bluuebunny/crossref_metadata_2025_split huggingface dataset:
Random waves and dynamo action
Authors: Soward A. M. 
Published: March 2006

The propagation of waves in an inviscid, electrically conducting fluid is considered. The fluid rotates with angular velocity Ω* and is permeated by a magnetic field b* which varies on the length scale L = Ql, where Q = Ω*l2/λ (l is the length scale of the waves, λ is the magnetic diffusivity) is assumed large (Q [Gt ] 1). A linearized theory is readily justified in the limit of zero Rossby number R0 (= U0/Ω*l, where U0 is a typical fluid velocity) and for this case it is shown that the total wave energy of a wave train is conserved and transported at the group velocity except for that which is lost by ohmic dissipation. The analysis is extended to encompass the propagation of a sea of random waves.A hydromagnetic dynamo model is considered in which the fluid is confined between two horizontal planes perpendicular to the rotation axis a distance L0(=O(L)) apart. Waves of given low frequency Ω*0 (= O(R0Q½Ω*)) and horizontal wavenumber l−1 but random orientation are excited at the lower boundary, where the kinetic energy density is 2πρU20. The waves are absorbed perfectly at the upper boundary, so that there is no reflexion. The linear wave energy equation remains valid in the double limit 1 [Gt ] R0Q½[Gt ]Q−½, for which it is shown that dynamo action is possible provided $\Delta = L_0U^2_0/l^3\omega_0^{*2} > 1 $. When dynamo action maintains a weak magnetic field (Δ −1 [Lt ] 1) which only slightly modifies the inertial waves analytic solutions are obtained. In the case of a strong magnetic field (Δ [Gt ] 1) for which Coriolis and Lorentz forces are comparable solutions are obtained numerically. The latter class includes the more realistic case (Δ → ∞) in which the upper boundary is absent.
Waves and turbulence on a beta-plane
Authors: Rhines Peter B. 
Published: March 2006

Two-dimensional eddies in a homogeneous fluid at large Reynolds number, if closely packed, are known to evolve towards larger scales. In the presence of a restoring force, the geophysical beta-effect, this cascade produces a field of waves without loss of energy, and the turbulent migration of the dominant scale nearly ceases at a wavenumber kβ = (β/2U)½ independent of the initial conditions other than U, the r.m.s. particle speed, and β, the northward gradient of the Coriolis frequency.The conversion of turbulence into waves yields, in addition, more narrowly peaked wavenumber spectra and less fine-structure in the spatial maps, while smoothly distributing the energy about physical space.The theory is discussed, using known integral constraints and similarity solutions, model equations, weak-interaction wave theory (which provides the terminus for the cascade) and other linearized instability theory. Computer experiments with both finite-difference and spectral codes are reported. The central quantity is the cascade rate, defined as
\[
T = 2\int_0^{\infty} kF(k)dk/U^3\langle k\rangle ,
\]
where F is the nonlinear transfer spectrum and 〈k〉 the mean wavenumber of the energy spectrum. (In unforced inviscid flow T is simply U−1d〈k〉−1/dt, or the rate at which the dominant scale expands in time t.) T is shown to have a mean value of 3·0 × 10−2 for pure two-dimensional turbulence, but this decreases by a factor of five at the transition to wave motion. We infer from weak-interaction theory even smaller values for k [Lt ] kβ.After passing through a state of propagating waves, the homogeneous cascade tends towards a flow of alternating zonal jets which, we suggest, are almost perfectly steady. When the energy is intermittent in space, however, model equations show that the cascade is halted simply by the spreading of energy about space, and then the end state of a zonal flow is probably not achieved.The geophysical application is that the cascade of pure turbulence to large scales is defeated by wave propagation, helping to explain why the energy-containing eddies in the ocean and atmosphere, though significantly nonlinear, fail to reach the size of their respective domains, and are much smaller. For typical ocean flows, $k_{\beta}^{-1} = 70\,{\rm km} $, while for the atmosphere, $k_{\beta}^{-1} = 1000\,{\rm km}$. In addition the cascade generates, by itself, zonal flow (or more generally, flow along geostrophic contours).
A study of turbulent boundary-layer separation and reattachment
Authors: Perry A. E. , Fairlie B. D. 
Published: March 2006

An experimental and theoretical study is made of a suddenly separating and reattaching two-dimensional turbulent boundary layer on a flat surface. A separation bubble is formed on the floor of a wide parallel-sided wind-tunnel duct with the pressure field causing the bubble formation produced by fixing the shape of the flexible roof of the duct. Boundary layers on the roof are controlled and remain attached. It is found that a very satisfactory model for the flow is an inviscid one.The boundary layer on the floor of the duct is represented by a region of constant vorticity with slip at the boundary, and it is assumed that the separation process is dominated by the interaction between this ‘vortical’ region and the irrotational field between the vortical region and the roof (of prescribed shape). The interface between the rotational and irrotational regions is a free boundary and may be located when all necessary boundary conditions are given. These conditions include two characteristic parameters for the adverse-pressure-gradient turbulent boundary layer which is developing upstream of the region of interest.The problem is solved by an electrical analog method. The theoretical size and shape of the bubble and positions of separation and reattachment are in agreement with observations. The advantage of the model over most previous attempts to predict separation is that the governing equations are elliptic rather than parabolic or hyperbolic and therefore the interaction between the boundary-layer flow and the irrotational free stream is included in the calculations.
Progress in the development of a Reynolds-stress turbulence closure
Authors: Launder B. E. , Reece G. J. , Rodi W. 
Published: March 2006

The paper develops proposals for a model of turbulence in which the Reynolds stresses are determined from the solution of transport equations for these variables and for the turbulence energy dissipation rate ε. Particular attention is given to the approximation of the pressure-strain correlations; the forms adopted appear to give reasonably satisfactory partitioning of the stresses both near walls and in free shear flows.Numerical solutions of the model equations are presented for a selection of strained homogeneous shear flows and for two-dimensional inhomogeneous shear flows including the jet, the wake, the mixing layer and plane channel flow. In addition, it is shown that the closure does predict a very strong influence of secondary strain terms for flow over curved surfaces.
Thermoacoustic effects in a resonance tube
Authors: Merkli P. , Thomann H. 
Published: March 2006

New experiments with a gas-filled resonance tube have shown that not only heating, but also cooling of the tube wall is possible and that these phenomena are not restricted to oscillation amplitudes that generate shocks. The present paper concentrates on amplitudes outside the shock region. For this case, an extended acoustic theory is worked out. The results show cooling in the section of the tube with maximum velocity amplitude (and thus dissipation) and marked heating in the region of the velocity nodes. A strong dependence of these effects on the Prandtl number is noted. The results are in good agreement with experiments. Although the theory is not valid for proper resonance conditions, it nevertheless sheds some light on what happens when nonlinear effects dominate.Closely related to the limit of validity of the thermoacoustic theory is the question of transition from laminar to turbulent flow in the viscous boundary layer (Stokes layer). This problem has also been investigated; the results are given in a separate paper (Merkli & Thomann 1975). In the present article laminar flow is assumed.
A proposed model of the bursting process in turbulent boundary layers
Authors: Offen G. R. , Kline S. J. 
Published: March 2006

A model is proposed which attempts to explain the complete ‘burst cycle’. This model views the wall streak as a sub-boundary layer, within the conventionally defined boundary layer, and the lift-up stage of bursting either as an upwelling motion of this sub-boundary layer which is similar to a local, convected separation or, equivalently, as the consequence of a vortex roll-up. ‘Sweeps’ are thought to represent the passage of a previous burst from further upstream. They appear either to impress on the wall streak the temporary adverse pressure gradient required to bring about its lifting or, alternatively, to provide the outer vortex which rolls up with the vortex associated with the wall streak. The model is also used to explain how the interactions between a burst and a sweep bring about (i) breakup, as well as (ii) new wall streaks further downstream.Arguments are presented to demonstrate that the three kinds of oscillatory growth reported by Kim, Kline & Reynolds (1971) may be associated with just one type of flow structure: the stretched and lifted vortex described by Klineet al.(1967).
Nonlinear wave interactions in shear flows. Part 2. Third-order theory
Authors: Usher J. R. , Craik A. D. D. , Hendriks F. 
Published: March 2006

The temporal evolution of a resonant triad of wave components in a parallel shear flow has been investigated at second order in the wave amplitudes by Craik (1971) and Usher & Craik (1974). The present work extends these analyses to include terms of third order and thereby develops the resonance theory to the same order of approximation as the non-resonant third-order theory of Stuart (1960, 1962).Asymptotic analysis for large Reynolds numbers reveals that the magnitudes of the third-order interaction coefficients, like certain of those at second order, are remarkably large. The implications of this are discussed with particular reference to the roles of resonance and of three-dimensionality in nonlinear instability and to the range of validity of the perturbation analysis.
The laminar flow of dilute polymer solutions through porous media
Authors: James David F. , Mclaren D. R. 
Published: March 2006

Measurements of the pressure drop and flow rate were obtained for dilute solutions of polyethylene oxide flowing through beds of packed beads. When the velocity was sufficiently high, the pressure drop was above that for a Newtonian fluid of equal viscosity, often considerably above, and this viscoelastic effect was explored by varying the concentration and molecular weight of the polymer, by testing solutions over a wide range of flow rates, and by using several bead sizes. The non-Newtonian behaviour was most pronounced at moderate flow rates; at the highest velocities, the data were pseudo-Newtonian in character, i.e. the pressure drop still exceeded that for a Newtonian fluid, but was linearly related to the velocity. For some solutions, the large deviation from Newtonian values occurred over such a short range of flow rates that there was an interval in which the pressure drop decreased with velocity. It was not possible, therefore, to obtain steady-state measurements in this regime and a gap appears in the data curve of pressure vs. velocity.The pressure drop was monitored in steps along the test section, so that it was possible to detect molecular degradation of the solutions as they flowed through the porous media. In general, degradation was not extensive and the solutions became stably degraded by the midpoint of the test section. Degradation increased with velocity and, quite surprisingly, became more severe as the bead size increased.A visual examination of the flow field revealed that the streamline pattern for the polymer solutions was the same as that for water. The large non-Newtonian effects were therefore due to changes in the stress field, and in an effort to understand these effects, an analysis was carried out which examined how the stresses generated by each component of the deformation, i.e. by shear and pure strain, influence the pressure drop. This analysis, combined with a study of onset data, indicates that onset and the sudden large departures from Newtonian values are probably due to an interaction between extensional and shearing deformation, and that the reduced viscoelastic effect of higher flow rates may be due to the dominance of extensional stresses.
The motion generated by a body moving through a stratified fluid at large Richardson numbers
Authors: Barnard B. J. S. , Pritchard W. G. 
Published: March 2006

Experiments are described in which a body was towed at large Richardson numbers through a uniformly stratified fluid, with particular attention being given to the parameter range in which diffusive effects are likely to play an important role. When the Richardson number is only moderately large (i.e. less than about 106) it appears that a linear viscous diffusive theory fails to model the experimental observations, but at larger Richardson numbers it seems that such a theory is a strong candidate for modelling the physical situation. At Richardson numbers of about 103 a non-diffusive viscous model (see the theories of Graebel 1969; Janowitz 1971) appears to give a fairly good description of the experimental results, except for some discrepancies between the theories and the observed flows in the wake downstream from the body. However, the conditions under which the experiments were carried out were not completely favourable for the application of these theories.A brief survey and new interpretations of some of the work on the rotatingfluid counterparts of the present experiments are also given. In view of the theoretical similarities between the two situations we have tried to assess and compare (where possible) the results of experimental investigations in each field and we feel that the observations in the rotating-fluid experiments are in good qualitative agreement with the present results. No measurements of the drag acting on the body were made in the present experiments but this has been done carefully in the rotating-fluid experiments, and the results of those measurements are in poor agreement with the theoretical predictions. Because of the close similarities between the axisymmetric model for viscous rotating fluids (cf. Moore & Saffman 1969) and the two-dimensional model for diffusive stratified fluids (Freund & Meyer 1972), an explanation for the discrepancy should be sought before the linear viscous diffusive model can be applied with any confidence to the flow of stratified fluids at very large Richardson numbers.
Circulations and density distributions in a deep, strongly stratified, two-layer estuary
Authors: Long Robert R. 
Published: March 2006

The paper discusses a theoretical model of statistically steady flow in a strongly stratified estuary. A halocline is assumed to be present and the lower layer is taken to be deep and non-turbulent. The outflowing upper fluid mixes with the salty lower fluid and the flux of the brackish water increases with distance from the head of the estuary. The mixing is assumed to be similar to that in laboratory models of mixing across density interfaces.Two equations of mass conservation are used, one for the steady-state mass flux across a vertical section from top to bottom of the channel and one for the mass flux into a section of the upper fluid. A buoyancy conservation equation is used for the buoyancy flux across a vertical section. A final equation is obtained by integrating the horizontal equation of motion across a section of the upper fluid. The flow in this layer is assumed to be opposed by a frictional force proportional to the square of the velocity averaged over the layer. The pressure-gradient force arising from the slope of the free surface is solved for in terms of the thickness of the upper layer, the buoyancy difference across the interface, the slope of the interface and the horizontal density gradient in the upper layer. The derivation shows that the horizontal pressure-gradient force vanishes in the lower layer.The mathematical problem reduces to two ordinary differential equations for the flux in the upper layer and its thickness. Attention is confined to the solution for subcritical flow, in which the interface falls with distance from the head, reaching a maximum depth at a certain section of the estuary. Beyond this the interface rises. At the mouth, where, by definition, the width of the estuary increases rapidly, it is shown that there must be a transition from subcritical to supercritical flow. This condition, applied to the solution for uniform width, determines a remaining unknown related to the depth of the halocline at the head of the estuary and the complete solution is obtained as a function of the freshwater influx per unit width, the r.m.s. turbulent velocity, the estuary length and the buoyancy of sea water.The solution is complicated but has reasonable behaviour for variations of the given parameters of the problem. A basic feature for values of the constants appropriate to fjord-type estuaries is the dominance of friction, omitted in an earlier, incomplete investigation by Stommel. This is also revealed by the large drop in the free surface over the length of the estuary.A comparison with two estuaries, Oslofjord and Knight Inlet, British Columbia, indicates that the former is very different from the model of this paper but that the latter may have a similar nature.
The large amplitude motion of a liquid-filled gyroscope and the non-interaction of inertial and Rossby waves
Authors: Scott W. E. 
Published: March 2006

An attempt is made to explain theoretically two curious phenomena involving the motion of the liquid in a spinning, gyrating, liquid-filled gyroscope. One of the phenomena is the periodic breakdown of the free-surface wave form of the spinning liquid in the gyroscope when it gyrates at angles larger than about 1°. The other is the resonant amplitude growth rate of the liquid-filled gyroscope at these angles, for then the small angle stability theory of Stewartson (1959) fails to make the correct predictions.The analysis exploits the experimental fact that the axis of rotation of liquid in the rotor of a spinning gyrating gyroscope does not remain coincident with the axis of rotation of the rotor when the gyroscope gyrates at amplitudes greater than the above-mentioned 1°. It is shown that this lack of coincidence generates Rossby waves and modifies the inertial wave frequencies that would ordinarily occur in a right circular cylinder. There is no nonlinear interaction between these Rossby and inertial waves; hence the free-surface breakdown remains unexplained. However, the modification of the inertial wave frequencies does seem to account for the curious amplitude growth rate.
Observations on turbulent-drag reduction in a dilute suspension of clay in sea-water
Authors: Gust Giselher 
Published: March 2006

Hot-wire anemometer measurements have been made in a dilute sea-water/claymineral suspension. For fully developed turbulent flows in an open channel with a smooth mud (from the North Sea) bottom, mean streamwise velocity profiles were measured for Reynolds numbers between 5400 and 27 800 (i.e. non-eroding and eroding flow rates) and compared with Newtonian flows under the same experimental conditions. For the clay-mineral suspensions, measurements of the kinematic viscosityv, Kármán's constantkand the mean streamwise velocity$\overline{u}$of the logarithmic layer seemed to verify a Newtonian flow structure. Although the distributions of concentration showed no substantial increase towards the wall, it was found that beneath this Newtonian core there existed a viscous sublayer whose thickness was enhanced by a factor of 2–5. The friction velocityu*determined by the gradient method in the viscous sublayer was reduced by as much as 40 %. The mean flow structure exhibited an additional new layer in the region 10 <y+< 30.The measurements indicate that turbulent-drag reduction occurs for the experimental clay-mineral suspension at non-eroding and also at eroding velocities. Agglomeration of suspended clay-mineral particles is suggested as possible explanation of this phenomenon.
An experimental study of the effects of Prandtl number on thermal convection in a rotating, differentially heated cylindrical annulus of fluid
Authors: Fein Jay S. , Pfeffer Richard L. 
Published: March 2006

This paper presents the results of experimental studies of the behaviour of different fluids (mercury, Pr = 0·0246; water, Pr = 7·16; and 5 cS silicone oil, Pr = 63) when each is contained in a rotating cylindrical annulus and subjected to an imposed radial temperature difference across the annulus. The results are summarized in the form of two-parameter regime diagrams (thermal Rossby number RoTvs. Taylor number Ta) at different Prandtl numbers Pr. The fluids are in contact above and below with rigid insulating boundaries. The range of thermal Rossby and Taylor numbers surveyed is 10−3 < RoT < 10, 105 < Ta < 109.The regime diagram for water with a rigid upper lid in contact with the fluid resembles in certain respects the more familiar regime diagram for water with a free upper surface obtained by Fultz (1956) and by Fowlis & Hide (1965). Significant differences do, however, occur and are discussed in a separate paper by Fein (1973). The regime diagram for silicone oil possesses no lower symmetric regime within the range of thermal Rossby and Taylor numbers surveyed; that for mercury possesses no upper symmetric regime within the range surveyed. In mercury, turbulence is observed at high Rossby numbers. An experimental traverse across the regime diagram in which the imposed temperature difference is held constant at ΔT = 5 °C and the rotation rate Ω is changed monotonically reveals a highly conductive temperature structure in mercury and a highly convective temperature structure in both water and silicone oil. The regular wave regime, which appears at all three Prandtl numbers, is found to shift towards higher Taylor and Rossby numbers with decreasing Prandtl number. As a result, a single point in two-dimensionless-parameter space (RoT = 5 × 10−1, Ta = 1 × 106) lies in the upper symmetric regime for 5 cS silicone oil (Pr = 63), in the regular wave regime for water (Pr = 7·16) and in the lower symmetric regime for mercury (Pr = 0·0246).
Numerical simulation of three-dimensional Bénard convection in air
Authors: Lipps Frank B. 
Published: March 2006

A numerical model is developed to simulate three-dimensional Bénard convection. This model is used to investigate thermal convection in air for Rayleigh numbers between 4000 and 25000. According to experiments, this range of Rayleigh numbers in air covers three regimes of thermal convection: (i) steady two-dimensional convection, (ii) time-periodic convection and (iii) aperiodic convection. Numerical solutions are obtained for each of these regimes and the results are compared with the available experimental data and theoretical predictions.At the Rayleigh number Ra = 4000 the present model is able to produce experimentally realistic wavelengths for the two-dimensional convection. The small amplitude wave disturbances at Ra = 6500 have period τ = 0·24. When they become finite amplitude travelling waves, the period is τ = 0·27. These values are in good agreement with theoretical and experimental results. A detailed study of the form of these waves and of their energetics is given in appendix A. As the Rayleigh number is increased to Ra = 9000 and 25 000, the convection manifests progressively more complex spatial and temporal variations.The vertical heat transport and other mean properties of the convection are calculated for the range of Ra considered and compared with experimental and theoretical data. A detailed comparison is also made between the mean properties of two- and three-dimensional convection at the larger values of Ra. It is found that the heat flux Nu is nearly independent of the dimensionality of the convection.