bluuebunny/crossref_metadata_2025_split huggingface dataset:
Stability of spatially developing boundary layers in pressure gradients
Authors: Govindarajan Rama , Narasimha R. 
Published: April 2006

A new formulation of the stability of boundary-layer flows in pressure gradients is presented, taking into account the spatial development of the flow and utilizing a special coordinate transformation. The formulation assumes that disturbance wavelength and eigenfunction vary downstream no more rapidly than the boundary-layer thickness, and includes all terms nominally of orderR−1in the boundary-layer Reynolds numberR. In Blasius flow, the present approach is consistent with that of Bertolottiet al.(1992) toO(R−1) but simpler (i.e. has fewer terms), and may best be seen as providing a parametric differential equation which can be solved without having to march in space. The computed neutral boundaries depend strongly on distance from the surface, but the one corresponding to the inner maximum of the streamwise velocity perturbation happens to be close to the parallel flow (Orr-Sommerfeld) boundary. For this quantity, solutions for the Falkner-Skan flows show the effects of spatial growth to be striking only in the presence of strong adverse pressure gradients. As a rational analysis toO(R−1) demands inclusion of higher-order corrections on the mean flow, an illustrative calculation of one such correction, due to the displacement effect of the boundary layer, is made, and shown to have a significant destabilizing influence on the stability boundary in strong adverse pressure gradients. The effect of non-parallelism on the growth of relatively high frequencies can be significant at low Reynolds numbers, but is marginal in other cases. As an extension of the present approach, a method of dealing with non-similar flows is also presented and illustrated.However, inherent in the transformation underlying the present approach is a lower-order non-parallel theory, which is obtained by dropping all terms of nominal orderR−1except those required for obtaining the lowest-order solution in the critical and wall layers. It is shown that a reduced Orr-Sommerfeld equation (in transformed coordinates) already contains the major effects of non-parallelism.
The interaction of an isotropic field of acoustic waves with a shock wave
Authors: Mahesh Krishnan , Lee Sangsan , Lele Sanjiva K. , Moin Parviz 
Published: April 2006

Moore's (1954) inviscid linear analysis of the interaction of a shock wave with a plane acoustic wave is evaluated by comparison to computation. The analysis is then extended to study the interaction of an isotropic field of acoustic waves with a normal shock wave. The evolution of fluctuating kinetic energy, sound level and thermodynamic fluctuations across the shock wave are examined in detail.The interaction of acoustic fluctuations with the shock is notably different from that of vortical fluctuations. The kinetic energy of the acoustic fluctuationsdecreasesacross the shock wave for Mach numbers between 1.25 and 1.8. For Mach numbers exceeding 3, the kinetic energy amplifies by levels that significantly exceed those found in the interaction of vortical fluctuations with the shock. Upon interacting with the shock wave, the acoustic waves generate vortical fluctuations whose contribution to the far-field kinetic energy increases with increasing Mach number. The level of sound increases across the shock wave. The rise in the sound pressure level across the shock varies from 5 to 20 dB for Mach number varying from 1.5 to 5. The fluctuations behind the shock wave are nearly isentropic for Mach number less than 1.5, beyond which the generation of entropy fluctuations becomes significant.
Parasitic capillary waves: a direct calculation
Authors: Longuet-Higgins Michael S. 
Published: April 2006

As in a previous theory (Longuet-Higgins 1963) parasitic capillary waves are considered as a perturbation due to the local action of surface tension forces on an otherwise pure progressive gravity wave. Here the theory is improved by: (i) making use of our more accurate knowledge of the profile of a steep Stokes wave; (ii) taking account of the influence of gravity on the capillary waves themselves, through the effective gravitational acceleration g* for short waves riding on longer waves.Nonlinearity in the capillary waves themselves is not included, and certain other approximations are made. Nevertheless, the theory is shown to be in essential agreement with experiments by Cox (1958), Ebuchi, Kawamura & Toba (1987) and Perlin, Lin & Ting (1993).A principal result is that for gravity waves of a given length L > 5 cm there is a critical steepness parameter (AK)c at which the surface velocity (in a frame of reference moving with the phase-speed) equals the minimum (local) speed of capillary-gravity waves. On subcritical gravity waves, with steepness AK < (AK)c, capillary waves may be generated at all points of the wave surface. On supercritical waves, with AK > (AK)c, capillary waves can only be generated in the wave troughs; they are trapped between two caustics near the crests. Generally, the amplitude of the parasitic capillaries is greatest on gravity waves of near critical (but not maximum) steepness.
Hydrodynamic stability of a sheared liquid film
Authors: Miesen Rob , Boersma Bendiks Jan 
Published: April 2006

We study the hydrodynamic stability of a thin layer of liquid that is sheared by a gas. First, the interface conditions for the free surface approximation of the problem are discussed. We then study the stability of the flow to disturbances with phase speeds smaller than the maximum velocity in the liquid film, i.e. the internal mode, extending previous results and resolving some apparent contradictions.The dynamic effect of the gas is studied by dropping the free surface approximation and solving the Orr-Sommerfeld equation for the gas together with that for the liquid. The effect on the stability of the liquid film is very large, which is explained by the fact that the imaginary part of the wave speed (which determines the stability of the film) is very small. Consequently the free surface approximation is, in general, not correct.We then study the dependence of the critical Reynolds number on the Weber number, on the curvature of the liquid velocity profile and on the properties of the gas. With the gas included, a second mode of instability is found which has a phase velocity that is, in general, larger than the maximum liquid velocity and corresponds to capillary-gravity waves. We compare results with experiments from the literature; good agreement is found. Finally, a suggestion on the relevance of this study to the generation of ‘roll waves’, which are important from a practical point of view, is given.
The inviscid transonic flow about a cylinder
Authors: Botta Nicola 
Published: April 2006

The two-dimensional inviscid transonic flow about a circular cylinder is investigated. To do this, the Euler equations are integrated numerically with a time-dependent technique. The integration is based on an high-resolution finite volume upwind method.Time scales are introduced and the flow at very short, short and large times is studied. Attention is focused on the behaviour of the numerical solution at large times, after the breakdown of symmetry and the onset of an oscillating solution have occurred. This solution is known to be periodic at Mach number between 0.5 and 0.6.At higher speed, however, a richer behaviour is observed. As the Mach number is increased from 0.6 to 0.98 the numerical solution undergoes two transitions. Through a first one the periodical, regular flow enters a chaotic, turbulent regime. Through the second transition the chaotic flow comes back to an almost stationary state. The flow in the chaotic and in the almost stationary regimes is investigated. A numerical conjecture for the behaviour of the solution at large times is advanced.
On improving a one-layer ocean model with thermodynamics
Authors: Ripa P. 
Published: April 2006

A popular method used to incorporate thermodynamic processes in a shallow water model (e.g. one used to study the upper layer of the ocean) is to allow for density variations in time and horizontal position, but keep all dynamical fields as depth independent. This is achieved by replacing the horizontal pressure gradient by its vertical average. These models have limitations, for instance they cannot represent the ‘thermal wind’ balance (between the horizontal density gradient and the vertical shear of the velocity) which dominates at low frequencies. A new model is now proposed which uses velocity and density fields varying linearly with depth, with coefficients that are functions of horizontal position and time. This model can explicitly represent the thermal wind balance, but its use is not restricted to low- frequency dynamics.Volume, mass, buoyancy variance, energy and momentum are conserved in the new model. Furthermore, these integrals of motion have the same dependence on the dynamical fields as the exact (continuously stratified) case. The evolution of the three components of the absolute vorticity field are correctly represented. Conservation of density–potential vorticity is not fulfilled, though, owing to artificial removal of the vertical curvature of the velocity field.The integrals of motion are used to construct a ‘free energy’ [Escr ]f, which is quadratic to the lowest order in the deviation from a steady state with (at most) a uniform velocity field. [Escr ]fis positive definite, and therefore the free evolution of the system cannot lead to an ‘explosion’ of the dynamical fields. (This is not the case if the velocity shear and/or the density vertical gradient is excluded in the model, which results in a non-negative definite free energy.)In a model with one active layer, linear waves on top of a steady state with no currents are, to a very good approximation, those of the first two vertical modes of the continuously stratified model. These are the familiar geophysical gravity and vortical waves (e.g. Poincaré, Rossby, and coastal Kelvin waves at mid-latitudes, equatorial waves, etc.).Finally, baroclinic instability is well represented in the new model. For long perturbations (wavelengths of the order of the deformation radius of the first mode) the agreement with more precise calculations is excellent. On the other hand, the comparison with the eigenvalues of Eady's problem (which corresponds to wavelengths of the order of the deformation radius of the second mode) shows differences of the order of 40%. Nevertheless, the new model does have a high-wavenumber cutoff, even though it is constrained to linear profiles in depth and therefore cannot reproduce the exponential trapping of Eady's problem eigensolutions.In sum, the integrals of motion, vorticity dynamics, free waves and baroclinic instability results all give confidence in the new model. Its main novelty, however, lies in the ability to incorporate thermodynamic processes.
On two approaches to the problem of instability of short-crested water waves
Authors: Badulin Sergei I. , Shrira Victor I. , Kharif Christian , Ioualalen Mansour 
Published: April 2006

The work is concerned with the problem of the linear instability of symmetric short-crested water waves, the simplest three-dimensional wave pattern. Two complementary basic approaches were used. The first, previously developed by Ioualalen & Kharif (1993, 1994), is based on the application of the Galerkin method to the set of Euler equations linearized around essentially nonlinear basic states calculated using the Stokes-like series for the short-crested waves with great precision. An alternative analytical approach starts with the so-called Zakharov equation, i.e. an integro-differential equation for potential water waves derived by means of an asymptotic procedure in powers of wave steepness. Both approaches lead to the analysis of an eigenvalue problem of the type
{\rm det}|{\boldmath A}-\gamma{\boldmath B}|=0
where A and B are infinite square matrices. The first approach should deal with matrices of quite general form although the problem is tractable numerically. The use of the proper canonical variables in our second approach turns the matrix B into the unit one, while the matrix A gets a very specific ‘nearly diagonal’ structure with some additional (Hamiltonian) properties of symmetry. This enables us to formulate simple necessary and sufficient a priori criteria of instability and to find instability characteristics analytically through an asymptotic procedure avoiding a number of additional assumptions that other authors were forced to accept.A comparison of the two approaches is carried out. Surprisingly, the analytical results were found to hold their validity for rather steep waves (up to steepness 0.4) for a wide range of wave patterns. We have generalized the classical Phillips concept of weakly nonlinear wave instabilities by describing the interaction between the elementary classes of instabilities and have provided an understanding of when this interaction is essential. The mechanisms of the relatively high stability of short-crested waves are revealed and explained in terms of the interaction between different classes of instabilities. A helpful interpretation of the problem in terms of an infinite chain of interacting linear oscillators was developed.
Merging flows in an arterial confluence: the vertebro-basilar junction
Authors: Ravensbergen J. , Krijger J. K. B. , Hillen B. , Hoogstraten H. W. 
Published: April 2006

The basilar artery is one of the three vessels providing the blood supply to the human brain. It arises from the confluence of the two vertebral arteries. In fact, it is the only artery of this size in the human body arising from a confluence instead of a bifurcation. Earlier work, concerning flow computations in simplified models of the basilar artery, has demonstrated that a junction causes distinctive flow phenomena. This paper presents three-dimensional finite-element computations of steady viscous flow in a rigid symmetrical junction geometry representing the anatomical situation in a more realistic way. The geometry consists of two round tubes merging into a single round outlet tube. The Reynolds number for the basilar artery ranges from 200 to 600, and both symmetrical and asymmetrical inflow from the two inlet tubes has been considered.Just downstream of the confluence a ‘double hump’ axial velocity profile is found. In the transition zone the flow pattern appears to have a complicated structure. In the symmetrical case the axial velocity profile shows a sharp central ridge, whereas in the asymmetrical case the highest ‘hump’ crosses the centreline of the tube. The flow has a highly three-dimensional character with secondary velocities easily exceeding 25% of the mean axial flow velocity. The secondary flow pattern consists of four vortices. Under all simulated flow conditions, the inlet length turns out to be much larger than the average length of the human basilar artery.To validate the computational model, a comparison is made between numerical and experimental results for a junction geometry consisting of tubes with a rectangular cross-section. The experiments have been performed in a Perspex model with laser Doppler velocimetry and dye injection techniques. Good agreement between experimental and computational results is found. Moreover, all essential flow phenomena turn out to be quite similar to those obtained for the circular tube geometry.
Turbulence, similarity scaling and vortex geometry in the wake of a towed sphere in a stably stratified fluid
Authors: Spedding G. R. , Browand F. K. , Fincham A. M. 
Published: April 2006

Late wakes (Nt> 20) of towed spheres in a stably stratified fluid were analysed in a plane using a reliable, customized DPIV technique that provides sufficient spatial and temporal resolution to cover all important scales of motion in this freely decaying geophysical flow. Systematic experiments were conducted with independent variation ofRe∈ [103, 104] andF∈ [1, 10] (F ≡ 2U/NDis an internal Froude number based on the buoyancy frequency,N, and the sphere radius,D/2), and for selected {Re, F} pairs above this range.The normalized wake width grows at approximately the same rate as in a three-dimensional unstratified wake, but it becomes narrower, not wider, with decreasingF(i.e. as stratification effects become more important). The centreline defect velocity, on the other hand, reaches values an order of magnitude above those measured for three-dimensional unstratified wakes at equivalent downstream locations. Both observations are argued to be consequences of the very high degree of order and coherence that emerge in the late-wake vortex structures.Streamwise-averaged turbulence quantities, such as the velocity fluctuation magnitude, and mean-square enstrophy, show similar power law behaviour for allRe≤ 5 × 103, with exponents equal to those expected in three-dimensional axisym-metric turbulent wakes. There is no obvious physical reason why three-dimensional arguments are so successful in such a flow, and at such long evolution times. The scaling collapses none of the cases forRebelow 4 – 5 × 103, appearing to establish a minimumRefor a class of self-similar stratified wake flows that evolve from fully turbulent initial conditions.Individual vortex cross-sections appear to be well approximated by Gaussian distributions at allRe, F andNtstudied here. The scaling behaviour of individual vortices mimics that of the statistical, wake-averaged quantities, and differs measurably from a simple two-dimensional viscous diffusion model. The importance of formulating a realistic three-dimensional model is discussed, and some limited steps in this direction point to future useful experiments and modelling efforts.
A numerical simulation of unsteady flow in a two-dimensional collapsible channel
Authors: Luo X. Y. , Pedley T. J. 
Published: April 2006

The collapse of a compressed elastic tube conveying a flow occurs in several physiological applications and has become a problem of considerable interest. Laboratory experiments on a finite length of collapsible tube reveal a rich variety of self-excited oscillations, indicating that the system is a complex, nonlinear dynamical system. Following our previous study on steady flow in a two-dimensional model of the collapsible tube problem (Luo & Pedley 1995), we here investigate the instability of the steady solution, and details of the resulting oscillations when it is unstable, by studying the time-dependent problem. For this purpose, we have developed a time-dependent simulation of the coupled flow – membrane problem, using the Spine method to treat the moving boundary and a second-order time integration scheme with variable time increments.It is found that the steady solutions become unstable as tension falls below a certain value, say Tu, which decreases as the Reynolds number increases. As a consequence, steady flow gives way to self-excited oscillations, which become increasingly complicated as tension is decreased from Tu. A sequence of bifurcations going through regular oscillations to irregular oscillations is found, showing some interesting dynamic features similar to those observed in experiments. In addition, vorticity waves are found downstream of the elastic section, with associated recirculating eddies which sometimes split into two. These are similar to the vorticity waves found previously for flow past prescribed, time-dependent indentations. It is speculated that the mechanism of the oscillation is crucially dependent on the details of energy dissipation and flow separation at the indentation.As tension is reduced even further, the membrane is sucked underneath the downstream rigid wall and, although this causes the numerical scheme to break down, it in fact agrees with another experimental observation for flow in thin tubes.
On finite-amplitude patterns of convection in a rectangular-planform container
Authors: Daniels P. G. , Weinstein M. 
Published: April 2006

This paper considers the development of finite-amplitude patterns of convection in rectangular-planform containers. The horizontal dimensions of the container are assumed to be large compared with the critical wavelength of the motion. An interaction between rolls parallel and perpendicular to the lateral boundaries is modelled by a coupled pair of nonlinear amplitude equations together with appropriate conditions on the four lateral boundaries. At Rayleigh numbers above a critical value a steady-state solution is established with rolls parallel to the shorter lateral sides, consistent with the predictions of linear theory. At a second critical value this solution becomes unstable to cross-rolls near the shorter sides and a new steady state evolves. This consists of the primary roll pattern together with regions near the shorter sides where there is a combination of rolls parallel and perpendicular to the boundary.Analytical and numerical methods are used to describe both the evolution and steady-state structure of the solution, and a comparison is made with the results of full numerical simulations and experiments.
Diascalar flux and the rate of fluid mixing
Authors: Winters Kraig B. , D'Asaro Eric A. 
Published: April 2006

We define the rate at which a scalar θ mixes in a fluid flow in terms of the flux of θ across isoscalar surfaces. This flux θd is purely diffusive and is, in principle, exactly known at all times given the scalar field and the coefficient of molecular diffusivity. In general, the complex geometry of isoscalar surfaces would appear to make the calculation of this flux very difficult. In this paper, we derive an exact expression relating the instantaneous diascalar flux to the average squared scalar gradient on an isoscalar surface which does not require knowledge of the spatial structure of the surface itself. To obtain this result, a time-dependent reference state θ(t,z*.) is defined. When the scalar is taken to be density, this reference state is that of minimum potential energy. The rate of change of the reference state due to diffusion is shown to equal the divergence of the diffusive flux, i.e. (∂/∂z*)θd.This result provides a mathematical framework that exactly separates diffusive and advective scalar transport in incompressible fluid flows. The relationship between diffusive and advective transport is discussed in relation to the scalar variance equation and the Osborn–Cox model. Estimation of water mass transformation from oceanic microstructure profiles and determination of the time-dependent mixing rate in numerically simulated flows are discussed.
Rossby wave interaction in a shear flow with critical levels
Authors: Vanneste Jacques 
Published: April 2006

An approach is presented for studying Rossby wave interaction in a shear flow with both regular and singular modes (i.e. those possessing a critical level). The approach relies on a truncated normal mode expansion of the equations of motion. Such an expansion remains valid in the presence of singular modes, provided that these modes are not considered individually, but that complete packets are taken into account in the truncated system. Mathematically, this means that the interaction equations need to be integrated with respect to the phase velocity (or, equivalently, the critical level position) of the singular modes.The action of two regular modes on a packet of singular modes is treated in detail; in particular, asymptotic results are deduced for the long-term behaviour of the packet. The case of a linear shear is considered as an illustration: analytical expressions are derived for the normal modes and their pseudomomentum, and they are used to present explicit results for the evolution of the packet of singular modes.