bluuebunny/crossref_metadata_2025_split huggingface dataset:
Fluid flow in loops driven by freshwater and heat fluxes
Authors: Dewar W. K. , Huang R. X. 
Published: April 2006

Thermohaline convection in a salt water loop is discussed. Fluid temperature is affected by relaxation on the loop surface and fluid salinity by a freshwater flux through the loop surface. In addition, other boundary conditions on salinity, such as the equivalent virtual salt flux or salinity relaxation condition, are examined and the dynamic role of diffusion in thermohaline convection is analysed.Both analytical and numerical analyses indicate that the system behaviour depends sensitively on the nature of the salinity boundary condition. For the saline-only loop model, analysis indicates that perturbations are advected by the mean flow, and flow stability is independent of the strength of the boundary forcing. In the full thermohaline loop problem, the virtual salt flux formulation accurately mirrors the freshwater flux results when the system is in the thermal mode. However, these formulations can differ substantially when the system is in the haline mode, especially in the strongly forced, weakly diffusive limit.For both types of loop configuration, salinity profiles governed by freshwater flux have scales determined by the internal parameters, while virtual salt flux profiles necessarily reflect the lengthscales of applied boundary conditions. Negative salinities can also appear under virtual salt flux owing to the inaccuracies inherent in the approximation, while freshwater flux ensures positive-definite salinity values.Our analysis supports the use of the physically more accurate freshwater flux boundary conditions when simulating thermohaline circulation.
Transverse motion of a disk through a rotating viscous fluid
Authors: Tanzosh John P. , Stone H. A. 
Published: April 2006

A thin rigid disk translates edgewise perpendicular to the rotation axis of an unbounded fluid undergoing solid-body rotation with angular velocity Ω. The disk face, with radius a, is perpendicular to the rotation axis. For arbitrary values of the Taylor number, [Tscr ] = Ωa2/ν, and in the limit of zero Reynolds number [Rscr ]e, the linearized viscous equations reduce to a complex-valued set of dual integral equations. The solution of these dual equations yields an exact representation for the velocity and pressure fields generated by the translating disk.For large rotation rates [Tscr ] [Gt ] 1, the O(1) disturbance velocity field is confined to a thin O([Tscr ]−1/2) boundary layer adjacent to the disk. Within this boundary layer, the flow field near the disk centre undergoes an Ekman spiral similar to that created by a nearly geostrophic flow adjacent to an infinite rigid plate. Additionally, flow within the boundary layer drives a weak O([Tscr ]−1/2) secondary flow which extends parallel to the rotation axis and into the far field. This flow consists of two counter-rotating columnar eddies, centred over the edge of the disk, which create a net in-plane flow at an angle of 45° to the translation direction of the disk. Fluid is transported axially toward/away from the disk within the core of these eddies. The hydrodynamic force (drag and lift) varies as O([Tscr ]1/2) for [Tscr ] [Gt ] 1; this scaling is consistent with the viscous stresses created in the Ekman boundary layer. Additionally, an approximate expression, suitable for all Taylor numbers, is given for the hydrodynamic force on a disk translating broadside along the rotation axis and edgewise transverse to the rotation axis.
The effect of rotation on double-diffusive convection in a laterally heated vertical slot
Authors: Kerr Oliver S. 
Published: April 2006

The effect of rotation about a vertical axis on the linear stability of a salt-stratified fluid enclosed in a vertical slot when subjected to a temperature difference between the walls is investigated. It is found that for large salinity stratifications there are three distinct regimes of instability for different values of the rotation rate. For small rotation rates the convection cells resemble the thin, almost flat, convection cells predicted by non-rotating theory. The effect of the rotation is to marginally destabilize the fluid whilst inducing a small slope in the convection cells along the parallel walls. As the rotation rate is increased there is an abrupt change in the form of the most unstable convection cells as their aspect ratio and slope parallel to the walls both become of order one in magnitude. As the rotation rate is further increased there is a second less abrupt transition when the internal Rossby radius of deformation based on the vertical scale of the cells becomes of the same order of size as the slot width. After this point the slope of the cells increases in proportion to the rotation rate. The asymptotic nature of these three regimes is found.The effect of rotation on double-diffusive instabilities caused by more general horizontal temperature and salinity gradients in a salt-stratified fluid is also investigated, with particular reference to the case of heating the salinity gradient from a single sidewall. This analysis is restricted to the case where the rotation rate is low.
Longitudinal streaks
Authors: Colombini Marco , Parker Gary 
Published: April 2006

A commonly observed bedform in wide erodible-bed channels consists of rows of streaks or stripes parallel to the flow. These stripes can be manifested in terms of transverse variation of bed elevation, characteristic grain size (and thus roughness or both. The former case is manifested most strongly in sediment with a nearly uniform size distribution and the latter most strongly in sediment with substantial heterogeneity in size. The amplitude of stripes is rarely larger than one or two grain diameters, and the transverse spacing is invariably of the order of the flow depth. They are closely linked to a pattern of paired cells of secondary flow in the flow cross-section.An existing theory of streak formation for the case of uniform sediment relies on a second-order turbulence closure which explicitly links the streamwise flow to transverse variations in bed elevation. The theory successfully predicts the formation of streaks, but only at rather high values of the Shields stress, i.e. rather strong sediment transport. Streaks are commonly observed, however, at Shields stresses as low as only slightly above the threshold of motion.In the present analysis the previous flow model is adapted to the case of transverse variation of roughness as well as elevation, and the constraint of uniform sediment is removed. The theory indicates that allowance for even slight heterogeneity of bed sediment results in the formation of streaks at any Shields stress above the threshold of motion. The resulting streaks are hybrid in the sense that they show transverse variation in both elevation and roughness. The model thus provides a general theory of streak formation.
A new boundary layer resonance enhanced by wave modulation: theory and experiment
Authors: Healey J. J. 
Published: April 2006

When more than one wave is present in a system there exists the possibilty of a resonant interaction. Resonant modes become nonlinear at smaller amplitudes than nonresonant modes. If the nonlinearity causes increased growth rates then it may be that, for a time at least, the behaviour of the resonant modes will be the dominant feature. In shear layers resonant triads can be found where two oblique modes resonate with a plane wave and this case has received much attention in the literature. For a given plane wave, the resonance condition selects oblique modes of a certain wave angle and agreement has been found between predicted wave angles and those measured in experiments.In this paper it is shown that resonance conditions can also be met between two planar waves in a Blasius boundary layer, where one of the waves is the usual unstable mode, and the other is a higher-order damped mode. The effects of wave modulation are modelled by performing a spatial analysis but allowing the frequency to become complex. It is found that for certain complex frequencies the strength of the nonlinear resonant interaction coefficients is greatly increased. Experiments have been performed in a low-turbulence wind tunnel in which disturbances with modulated and unmodulated sections were introduced into the boundary layer over a flat plate. It was found that disturbances with the frequency and modulation predicted by the theory do indeed show a much greater susceptibility to nonlinear breakdown than nonresonant disturbances.
Compressible magnetoconvection in three dimensions: planforms and nonlinear behaviour
Authors: Matthews P. C. , Proctor M. R. E. , Weiss N. O. 
Published: April 2006

Convection in a compressible fiuid with an imposed vertical magnetic field is studied numerically in a three-dimensional Cartesian geometry with periodic lateral boundary conditions. Attention is restricted to the mildly nonlinear regime, with parameters chosen first so that convection at onset is steady, and then so that it is oscillatory.Steady convection occurs in the form of two-dimensional rolls when the magnetic field is weak. These rolls can become unstable to a mean horizontal shear flow, which in two dimensions leads to a pulsating wave in which the direction of the mean flow reverses. In three dimensions a new pattern is found in which the alignment of the rolls and the shear flow alternates.If the magnetic field is sufficiently strong, squares or hexagons are stable at the onset of convection. Both the squares and the hexagons have an asymmetrical topology, with upflow in plumes and downflow in sheets. For the squares this involves a resonance between rolls aligned with the box and rolls aligned digonally to the box. The preference for three-dimensional flow when the field is strong is a consequence of the compressibility of the layer- for Boussinesq magnetoconvection rolls are always preferred over squares at onset.In the regime where convection is oscillatory, the preferred planform for moderate fields is found to be alternating rolls - standing waves in both horizontal directions which are out of phase. For stronger fields, both alternating rolls and two-dimensional travelling rolls are stable. As the amplitude of convection is increased, either by dcereasing the magnetic field strength or by increasing the temperature contrast, the regular planform structure seen at onset is soon destroyed by secondary instabilities.
Convection in3He–superfluid-4He mixtures. Part 2. A survey of instabilities
Authors: Metcalfe Guy , Behringer R. P. 
Published: April 2006

Dilute mixtures of3He in superfluid4He have Prandtl numbers easily tunable between those of liquid metals and water: 0.04 <Pr< 2. Moreover, superfluid mixture convection is closely analogous to classical Rayleigh–Bénard convection, i.e. superfluid mixtures convect as if they were classical, single-component fluids. This work has two goals. The first, accomplished in Part 1, is to experimentally validate the superfluid mixture convection analogue to Rayleigh–Bénard convection.With superfluid effects understood and under control, the second goal is to identify and characterize time-dependence and chaos and to discover new dynamical behaviour in strongly nonlinear convective flows. In this paper, Part 2, we exploit the uniquePrrange of superfluid mixtures and the variable aspect ratio (Γ) capabilities of our experiment to survey convective instabilities in the broad, and heretofore largely unexplored, parameter space 0.12 <Pr< 1.4 and 2 < Γ < 95. Within this large parameter space, we have focused on small to moderate Γ andPrand on large Γ withPr≈ 1. The novel behaviour uncovered in the survey includes the following.Changing attractors: at Γ = 6.0 andPr= 0.3, we observe intermittent bursting destabilizing a fully developed chaotic state. Above the onset of bursting the average length of a burst-free interval and the average length of a burst vary as power laws. At Γ = 4.25 andPr= 0.12 we observe a particularly novel reversible switching transition involving two chaotic attractors.Instability competition: near the codimension-2 point at the crossing of the skewed-varicose and oscillatory instabilities we find that the effects of instability competition greatly increase the complexity and multiplicity of states. A heat-pulse method allows selection of the active state. Decreasing Γ suppresses the available complexity.Superfluid turbulence: we find that the large-amplitude noisy states, previously believed due to superfluid turbulence, are confined to small values of Γ andPrand are not consistent with superfluid turbulence.Changing instabilities: atPr= 0.19 a wavevector detuning changes the type of secondary instability from oscillatory to saddle-node, with an unusual 3/4 exponent time scaling.Very largeΓ: atPr= 1.3 for Γ increasing from 44 to 90, we observe the onset of convection changing from ordered and stationary to disordered and time-dependent. At the beginning of the crossover there are hysteretic transitions to coherent oscillations close to the onset of convection. By the end of the crossover convection is time-dependent and irregular at onset with the fluctuation amplitude correlated with the mean Nusselt number.
Mechanics of collisional motion of granular materials. Part 3. Self-similar shock wave propagation
Authors: Goldshtein A. , SHAPIRO M. , Gutfinger C. 
Published: April 2006

Shock wave propagation arising from steady one-dimensional motion of a piston in a granular gas composed of inelastically colliding particles is treated theoretically. A self-similar long-time solution is obtained in the strong shock wave approximation for all values of the upstream gas volumetric concentration v0. Closed form expressions for the long-time shock wave speed and the granular pressure on the piston are obtained. These quantities are shown to be independent of the particle collisional properties, provided their impacts are accompanied by kinetic energy losses. The shock wave speed of such non-conservative gases is shown to be less than that for molecular gases by a factor of about 2.The effect of particle kinetic energy dissipation is to form a stagnant layer (solid block), on the surface of the moving piston, with density equal to the maximal packing density, vM. The thickness of this densely packed layer increases indefinitely with time. The layer is separated from the shock front by a fluidized region of agitated (chaotically moving) particles. The (long-time, constant) thickness of this layer, as well as the kinetic energy (granular temperature) distribution within it are calculated for various values of particle restitution and surface roughness coefficients. The asymptotic cases of dilute (v0 [Lt ] 1) and dense (v0 ∼ vM) granular gases are treated analytically, using the corresponding expressions for the equilibrium radial distribution functions and the pertinent equations of state. The thickness of the fluidized region is shown to be independent of the piston velocity.The calculated results are discussed in relation to the problem of vibrofluidized granular layers, wherein shock and expansion waves were registered. The average granular kinetic energy in the fluidized region behind the shock front calculated here compared favourably with that measured and calculated (Goldshtein et al. 1995) for vibrofluidized layers of spherical granules.
Disturbance growth in an unstable three-dimensional boundary layer and its dependence on environmental conditions
Authors: Deyhle H. , Bippes H. 
Published: April 2006

Experimental investigations in the three-dimensional boundary layer of a swept flat plate with the pressure gradient induced from outside are aimed at enhancing knowledge of the transition process in the presence of pure crossflow instability. The development of disturbances is characterized by the occurrence of both stationary and travelling instability modes, by early nonlinear development and by complex dependence upon the environmental conditions. Experiments under natural conditions of transition showed a good correspondence of the identified modes with those predicted by local linear stability theory. The disturbance growth, however, is generally overpredicted. Controlled excitation of crossflow vortices allowing measurements closer to the linear range of amplification confirmed this result. Nonlinear effects such as interaction between stationary disturbances and base flow and between travelling and stationary modes have already been observed when the naturally excited instabilities become of measurable size.The most striking feature of the disturbance development is the complex dependence on initial conditions. Experiments under systematically varied environments showed that surface roughness represents the key parameter responsible for the initiation of stationary crossflow vortices. In contrast to two-dimensional boundary layers, free-stream turbulence influences the transition process indirectly. Only for turbulence levels Tu > 0.2% and smooth surfaces do the travelling instability waves dominate. The location of the final breakdown of laminar flow is clearly determined by the saturation amplitude of crossflow vortices. The receptivity to sound, two-dimensional surface roughness and non-uniformities of the test-section mean flow was found to be very weak.
A random-flight evaluation of the constants of relative dispersion in idealized turbulence
Authors: Faller Alan J. 
Published: April 2006

In the idealized problem of homogeneous isotropic stationary inertial-range turbulence the rate of relative dispersion of an ensemble of tracer pairs can be characterized by a constantC0. In order to compute this constant with random-flight equations, however, it is necessary first to know the values of two other constants,C1andC2, that occur in the two-particle velocity-component relations of Lagrangian tracers (Faller 1992).C1andC2are found by an elaborate trial and error procedure in a new two-tracer random-flight model of dispersion that matches input and output values of these two variates. The constantC0is then computed using the Lagrangian relations and is found to be significantly smaller than when the Eulerian Kármán/Howarth correlations are used.The probability density distribution of tracer separations has a kurtosis slightly larger than that of a comparable Gaussian distribution. At small spacings the frequency of tracer spacings is six to ten times larger than would be expected from a Gaussian distribution. The distribution function for the speed of separation of the Lagrangian tracers has a negative skewness similar to that found for two-point Eulerian velocities.
Linear dynamics of wind waves in coupled turbulent air–water flow. Part 2. Numerical model
Authors: Harris J. A. , Belcher S. E. , Street R. L. 
Published: April 2006

We develop a numerical model of the interaction between wind and a small-amplitude water wave. The model first calculates the turbulent flows in both the air and water that would be obtained with a flat interface, and then calculates linear perturbations to this base flow caused by a travelling surface wave. Turbulent stresses in the base flow are parameterized using an eddy viscosity derived from a low-turbulent-Reynolds-number κ – ε model. Turbulent stresses in the perturbed flow are parameterized using a new damped eddy viscosity model, in which the eddy viscosity model is used only in inner regions, and is damped exponentially to zero outside these inner regions. This approach is consistent with previously developed physical scaling arguments. Even on the ocean the interface can be aerodynamically smooth, transitional or rough, so the new model parameterizes the interface with a roughness Reynolds number and retains effects of molecular stresses (on both mean and turbulent parts of the flow).The damped eddy viscosity model has a free constant that is calibrated by comparing with results from a second-order closure model. The new model is then used to calculate the variation of form drag on a stationary rigid wave with Reynolds number, R. The form drag increases by a factor of almost two as R drops from 2 × 104 to 2 × 103 and shows remarkably good agreement with the value measured by Zilker & Hanratty (1979). These calculations show that the damped eddy viscosity model captures the physical processes that produce the asymmetric pressure that leads to form drag and also wave growth.Results from the numerical model show reasonable agreement with profiles measured over travelling water waves by Hsu & Hsu (1983), particularly for slower moving waves. The model suggests that the wave-induced flow in the water is irrotational except in an extremely thin interface layer, where viscous stresses are as likely to be important as turbulent stresses. Thus our study reinforces previous suggestions that the region very close to the interface is crucial to wind-wave interaction and shows that scales down to the viscous length may have an order-one effect on the development of the wave.The energy budget and growth rate of the wave motions, including effects of the sheared current and Reynolds number, will be examined in a subsequent paper.
Manifestations of bottom topography on the ocean surface: the physical mechanism for large scales
Authors: Shrira Victor I. , Annenkov Sergei Yu. 
Published: April 2006

The paper is a first attempt at theoretical investigation of the experimentally observed enigmatic phenomenon of surface manifestations of bottom topography reproducing well the image of the relief despite several kilometres of ocean depth. Both satellite observations and direct measurements have been repeatedly reported in the last two decades. We suggest a possible mechanism for these manifestations in a large scale range (of the order 5 × 101–103 km), based on the hydrodynamic theory of quasi-geostrophic stratified flow over topography on a β-plane.The classical theories of quasi-geostrophic flow over topography on a β-plane do not include vertical shear, and it is well-known that the disturbance caused by topography cannot reach the surface of a stratified ocean unless the stratification or current velocity is unrealistic. The new element changing the situation qualitatively is the taking into account of the influence of near-bottom and near-surface boundary layers, where flow velocities, velocity gradients and stratification can significantly exceed the corresponding values for the flow in the main body. The asymptotic solution derived shows the considerable increase of the normal mode amplitude towards the boundaries. Thus, this specific distortion of the eigenmode structure results in effective forcing of the modes by topography and, on the other hand, leads to pronounced disturbances in the fields of near-surface characteristics. The mechanism effectiveness is demonstrated by the fact that the surface disturbance amplitude normally significantly exceeds the corresponding value for the barotropic current equal to the maximum of the shear flow. A remarkable feature of the solution is that the Green's function is strongly localized in the horizontal plane for a wide range of relevant parameters, thus leading to the close resemblance of surface patterns and bottom relief. To get a better understanding of the quantitative characteristics of the mechanism, the dependence of the effect on the parameters of an N-layer model was studied in detail. The amplification of the surface manifestations due to the presence of boundary layers can reach several orders of magnitude and thus make the manifestations easily observable. The surface temperature anomalies due to topography were estimated and found to be observable under favourable conditions.