ALBERT

Beschreibung: The dynamics of gravity currents are believed to be strongly influenced by dissipation due to turbulence and mixing between the current and the surrounding ambient fluid. This paper describes new theory and experiments on gravity currents produced by lock exchange which suggest that dissipation is unimportant when the Reynolds number is sufficiently high. Although there is mixing, the amount of energy dissipated is small, reducing the current speed by a few percent from the energy-conserving value. Benjamin (J. Fluid Mech. vol. 31, 1968, p. 209) suggests that dissipation is an essential ingredient in gravity current dynamics. We show that dissipation is not important at high Reynolds number, and provide an alternative theory that predicts the current speed and depth based on energy-conserving flow that is in good agreement with experiments. We predict that in a deep ambient the front Fronde number is 1, rather than the previously accepted value of √ 2. New experiments are reported for this case that support the new theoretical value. © 2004 Cambridge University Press.

Beschreibung: A detailed parametric study of the noise from dual-stream jets has been carried out to assess the importance of the noise generated by the primary and secondary shear layers and their principal radiation directions under different operating conditions. Realistic geometries and engine conditions are chosen to enhance the relevance and the usefulness of the experimental results reported here. The effects of different operating conditions in the two streams on both the turbulent mixing noise and shock-associated noise are evaluated under static conditions as well as in the presence of an external co-flowing stream. The results indicate that the secondary-to-primary jet velocity ratio is an important parameter for mixing noise while its effect is negligible on shock-associated noise. The shock-associated noise, not surprisingly, is dependent on the geometric details of the nozzle. The characteristics of this noise component are very different depending on whether shocks are present in the primary or secondary stream. There is strong radiation of shock noise to the aft angles when the secondary stream is supersonic. This trend is troublesome since this component is transmitted into the aft cabin of certain aircraft with engines mounted close to the fuselage. The intensity of the shock-associated noise at the lower angles, in general, is proportional to the strength of the shocks and scales with (Mp2 - Md 2)2 or (Ms2 - M d2)2 (Mp and M s denote the Mach numbers of the primary and secondary streams and Md is the design Mach number). Just as for a single jet, the effect of forward flight on mixing noise and shock-associated noise is very different. While there is a progressive reduction in levels of mixing noise with increasing free-stream velocity, there is amplification of the shock-associated noise. This is particularly so for the aft-radiated component of shock noise from the secondary stream. This effect could further exacerbate the interior noise in the aft cabin. © 2004 Cambridge University Press.

Beschreibung: In this paper we consider the possibility of generating homogeneous flows with a nearly constant strain rate. This is achieved by stretching an almost cylindrical liquid bridge under microgravity. One key issue is the adjustability of the disk diameters, necessary for maintaining ideal boundary conditions. We first study the stretching of two different fluids by both numerical and experimental means. The numerical results are compared with the experimental data and very good agreement is found. The numerical method is then used to study the behaviour of liquid bridges for quite a large range of the flow parameters (capillary number Ca and Weber number We) in order to detect those regimes with most suitable flow conditions. © 2004 Cambridge University Press.

Beschreibung: Real turbulent flows are difficult to classify as either spatially homogeneous or isotropic. Nonetheless these idealizations allow the identification of certain universal features associated with the small-scale motions almost invariably observed in a variety of different conditions. The single most significant aspect is a flux of energy through the spectrum of inertial scales related to the phenomenology commonly referred to as the Richardson cascade. Inhomogeneity, inherently present in near-wall turbulence, generates additional energy fluxes of a different nature, corresponding to the spatial redistribution of turbulent kinetic energy. Traditionally the spatial flux is associated with a single-point observable, namely the turbulent kinetic energy density. The flux through the scales is instead classically related to two-point statistics, given in terms of an energy spectrum or, equivalently, in terms of the second-order moment of the velocity increments. In the present paper, starting from a suitably generalized form of the classical Kolmogorov equation, a scale-by-scale balance for the turbulent fluctuations is evaluated by examining in detail how the energy associated with a specific scale of motion - hereafter called the scale energy - is transferred through the spectrum of scales and, simultaneously, how the same scale of motion exchanges energy with a properly defined spatial flux. The analysis is applied to a data set taken from a direct numerical simulation (DNS) of a low-Reynolds-number turbulent channel flow. The detailed scale-by-scale balance is applied to the different regions of the flow in the various ranges of scales, to understand how - i.e. through which mechanisms, at which scales and in which regions of the flow domain - turbulent fluctuations are generated and sustained. A complete and formally precise description of the dynamics of turbulence in the different regions of the channel flow is presented, providing rigorous support for previously proposed conceptual models. © 2004 Cambridge University Press.

Beschreibung: A flow of electrically conducting fluid in the presence of a steady magnetic field has a tendency to become quasi-two-dimensional, i.e. uniform in the direction of the magnetic field, except in thin so-called Hartmann boundary layers. The condition for this tendency is that of a strong magnetic field, corresponding to large values of the dimensionless Hartmann number (Ha ≫ 1). This is analogous to the case of low-Ekman-number rotating flows, with Ekman layers replacing Hartmann layers. This has been at the origin of the homogeneous model for flows in a rotating frame of reference, with its rich structure: geostrophic contours and shear layers. In magnetohydrodynamics, the characteristic surfaces introduced by Kulikovskii (Isv. Akad. Nauk SSSR Mekh. Zhidk Gaza, vol. 3, 1968, p. 3) play a role similar to that of the geostrophic contours. However, a general theory for quasi-two-dimensional magnetohydrodynamics is lacking. In this paper, a model is proposed which provides a general framework. Not only can this model account for otherwise disconnected past results, but it is also used to predict a new type of shear layer, of typical thickness Ha-1/4 . Two practical cases are then considered: the classical problem of a fringing transverse magnetic field across a circular pipe flow, treated by Holroyd & Walker (J. Fluid Mech. vol. 84, 1978, p. 471), and the problem of a rectangular cross-section duct flow in a slowly varying transverse magnetic field. For the first problem, the existence of thick shear layers of dimensionless thickness of order of magnitude Ha-1/4 explains why the flow expected at large Hartmann number was not observed in experiments. The second problem exemplifies a situation where an analytical solution had been obtained in the past Walker & Ludford (J. Fluid Mech. vol. 56, 1972, p. 481) for the so-called 'M-shaped' velocity profile, which is here understood as an aspect of general quasi-two-dimensional magnetohydrodynamics. © 2004 Cambridge University Press.

Beschreibung: An upper bound on the mixing efficiency is derived for a passive scalar under the influence of advection and diffusion with a body source. For a given stirring velocity field, the mixing efficiency is measured in terms of an equivalent diffusivity, which is the molecular diffusivity that would be required to achieve the same level of fluctuations in the scalar concentration in the absence of stirring, for the same source distribution. The bound on the equivalent diffusivity depends only on the functional 'shape' of both the source and the advecting field. Direct numerical simulations performed for a simple advecting flow to test the bounds are reported. © 2004 Cambridge University Press.

Beschreibung: The classical problem of linear stability of a regular N-gon of point vortices to infinitesimal space displacements from an equilibrium of the vortex configuration is generalized to the one for N helical vortices (couple, triplet, etc., N 〉 1) for the first time. As a consequence of this consideration, the analytical form for the stability boundaries has been obtained. This solution allows an efficient analysis to be made of the existence of stable helical vortex arrays, which were repeatedly observed in practice. Such a stability problem was earlier considered in theory, but only for the case of a plane polygonal array of N point vortices. As for helical vortices, owing to their complexity, intensive study has been mainly on the self-induced motion of the vortex. The algebraic representation forthe velocity of motion of the N helical vortex array was originally obtained as an additional intermediate result. The new formula allows accurate calculations to be made within the whole range of helical pitch variations and has a simpler form than the known asymptotic expressions. Solution of these two classical problems of vortex dynamics has significance both for theoretic and applied mechanics, as well as for many other areas of natural science, where the rotor (vortex) concept is the basic one. © 2004 Cambridge University Press.

Beschreibung: A new class of large-eddy simulation (LES) models (optimal LES) was previously introduced by the authors. These models are based on multi-point statistical information, which here is provided by direct numerical simulation (DNS). In this paper, the performance of these models in LES of forced isotropic turbulence is investigated. It is found that both linear and quadratic optimal models yield good simulation results, with an excellent match between the LES and filtered DNS for spectra, and low-order structure functions. Optimal models werethen used as a vehicle to investigate the effects of filter shape and the locality of model dependence on LES performance. Results indicate that a Fourier cutoff filter yields more accurate simulations than graded cutoff filters, leaving no motivation to use graded filters in spectral simulations. It was also found that optimal models formulated to depend on local information performed nearly as well as global models. This is important because in practical LES simulations in which spectral methods are not applicable, global model dependence would be prohibitively expensive. © 2004 Cambridge University Press.

Beschreibung: An asymptotic method for analysing slender non-axisymmetric drops, bubbles and jets in a general straining flow is developed. The method relies on the slenderness of the geometry to reduce the three-dimensional equations to a sequence of weakly coupled, quasi-two-dimensional Stokes flow problems for the cross-sectional evolution. Exact solution techniques for the flow outside a bubble in two-dimensional Stokes flow are generalized to solve for the transverse flow field, allowing large non-axisymmetric deformations to be described. A generalization to the case where the interior of the bubble contains a slightly viscous fluid is also presented. Our method is usedto compute steady non-axisymmetric solution branches for inviscid bubbles and slightly viscous drops. We also present unsteady numerical solutions showing how the eccentricity of the cross-section adjusts to a non-axisymmetric external flow. Finally, we use our theory to investigate how the pinch-off of a jet of relatively inviscid fluid is affected by a two-dimensional straining cross-flow. © 2004 Cambridge University Press.