sheds light on the instantaneous and highly three-dimensional organisation of both the wake and the shock waves induced by the microramp. The full access to the flow field provided by DNS allows us to develop a qualitative model of the near wake, explaining the internal convolution of the Kelvin–Helmholtz vortices around the low-momentum region behind the ramp. The overall analysis shows that numerical results agree excellently with recent experimental measurements in similar operating conditions and confirms that microramps effectively induce a significantly fuller boundary layer even far downstream of the ramp. Moreover, results highlight significant Reynolds number effects, which in general do not scale with the ramp height. Increasing Reynolds number leads to enhanced coherence of the typical vortical structures in the field, faster and stronger development of the momentum deficit region, increased upwash between the primary vortices from the sides of the ramp – and thus increased lift-up of the wake – and faster transfer of momentum towards the wall.

Metachronal rowing is a biological propulsion mechanism employed by many swimming invertebrates (e.g. copepods, ctenophores, krill and shrimp). Animals that swim using this mechanism feature rows of appendages that oscillate in a coordinated wave. In this study, we used observations of a swimming ctenophore (comb jelly) to examine the hydrodynamic performance and vortex dynamics associated with metachronal rowing. We first reconstructed the beating kinematics of ctenophore appendages based on a high-speed video of a metachronally coordinated row. Following the reconstruction, two numerical models were developed and simulated using an in-house immersed-boundary-method-based computational fluid dynamics solver. The two models included the original geometry (16 appendages in a row) and a sparse geometry (8 appendages, formed by removing every other appendage along the row). We found that appendage tip vortex interactions contribute to hydrodynamic performance via a vortex-weakening mechanism. Through this mechanism, appendage tip vortices are significantly weakened during the drag-producing recovery stroke. As a result, the swimming ctenophore produces less overall drag, and its thrust-to-power ratio is significantly improved (up to 55.0 % compared with the sparse model). Our parametric study indicated that such a propulsion enhancement mechanism is less effective at higher Reynolds numbers. Simulations were also used to investigate the effects of substrate curvature on the unsteady hydrodynamics. Our results illustrated that, compared with a flat substrate, arranging appendages on a curved substrate can boost the overall thrust generation by up to 29.5 %. These findings provide new insights into the fluid dynamic principles of propulsion enhancement underlying metachronal rowing.

A one-dimensional mechanism of deflagration to detonation transition is identified and investigated by an asymptotic analysis in the double limit of large activation energy and small Mach number of the laminar flame velocity. The unsteady analysis concerns the self-accelerating tip of an elongated flame in a smooth walled tube. The flame on the tip, considered as plane and orthogonal to the tube axis, is pushed from behind by the longitudinal flow resulting from the cumulative effect of the radial flows of burned gas issued from the lateral flame of the finger-like front (called backflow in the following). The analysis of the one-dimensional dynamics is performed by coupling the flame structure with the downstream-running compression waves propagating in the external flows. A critical elongation is identified from which the slightest increase in elongation leads to a pressure runaway producing the flame blow-off. The dynamics of the inner structure of the laminar flame on the tip which is accelerated by the self-induced backflow is characterized by a finite-time singularity of the reacting flow in the form of a dynamical saddle-node bifurcation.

A turbulent circular disk wake database (Chongsiripinyo & Sarkar, J. Fluid Mech., vol. 885, 2020) at Reynolds number $Re = U_\infty D/\nu = 5 \times 10^{4}$ is interrogated to identify the presence of large-scale streaks – coherent elongated regions of streamwise velocity. The unprecedented streamwise length – until $x/D \approx 120$ – of the simulation enables investigation of the near and far wakes. The near wake is dominated by the vortex shedding (VS) mode residing at azimuthal wavenumber $m=1$ and Strouhal number $St = 0.135$. After filtering out the VS structure, conclusive evidence of large-scale streaks with frequency $St \rightarrow 0$, equivalently streamwise wavenumber $k_x \rightarrow 0$ in the wake, becomes apparent in visualizations and spectra. These streaky structures are found throughout the simulation domain beyond $x/D \approx 10$. Conditionally averaged streamwise vorticity fields reveal that the lift-up mechanism is active in the near as well as the far wake, and that ejections contribute more than sweeps to events of intense $-u'_xu'_r$. Spectral proper orthogonal decomposition is employed to extract the energy and the spatiotemporal features of the large-scale streaks. The streak energy is concentrated in the $m=2$ azimuthal mode over the entire domain. Finally, bispectral mode decomposition is conducted to reveal strong interaction between $m=1$ and $St = \pm 0.135$ modes to give the $m=2$, $St \rightarrow 0$ streak mode. Our results indicate that the self-interaction of the VS mode generates the $m=2$, $St \rightarrow 0$ streamwise vortices, which leads to streak formation through the lift-up process. To the authors’ knowledge, this is the first study that reports and characterizes large-scale low-frequency streaks and the associated lift-up mechanism in a turbulent wake.

In this paper we report on an experimental study focusing on the manifestation and dynamics of the large-scale circulation (LSC) in turbulent liquid metal convection. The experiments are performed inside a cylinder of aspect ratio $\varGamma = 0.5$ filled with the ternary alloy GaInSn, which has a Prandtl number of $Pr = 0.03$. The large-scale flow structures are classified and characterized at Rayleigh numbers of ${Ra} = 9.33 \times 10^6, 5.31 \times 10^7$ and $6.02 \times 10^8$ by means of the contactless inductive flow tomography which enables the full reconstruction of the three-dimensional (3-D) flow structures in the entire convection cell. This is complemented with the multi-thermal-probe method for capturing the azimuthal temperature variation induced by the LSC at the sidewall. We use proper orthogonal decomposition (POD) to identify the dominating modes of the turbulent convection. The analysis reveals that a single-roll structure of the LSC alternates in short succession with double-roll structures or a three-roll structure. This is accompanied by dramatic fluctuations of the Reynolds number, whose instantaneous values can deviate by more than 50 % from the time-average value. No coherent oscillations are observed, whereas a correlation analysis indicates a residual contribution of the torsion and sloshing modes. Results of the POD analysis suggest a stabilization of the single-roll LSC with increasing $Ra$ at the expense of flow structures with multiple rolls. Moreover, the relative lifetime of all identified flow states, measured in units of free-fall times, increases with rising $Ra$.

The objective of the present study is to provide a numerical database of thermal boundary layers and to contribute to the understanding of the dynamics of passive scalars at different Prandtl numbers. In this regard, a direct numerical simulation (DNS) of an incompressible zero-pressure-gradient turbulent boundary layer is performed with the Reynolds number based on momentum thickness ${\textit {Re}}_{\theta }$ ranging up to $1080$. Four passive scalars, characterized by the Prandtl numbers ${\textit {Pr}} = 1,2,4,6$ are simulated using the pseudo-spectral code SIMSON (Chevalier et al., SIMSON : a pseudo-spectral solver for incompressible boundary layer flows. Tech. Rep. TRITA-MEK 2007:07. KTH Mechanics, Stockholm, Sweden, 2007). To the best of our knowledge, the present DNS provides the thermal boundary layer with the highest Prandtl number available in the literature. It corresponds to that of water at ${\sim }24\,^{\circ }{\rm C}$, when the fluid temperature is considered as a passive scalar. Turbulence statistics for the flow and thermal fields are computed and compared with available numerical simulations at similar Reynolds numbers. The mean flow and scalar profiles, root-mean-squared velocity and scalar fluctuations, turbulent heat flux, turbulent Prandtl number and higher-order statistics agree well with the numerical data reported in the literature. Furthermore, the pre-multiplied two-dimensional spectra of the velocity and of the passive scalars are computed, providing a quantitative description of the energy distribution at the different length scales for various wall-normal locations. The energy distribution of the heat-flux fields at the wall is concentrated on longer temporal structures with increasing Prandtl number. This is due to the thinner thermal boundary layer as thermal diffusivity decreases and, thereby, the longer temporal structures exhibit a different footprint at the wall.

The present paper finds that the coexistence of multiple primary instability waves may cause a non-trivial nonlinear interaction and breakdown process, which has not been reported before. In the considered Mach 6 flat-plate boundary layer, a global resolvent analysis reports three optimal disturbances (local maxima): a high-frequency planar wave, a low-frequency oblique wave and a stationary streak. For the dominant planar and oblique waves, a parabolised stability equation analysis identifies the initial non-modal transient growth and downstream modal growth. Initiated by these two optimal disturbances jointly, the complete linear and nonlinear instability processes until breakdown to turbulence are shown with direct numerical simulation. Owing to the transient growth, the oblique wave may be more significant than the planar wave in the breakdown. The oblique wave and scales of nonlinear interactions are pronounced in the outer layer, whose significance may not be comprehensively characterised by the wall pressure measurement. Fourier modes characterising the oblique-wave oblique breakdown, the planar-wave fundamental resonance, the planar-wave subharmonic resonance and the combination resonance related to a detuned mode are observed successively. The detuned mode seems to dominate the near-wall dynamics in the late nonlinear stage, characterised by $\varLambda$-like structures. Meanwhile, the existence of this detuned mode is independent of the initial amplitude ratio and the absolute amplitude of the oblique and planar waves. Weakly nonlinear stability analyses demonstrate that the detuned mode is mainly a consequence of the secondary instability under the combination of planar and oblique primary waves. Wave vector plots reveal the resonant state of multiple triads. Energy budget and amplitude-correction analyses provide a clear physical image of energy transfer.

The recent Lagrangian relaxation towards equilibrium (LaRTE) approach (Fowler et al., J. Fluid Mech., vol. 934, 2022, A44) is a wall model for large-eddy simulations (LES) that isolates quasi-equilibrium wall-stress dynamics from non-equilibrium responses to time-varying LES inputs. Non-equilibrium physics can then be modelled separately, such as the laminar Stokes layers that form in the viscous region and generate rapid wall-stress responses to fast changes in the pressure gradient. To capture additional wall-stress contributions due to near-wall turbulent eddies, a model term motivated by the attached eddy hypothesis is proposed. The total modelled wall stress thus includes contributions from various processes operating at different time scales (i.e. the LaRTE quasi-equilibrium plus laminar and turbulent non-equilibrium wall stresses) and is called the multi-time-scale (MTS) wall model. It is applied in LES of turbulent channel flow subject to a wide range of unsteady conditions from quasi-equilibrium to non-equilibrium. Flows considered include pulsating and linearly accelerating channel flow for several forcing frequencies and acceleration rates, respectively. We also revisit the sudden spanwise pressure gradient flow (considered in Fowler et al., J. Fluid Mech., vol. 934, 2022, A44) to review how the newly introduced model features affect this flow. Results obtained with the MTS wall model show good agreement with direct numerical simulation data over a vast range of conditions in these various non-equilibrium channel flows. To further understand the MTS model, we also describe and test the instantaneous-equilibrium limit of the MTS wall model. In this limit, good wall-stress predictions are obtained with reduced model complexity but providing less complete information about the wall-stress physics.

This study examined the impact of coherent structures on the aerodynamic forces exerted on a NACA0012 aerofoil with angles of attack $7.5^{\circ }$ and $10^{\circ }$, and a chord-based Reynolds number $50\,000$. The study utilized the spectral proper orthogonal decomposition (SPOD) algorithm to identify the coherent structures, and vorticity force analysis to quantify their impact on lift and drag forces. Results showed that at $10^{\circ }$, the zeroth frequency of the first SPOD mode had a significant impact on drag and lift forces due to a large vortex structure that caused a strong flow along the suction side of the aerofoil. The first and second frequencies of the first SPOD mode represented asymmetric vortex pairs and a series of vortex pairs that determined the leading-edge separation, respectively. At $7.5^{\circ }$, the zeroth frequency of the first mode corresponded to an oscillating near-wall stream that followed the reattachment flow pattern, while the first frequency corresponded to a counter-rotating vortex pair that originated where the flow reattaches. Finally, the second frequency of the first mode corresponded to smaller counter-rotating vortex pairs at the shear layer originated near the reattachment point. These findings suggest that coherent structures have a significant impact on aerodynamic forces exerted on aerofoils, and can be identified and quantified using the SPOD algorithm and vorticity force analysis.

The Earth's landscape hosts a variety of patterns resulting from the interaction between a sediment-carrying fluid and an erodible boundary. Here, the morphodynamics of river bifurcations is interpreted as a second-order phase transition. A consolidated one-dimensional bifurcation model is re-examined in the light of classical Landau theory of critical phenomena. The transition from a balanced to an unbalanced flux partition is described in terms of an order parameter. The equilibrium states of the system are shown to be minima of a morphodynamic potential function. Finally, the role of a generic external forcing is investigated. A threshold value of the forcing is shown to set bounds separating two different morphodynamic responses to allogenic and autogenic dynamics.

This paper focuses on the discovery of optimal flapping wing kinematics using a deep learning surrogate model for unsteady aerodynamics and multi-objective optimisation. First, a surrogate model of the unsteady forces experienced by a 3-D flapping wing is built, based on deep neural networks. The model is trained on a dataset of randomly generated kinematics simulated using direct numerical simulation (DNS). Once trained, the neural networks can quickly predict the unsteady lift and torques experienced by the wing, using sparse information on the kinematics. This fast surrogate model allows multi-objective optimisation to be performed. The resulting Pareto front consists of new kinematics that may be very different from the kinematics of the initial dataset. A few arbitrarily chosen kinematics on the Pareto front are thus simulated using DNS and used to enhance the database. The new dataset is used to train again the networks, and this active deep learning/optimisation framework is performed until convergence, obtained after only two iterations. Overall, this method reduced the cost of optimisation by 83 %. Results reveal two distinct families of motions. Kinematics promoting high efficiency are characterised by large stroke amplitudes and relatively low angles of attack, as observed for fruit flies, honeybees or hawkmoths. For those, lift production is driven by quasi-steady effects and the formation of a stable leading edge vortex. Kinematics promoting high lift are characterised by small stroke amplitudes and high angles of attack, reminiscent of mosquitoes. Lift production is driven by the rapid generation of vorticity at the trailing edge.

The wall cooling effect on the spectra and structures of thermodynamic variables are investigated in hypersonic turbulent boundary layers. The density and temperature can be divided into the acoustic and entropic modes based on the Kovasznay decomposition. The intensities of the pressure and the acoustic modes of density and temperature attain the maximum values near the wall, while those of the entropy and the entropic modes of density and temperature achieve their primary peaks near the edge of the boundary layer. In the near-wall region, the pressure and the acoustic modes of density and temperature are significantly enhanced when the wall is strongly cooled, which can be attributed to the appearance of the travelling-wave-like alternating positive and negative structures. Moreover, the intensities of the entropy and the entropic modes of density and temperature become stronger near the wall as the wall temperature decreases, due to the appearance of the streaky entropic structures (SES). The SES are mainly caused by the advection effect of the strong positive wall-normal gradient of the mean temperature associated with ejection and sweep events. It is also found that the profiles of the intensities of the entropy, density and temperature are similar to each other far from the wall, which is mainly due to the reason that the entropic modes are dominant in the fluctuating density and temperature in the far-wall region. The acoustic modes of density and temperature only have significant contributions in the near-wall region.

This paper investigates the steady-state pattern evolution of symmetric Faraday waves excited in a brimful cylindrical container when driving parameters much exceed critical thresholds. In such liquid systems, parametric surface responses are typically considered as the resonant superposition of unstable standing waves. A modified free-surface synthetic Schlieren method is employed to obtain full three-dimensional spatial reconstructions of instantaneous surface patterns. Multi-azimuth structures and localized travelling waves during the small-elevation phases of the oscillation cycle give rise to modal decomposition in the form of $\nu$-basis modes. Two-step surface-fitting results provide insight into the spatiotemporal characteristics of dominant wave components and corresponding harmonics in the experimental observations. Arithmetic combination of modal indices and uniform frequency distributions reveal the nonlinear mechanisms behind pattern formation and the primary pathways of energy transfer. Taking the hypothetical surface manifestation of multiple azimuths as the modal solutions, a linear stability analysis of the inviscid system is utilised to calculate fundamental resonance tongues (FRTs) with non-overlapping bottoms, which correspond to subharmonic or harmonic $\nu$-basis modes induced by surface instability at the air–liquid interface. Close relationships between experimental observations and corresponding FRTs provide qualitative verification of dominant modes identified using surface-fitting results. This supports the validity and rationality of the applied $\nu$-basis modes.

Self-propulsion of chemically active droplets and phoretic disks has been studied widely; however, most research overlooks the influence of disk shape on swimming dynamics. Inspired by experimentally observed prolate composite droplets and elliptical camphor disks, we employ simulations to investigate the phoretic dynamics of an elliptical disk that emits solutes uniformly in the creeping flow regime. By varying the disk's eccentricity $e$ and the Péclet number $Pe$, we distinguish five disk behaviours: stationary, steady, orbiting, periodic and chaotic. We perform a linear stability analysis (LSA) to predict the onset of instability and the most unstable eigenmode when a stationary disk transitions spontaneously to steady self-propulsion. In addition to the LSA, we use an alternative approach to determine the perturbation growth rate, illustrating the competing roles of advection and diffusion. The steady motion features a transition from a puller-type to a neutral-type swimmer as $Pe$ increases, which occurs as a bimodal concentration profile at the disk surface shifts to a polarized solute distribution, driven by convective solute transport. An elliptical disk achieves an orbiting motion through a chiral symmetry-breaking instability, wherein it repeatedly follows a circular path while simultaneously rotating. The periodic swinging motion, emerging from a steady motion via a supercritical Hopf bifurcation, is characterized by a wave-like trajectory. We uncover a transition from normal diffusion to superdiffusion as eccentricity $e$ increases, corresponding to a random-walking circular disk and a ballistically swimming elliptical counterpart, respectively.