New perspectives on the impulsive roughness-perturbation of a turbulent boundary layer

The zero-pressure-gradient turbulent boundary layer over a flat plate was perturbed by a short strip of two-dimensional roughness elements, and the downstream response of the flow field was interrogated by hot-wire anemometry and particle image velocimetry. Two internal layers, marking the two transitions between rough and smooth boundary conditions, are shown to represent the edges of a ‘stress bore’ in the flow field. New scalings, based on the mean velocity gradient and the third moment of the streamwise fluctuating velocity component, are used to identify this ‘stress bore’ as the region of influence of the roughness impulse. Spectral composite maps reveal the redistribution of spectral energy by the impulsive perturbation – in particular, the region of the near-wall peak was reached by use of a single hot wire in order to identify the significant changes to the near-wall cycle. In addition, analysis of the distribution of vortex cores shows a distinct structural change in the flow associated with the perturbation. A short spatially impulsive patch of roughness is shown to provide a vehicle for modifying a large portion of the downstream flow field in a controlled and persistent way

Large-eddy simulation of large-scale structures in long channel flow

We investigate statistics of large-scale structures from large-eddy simulation (LES) of turbulent channel flow at friction Reynolds numbers Re_τ = 2K and 200K (where K denotes 1000). In order to capture the behaviour of large-scale structures properly, the channel length is chosen to be 96 times the channel half-height. In agreement with experiments, these large-scale structures are found to give rise to an apparent amplitude modulation of the underlying small-scale fluctuations. This effect is explained in terms of the phase relationship between the large- and small-scale activity. The shape of the dominant large-scale structure is investigated by conditional averages based on the large-scale velocity, determined using a filter width equal to the channel half-height. The conditioned field demonstrates coherence on a scale of several times the filter width, and the small-scale–large-scale relative phase difference increases away from the wall, passing through π/2 in the overlap region of the mean velocity before approaching π further from the wall. We also found that, near the wall, the convection velocity of the large scales departs slightly, but unequivocally, from the mean velocity

Static pressure correction in high Reynolds number fully developed turbulent pipe flow

Measurements are reported of the error in wall static pressure reading due to the finite size of the pressure tapping. The experiments were performed in incompressible turbulent pipe flow over a wide range of Reynolds numbers, and the results indicate that the correction term (as a fraction of the wall stress) continues to increase as the hole Reynolds number $d^+=u_\tau d/\nu$ increases, contrary to previous studies. For small holes relative to the pipe diameter the results follow a single curve, but for larger holes the data diverge from this universal behaviour at a point that depends on the ratio of the hole diameter to the pipe diameter

Debt Financing and Financial Flexibility Evidence from Pro-active Leverage Increases

Firms that intentionally increase leverage through substantial debt issuances do so primarily as a response to operating needs rather than a desire to make a large equity payout. Subsequent debt reductions are neither rapid, nor the result of pro-active attempts to rebalance the firm’s capital structure towards a long-run target. Instead, the evolution of the firm’s leverage ratio depends primarily on whether or not the firm produces a financial surplus. In fact, firms that generate subsequent deficits tend to cover these deficits predominantly with more debt even though they exhibit leverage ratios that are well above estimated target levels. While many of our findings are difficult to reconcile with traditional capital structure models, they are broadly consistent with a capital structure theory in which financial flexibility, in the form of unused debt capacity, plays an important role in capital structure choices.

Interactions within the turbulent boundary layer at high Reynolds number

Simultaneous streamwise velocity measurements across the vertical direction obtained in the atmospheric surface layer (Re_τ ≃ 5 × 10^5) under near thermally neutral conditions are used to outline and quantify interactions between the scales of turbulence, from the very-large-scale motions to the dissipative scales. Results from conditioned spectra, joint probability density functions and conditional averages show that the signature of very-large-scale oscillations can be found across the whole wall region and that these scales interact with the near-wall turbulence from the energy-containing eddies to the dissipative scales, most strongly in a layer close to the wall, z^+ ≲ 10^3. The scale separation achievable in the atmospheric surface layer appears to be a key difference from the low-Reynolds-number picture, in which structures attached to the wall are known to extend through the full wall-normal extent of the boundary layer. A phenomenological picture of very-large-scale motions coexisting and interacting with structures from the hairpin paradigm is provided here for the high-Reynolds-number case. In particular, it is inferred that the hairpin-packet conceptual model may not be exhaustively representative of the whole wall region, but only of a near-wall layer of z^+ = O(10^3), where scale interactions are mostly confined

Water quality map of Saginaw Bay from computer processing of LANDSAT-2 data

There are no author-identified significant results in this report

A critical layer model for turbulent pipe flow

A model-based description of the scaling and radial location of turbulent fluctuations in turbulent pipe flow is presented and used to illuminate the scaling behaviour of the very large scale motions. The model is derived by treating the nonlinearity in the perturbation equation (involving the Reynolds stress) as an unknown forcing, yielding a linear relationship between the velocity field response and this nonlinearity. We do not assume small perturbations. We examine propagating modes, permitting comparison of our results to experimental data, and identify the steady component of the velocity field that varies only in the wall-normal direction as the turbulent mean profile. The "optimal" forcing shape, that gives the largest velocity response, is assumed to lead to modes that will be dominant and hence observed in turbulent pipe flow. An investigation of the most amplified velocity response at a given wavenumber-frequency combination reveals critical layer-like behaviour reminiscent of the neutrally stable solutions of the Orr-Sommerfeld equation in linearly unstable flow. Two distinct regions in the flow where the influence of viscosity becomes important can be identified, namely a wall layer that scales with $R^{+1/2}$ and a critical layer, where the propagation velocity is equal to the local mean velocity, that scales with $R^{+2/3}$ in pipe flow. This framework appears to be consistent with several scaling results in wall turbulence and reveals a mechanism by which the effects of viscosity can extend well beyond the immediate vicinity of the wall.Comment: Submitted to the Journal of Fluid Mechanics and currently under revie

On the design of optimal compliant walls for turbulence control

This paper employs the theoretical framework developed by Luhar et al. (J. Fluid Mech., 768, 415-441) to consider the design of compliant walls for turbulent skin friction reduction. Specifically, the effects of simple spring-damper walls are contrasted with the effects of more complex walls incorporating tension, stiffness and anisotropy. In addition, varying mass ratios are tested to provide insight into differences between aerodynamic and hydrodynamic applications. Despite the differing physical responses, all the walls tested exhibit some important common features. First, the effect of the walls (positive or negative) is greatest at conditions close to resonance, with sharp transitions in performance across the resonant frequency or phase speed. Second, compliant walls are predicted to have a more pronounced effect on slower-moving structures because such structures generally have larger wall-pressure signatures. Third, two-dimensional (spanwise constant) structures are particularly susceptible to further amplification. These features are consistent with many previous experiments and simulations, suggesting that mitigating the rise of such two-dimensional structures is essential to designing performance-improving walls. For instance, it is shown that further amplification of such large-scale two-dimensional structures explains why the optimal anisotropic walls identified by Fukagata et al. via DNS (J. Turb., 9, 1-17) only led to drag reduction in very small domains. The above observations are used to develop design and methodology guidelines for future research on compliant walls

Natural logarithms

Marusic et al. (J. Fluid Mech., vol. 716, 2013, R3) show the first clear evidence of universal logarithmic scaling emerging naturally (and simultaneously) in the mean velocity and the intensity of the streamwise velocity fluctuations about that mean in canonical turbulent flows near walls. These observations represent a significant advance in understanding of the behaviour of wall turbulence at high Reynolds number, but perhaps the most exciting implication of the experimental results lies in the agreement with the predictions of such scaling from a model introduced by Townsend (J. Fluid Mech., vol. 11, 1961, pp. 97–120), commonly termed the attached eddy hypothesis. The elegantly simple, yet powerful, study by Marusic et al. should spark further investigation of the behaviour of all fluctuating velocity components at high Reynolds numbers and the outstanding predictions of the attached eddy hypothesis

The effect of small-amplitude time-dependent changes to the surface morphology of a sphere

Typical approaches to manipulation of flow separation employ passive means or active techniques such as blowing and suction or plasma acceleration. Here it is demonstrated that the flow can be significantly altered by making small changes to the shape of the surface. A proof of concept experiment is performed using a very simple time-dependent perturbation to the surface of a sphere: a roughness element of 1% of the sphere diameter is moved azimuthally around a sphere surface upstream of the uncontrolled laminar separation point, with a rotational frequency as large as the vortex shedding frequency. A key finding is that the non-dimensional time to observe a large effect on the lateral force due to the perturbation produced in the sphere boundary layers as the roughness moves along the surface is ˆt =tU_(∞)/D ≈4. This slow development allows the moving element to produce a tripped boundary layer over an extended region. It is shown that a lateral force can be produced that is as large as the drag. In addition, simultaneous particle image velocimetry and force measurements reveal that a pair of counter-rotating helical vortices are produced in the wake, which have a significant effect on the forces and greatly increase the Reynolds stresses in the wake. The relatively large perturbation to the flow-field produced by the small surface disturbance permits the construction of a phase-averaged, three-dimensional (two-velocity component) wake structure from measurements in the streamwise/radial plane. The vortical structure arising due to the roughness element has implications for flow over a sphere with a nominally smooth surface or distributed roughness. In addition, it is shown that oscillating the roughness element, or shaping its trajectory, can produce a mean lateral force