The silent base flow and the sound sources in a laminar jet.

An algorithm to compute the silent base flow sources of sound in a jet is introduced. The algorithm is based on spatiotemporal filtering of the flow field and is applicable to multifrequency sources. It is applied to an axisymmetric laminar jet and the resulting sources are validated successfully. The sources are compared to those obtained from two classical acoustic analogies, based on quiescent and time-averaged base flows. The comparison demonstrates how the silent base flow sources shed light on the sound generation process. It is shown that the dominant source mechanism in the axisymmetric laminar jet is "shear-noise," which is a linear mechanism. The algorithm presented here could be applied to fully turbulent flows to understand the aerodynamic noise-generation mechanism.

The unidirectional emptying box

A theoretical description of the turbulent mixing within and the draining of a dense fluid layer from a box connected to a uniform density, quiescent environment through openings in the top and the base of the box is presented in this paper. This is an extension of the draining model developed by Linden et al. (Annu. Rev. Fluid Mech. vol. 31, 1990, pp. 201-238) and includes terms that describe localized mixing within the emptying box at the density interface. Mixing is induced by a turbulent flow of replacement fluid into the box and as a consequence we predict, and observe in complementary experiments, the development of a three-layer stratification. Based on the data collated from previous researchers, three distinct formulations for entrainment fluxes across density interfaces are used to account for this localized mixing. The model was then solved numerically for the three mixing formulations. Analytical solutions were developed for one formulation directly and for a second on assuming that localized mixing is relatively weak though still significant in redistributing buoyancy on the timescale of the draining process. Comparisons between our theoretical predictions and the experimental data, which we have collected on the developing layer depths and their densities show good agreement. The differences in predictions between the three mixing formulations suggest that the normalized flux turbulently entrained across a density interface tends to a constant value for large values of a Froude number FrT, based on conditions of the inflow through the top of the box, and scales as the cube of FrT for small values of FrT. The upper limit on the rate of entrainment into the mixed layer results in a minimum time (tD) to remove the original dense layer. Using our analytical solutions, we bound this time and show that 0.2tE ≈tD tE, i.e. the original dense layer may be depleted up to five times more rapidly than when there is no internal mixing and the box empties in a time tE. © 2010 Cambridge University Press.

Closely correlating lower and upper bound plastic analysis of real slabs

An engineer assessing the load-carrying capacity of an existing reinforced concrete slab is likely to use elastic analysis to check the load at which the structure might be expected to fail in flexure or in shear. In practice, many reinforced concrete slabs are highly ductile in flexure, so an elastic analysis greatly underestimates the loads at which they fail in this mode. The use of conservative elastic analysis has led engineers to incorrectly condemn many slabs and therefore to specify unnecessary and wasteful flexural strengthening or replacement. The lower bound theorem is based on the same principles as the upper bound theorem used in yield line analysis, but any solution that rigorously satisfies the lower bound theorem is guaranteed to be a safe underestimate of the collapse load. Jackson presented a rigorous lower bound method that obtains very accurate results for complex real slabs.

Transducer and base compliance alter the in situ 6 dof force measured from muscle during an isometric contraction in a multi-joint limb.

Although musculoskeletal models are commonly used, validating the muscle actions predicted by such models is often difficult. In situ isometric measurements are a possible solution. The base of the skeleton is immobilized and the endpoint of the limb is rigidly attached to a 6-axis force transducer. Individual muscles are stimulated and the resulting forces and moments recorded. Such analyses generally assume idealized conditions. In this study we have developed an analysis taking into account the compliances due to imperfect fixation of the skeleton, imperfect attachment of the force transducer, and extra degrees of freedom (dof) in the joints that sometimes become necessary in fixed end contractions. We use simulations of the rat hindlimb to illustrate the consequences of such compliances. We show that when the limb is overconstrained, i.e., when there are fewer dof within the limb than are restrained by the skeletal fixation, the compliances of the skeletal fixation and of the transducer attachment can significantly affect measured forces and moments. When the limb dofs and restrained dofs are matched, however, the measured forces and moments are independent of these compliances. We also show that this framework can be used to model limb dofs, so that rather than simply omitting dofs in which a limb does not move (e.g., abduction at the knee), the limited motion of the limb in these dofs can be more realistically modeled as a very low compliance. Finally, we discuss the practical implications of these results to experimental measurements of muscle actions.