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Three-dimensional schools of hydrodynamically axisymmetric swimmers self-propelling at a constant velocity are studied. We introduce a low-order model for the induced velocity based on the far-field approximation. We inquire if, by holding suitable relative positions in the three-dimensional space, the swimmers can reduce the overall energy consumption of the school in comparison with the same number of isolated individuals at the same velocity. We find a considerable (several per cent) energy saving achievable by chain formations. The benefit increases asymptotically with the number of individuals, towards a finite limit that is a function of the minimum allowed spacing between each pair of neighbours.

Temporal or spatial structures are readily extracted from complex data by modal decompositions like proper orthogonal decomposition (POD) or dynamic mode decomposition (DMD). Subspaces of such decompositions serve as reduced order models and define either spatial structures in time or temporal structures in space. On the contrary, convecting phenomena pose a major problem to those decompositions. A structure traveling with a certain group velocity will be perceived as a plethora of modes in time or space, respectively. This manifests itself for example in poorly decaying singular values when using a POD. The poor decay is counterintuitive, since a single structure is expected to be represented by a few modes. The intuition proves to be correct, and we show that in a properly chosen reference frame along the characteristics defined by the group velocity, a POD or DMD reduces moving structures to a few modes, as expected. Beyond serving as a reduced model, the resulting entity can be used to define a constant or minimally changing structure in turbulent flows. This can be interpreted as an empirical counterpart to exact coherent structures. We present the method and its application to a head vortex of a compressible starting jet.

The dominant feature of the compressible starting jet is the interaction between the emerging vortex ring and the trailing jet. There are two types of interaction: the shock–shear layer–vortex interaction and the shear layer–vortex interaction. The former is clearly not present in the incompressible case, since there are no shocks. The shear layer–vortex interaction has been reported in the literature in the incompressible case and it was found that compressibility reduces the critical Reynolds number for the interaction. Four governing parameters describe the compressible starting jet: the non-dimensional mass supply, the Reynolds number, the reservoir to unbounded chamber temperature ratio and the reservoir to unbounded chamber pressure ratio. The latter parameter does not exist in the incompressible case. For large Reynolds numbers, the vortex pinch-off takes place in a multiple way. We studied the compressible starting jet numerically and found that the interaction strongly links the vortex ring and the trailing jet. The shear layer–vortex interaction leads to a rapid breakdown of the head vortex ring when the flow impacted by the Kelvin–Helmholtz instabilities is ingested into the head vortex ring. The shock–shear layer–vortex interaction is similar to the noise generation mechanism of broadband shock noise in a continuously blowing jet and results in similar sound pressure amplitudes in the far field.

Acoustic models of resonant duct systems with turbulent flow depend on fitted constants based on expensive experimental test series. We introduce a new model of a resonant cavity, flush mounted in a duct or flat plate, under grazing turbulent flow. Based on previous work by Goody, Howe and Golliard, we present a more universal model where the constants are replaced by physically significant parameters. This enables the user to understand and to trace back how a modification of design parameters (geometry, fluid condition) will affect acoustic properties. The derivation of the model is supported by a detailed three-dimensional direct numerical simulation as well as an experimental test series. We show that the model is valid for low Mach number flows (\\[M=0.01{-}0.14\\]) and for low frequencies (below higher transverse cavity modes). Hence, within this range, no expensive simulation or experiment is needed any longer to predict the sound spectrum. In principle, the model is applicable to arbitrary geometries: Just the provided definitions need to be applied to update the significant parameters. Utilizing the lumped-element method, the model consists of exchangeable elements and guarantees a flexible use. Even though the model is linear, resonance conditions between acoustic cavity modes and fluid dynamic unstable modes are correctly predicted.

To explore the effect of conduit roughness on volcanic jet dynamics and on the related seismo‐acoustic radiation we performed a series of shock‐tube experiments using pipes with variable inner surface fractal dimension D. Variable starting pressure produced subsonic to supersonic jets visualized using high‐speed shadowgraph and recorded with an array of accelerometers and microphones. At all starting pressures, increasing D increases the energy transfer from the gas to the conduit walls, decreasing the jet exit velocity (Mach number) and, for supersonic cases, the related shock‐cell spacing, and increasing the seismic to acoustic radiation amplitude ratio. The roughness‐induced changes in jet velocity and turbulence affect the dominant sources of the jet noise and modulates the spectral properties of the acoustic signals. From our study we show that conduit wall roughness is an important and yet largely neglected factor in the dynamics of explosive volcanic eruptions and their monitored geophysical signals. Plain Language Summary Volcanoes are amongst the most fascinating and mysterious subjects of science, for they allow no direct observation of what is happening within the conduit during eruptive activity. Indirect observations (such as measurements of the sound and vibration accompanying eruptions) are routinely performed for monitoring and research purposes. Laboratory studies mimicking the eruptive processes in small‐scale devices, are of great support for correctly interpreting such data. As such, we investigated the effect of the irregularity of conduit surface, amongst the most relevant and poorly known variables characterizing the eruptive processes, on volcanic jets and on their seismic and acoustic signals. We performed a series of laboratory experiments using conduits with different roughness of the internal surface and various starting pressures. Microphones and accelerometers, capable of measuring conduit sounds and vibration, respectively, in synch with high‐speed camera were used to constrain the characteristics of the generated subsonic and supersonic jets. Results show that conduit roughness controls: (a) the relative amplitude of seismic and acoustic signals; (b) the velocity, turbulence and properties of the sound of these jets. Our results will shed light on the link between observation at the surface and dynamic evolution of conduit geometry at depth. Key Points Elastic radiation of analogue experimental volcanic subsonic to supersonic jets was compared against high‐speed shadowgraph analysis We quantified variation in the spectral features, energy partitioning and jet structure due to differences in conduit roughness Different behavior in subsonic versus supersonic regime was observed due to distinct dominating noise sources at different roughness

The global linear stability of a three-dimensional compressible flow around a yawed parabolic body of infinite span is investigated using an iterative eigenvalue method in conjunction with direct numerical simulations. The computed global spectrum shows an unstable branch consisting of three-dimensional boundary layer modes whose amplitude distributions exhibit typical characteristics of both attachment-line and crossflow modes. In particular, global eigenfunctions with smaller phase velocities display a more pronounced structure near the stagnation line, reminiscent of attachment-line modes while still featuring strong crossflow vortices further downstream. This analysis establishes a link between the two prevailing instability mechanisms on a swept parabolic body which, so far, have only been studied separately and locally. A parameter study shows maximum modal growth for a spanwise wavenumber of β = 0.213, suggesting a preferred disturbance length scale in the sweep direction.

Direct numerical simulations (DNS) of subsonic and supersonic impinging jets with Reynolds numbers of 3300 and 8000 are carried out to analyse their statistical properties with respect to heat transfer. The Reynolds number range is at low or moderate values in terms of practical applications, but very high regarding the technical possibilities of DNS. A Reynolds number of 8000 is technically relevant for the cooling of turbine blades. In this case, the flow is dominated by primary and secondary vortex rings. Statistics of turbulent heat fluxes and Reynolds stresses as well as the Nusselt number are provided and brought into accordance with these vortices. Velocity and temperature fluctuations were found to have a positive influence on cooling of the impinging plate. Beside the description of the flow, a second aim of this article is the provision of data for improvement of turbulence models. Modern large eddy simulations are still not able to precisely predict impingement heat transfer (Dairay et al., Intl J. Heat Fluid Flow, vol. 50 (0), 2014, pp. 177–187). Common relations between heat and mass transfer respectively temperature and velocity fields are applied to the impinging jet. These relations include the Reynolds and Chilton Colburn analogy, the Crocco–Busemann relation and the generalised Reynolds analogy (GRA). It was found that the first two deliver useful values if the distance to the jet axis is larger than one diameter, away from the strong pressure gradient around the stagnation point. The GRA, in contrast, precisely predicts the mean temperature field if no axial velocity gradient is present. The estimation of temperature fluctuations according to the GRA fails. As third main topic of this article, the influence of the Mach number on heat transfer and the flow field, is studied. Against the common practise of neglecting compressibility effects in experimental Nusselt correlations, we observed that higher Mach numbers (up to 1.1) have a positive influence on heat transfer in the deflection zone due to higher flow fluctuations.

We study the influence of side walls on the stability of falling liquid films. We combine a temporal biglobal stability analysis based on the linearised Navier–Stokes equations with experiments measuring the spatial growth rate of sinusoidal waves flowing downstream an inclined channel. Very good agreement was found when comparing the theoretical and experimental results. Strong lateral confinement of the channel stabilises the flow. In the wavenumber-Reynolds number space, the instability region experiences a fragmentation due to selective damping of moderate wavenumbers. For this range of parameters, the three-dimensional confined problem shows several prominent stability modes which are classified into two categories, the well-known Kapitza hydrodynamic instability mode (H-mode) and a new unstable mode, we refer to it as wall-mode (W-mode). The two mode types are stabilised differently, where the H-modes are stabilised at small wavenumbers, while the W-modes experience stabilisation at high wavenumbers, and at sufficiently small channel widths, only the W-mode is observed. The reason behind the unique H-modes stabilisation is that they become analogous to waveguide modes, which can not propagate below a certain cut-off wavenumber. The spatial structure of the eigenmodes experiences significant restructuring at wavenumbers smaller than the most damped wavenumber. The mode switching preserves the spatial symmetry of the unstable mode.

Coherent structures in two-dimensional Navier–Stokes turbulence are ubiquitously observed in nature, experiments and numerical simulations. The present study conducts a comparison between several structure detection schemes based on the Okubo–Weiss criterion, the vorticity magnitude and Lagrangian coherent structures (LCSs), focusing on the inverse cascade in two-dimensional hydrodynamic turbulence. A recently introduced vortex scaling phenomenology (Burgess & Scott, J. Fluid Mech., vol. 811, 2017, pp. 742–756) allows the quantification of the respective thresholds required by these methods based on physical properties of the flow. The resulting improved comparability allows us to identify characteristic relative differences in the detection sensitivity between the employed structure detection techniques. With respect to the inverse cascade of energy, coherent structures contribute, as expected, substantially less to the cross-scale flux than the residual incoherent parts of the flow although the energetically dominant coherent structures lead to an important large-scale deformation of the energy spectrum. This cascade inactivity can be understood by an increased misalignment of strain-rate and subgrid stress tensors within coherent structures. At the same time, the structures exhibit strong and localised nonlinear cross-scale interactions that appear to stabilise them. We quantify and interpret the resulting shape preservation of coherent structures in terms of a multi-scale gradient approach (Eyink, J. Fluid Mech., vol. 549, 2006, pp. 191–214) as the depletion of strain rotation and vorticity gradient stretching whereas the dynamics of the residual fluctuations are consistent with the vortex thinning picture.

The natural wind environment that volant insects encounter is unsteady and highly complex, posing significant flight-control and stability challenges. It is critical to understand the strategies insects employ to safely navigate in natural environments. We combined experiments on free flying bumblebees with high-fidelity numerical simulations and lower-order modeling to identify the mechanics that mediate insect flight in unsteady winds. We trained bumblebees to fly upwind towards an artificial flower in a wind tunnel under steady wind and in a von Kármán street formed in the wake of a cylinder. Analysis revealed that at lower frequencies in both steady and unsteady winds the bees mediated lateral movement with body roll - typical casting motion. Numerical simulations of a bumblebee in similar conditions permitted the separation of the passive and active components of the flight trajectories. Consequently, we derived simple mathematical models that describe these two motion components. Comparison between the free-flying live and modeled bees revealed a novel mechanism that enables bees to passively ride out high-frequency perturbations while performing active maneuvers at lower frequencies. The capacity of maintaining stability by combining passive and active modes at different timescales provides a viable means for animals and machines to tackle the challenges posed by complex airflows.