bluuebunny/crossref_metadata_2025_split huggingface dataset:
Coupling between a surface-wave spectrum and an internal wave: modulational interaction
Authors: Dysthe K. B. , Das K. P. 
Published: April 2006

Using a simple three-layer model of the ocean, we study a generation mechanism for the lowest internal-wave mode by nonlinear coupling to modulations of the surface-wave spectrum. We first examine the case of a narrow-band surface-wave spectrum, applying a method developed by Alber (1978) to derive a transport equation for the spectral density. Alber demonstrated that, when the spectral width (in the main wave direction) exceeds some critical value, the spectrum is stable against modulational perturbation (i.e. the Benjamin–Feir-type instability is suppressed). We show, however, that, for a stratified ocean, a modulational instability may persist because of a coupling between a ‘modulational mode’ of the surface-wave spectrum and an internal wave. The growth rate is calculated for a simple model of the angular distribution of the spectrum. It turns out that an important parameter is 〈(∇ξ)2〉/Δθ, the ratio between the averaged square of the wave steepness, and the angular width of the spectrum.For appreciable growth one must have roughly
\[
2\times 10^{-3}\lesssim kd \langle (\nabla\zeta)^2\rangle / \Delta\theta,
\]
where k is a characteristic wavenumber for the surface-wave spectrum, and d is the depth of the thermocline (50-100 m). This condition is probably too limiting for the above-mentioned modulational instability to be of any practical interest in the oceans.We also consider the broad-band case of modulational interaction, and show the connection with incoherent three-wave interactions.
Self-sustained low-frequency components in an impinging shear layer
Authors: Knisely C. , Rockwell D. 
Published: April 2006

Oscillations of a cavity shear layer, involving a downstream-travelling wave and associated vortex formation, its impingement upon the cavity corner, and upstream influence of this vortex-corner interaction are the subject of this experimental investigation.Spectral analysis of the downstream-travelling wave reveals low-frequency components having substantial amplitudes relative to that of the fundamental (instability) frequency component; using bicoherence analysis it is shown that the lowest-frequency component can interact with the fundamental either to reinforce itself or to produce an additional (weaker) low-frequency component. In both cases, all frequency components exhibit an overall phase difference of almost 2kπ(k = 1, 2,…) between separation and impingement. Furthermore, the low-frequency and fundamental components have approximately the same amplitude growth rates and phase speeds; this suggests that the instability wave is amplitude-modulated at the low frequency, as confirmed by the form of instantaneous velocity traces.At the downstream corner of the cavity, successive vortices, arising from the amplified instability wave, undergo organized variations in (transverse) impingement location, producing a low-frequency component(s) of corner pressure. The spectral content and instantaneous trace of this impingement pressure are consistent with those of velocity fluctuations near the (upstream) shear-layer separation edge, giving evidence of the strong upstream influence of the corner region.
The drift velocity of water waves
Authors: Craik A. D. D. 
Published: April 2006

The important role of viscosity in producing second-order Eulerian drift currents in the presence of small-amplitude water waves was first recognized by Longuet-Higgins (1953).The theoretical and experimental background is first reviewed. It is then shown that, contrary to previous belief, the presence of surface contamination must greatly enhance the drift velocity of short waves. We then solve an initial-value problem for the drift current associated with temporally decaying waves, thereby resolving questions raised by the work of Liu & Davis (1977), whose solution exhibits anomalous singularities. Next, the steady drift velocity of spatially decaying waves is calculated and shown to bear a close resemblance to Longuet-Higgins’ ‘conduction solution’ for unattenuated waves.Finally, we establish that unidirectional drift currents of both surface and inter-facial waves are sure to be unstable to spanwise-periodic disturbances; the instability mechanism being identical to that first proposed by Craik (1977), and recently developed by Leibovich & Paolucci (1981), to explain the generation of Langmuir circulations.
An amplitude-evolution equation for linearly unstable modes in stratified shear flows
Authors: Engevik L. 
Published: April 2006

A nonlinear amplitude equation of second order in time, which governs the temporal evolution of linearly unstable modes in stratified shear flows, is derived. It applies to a class of flows with continuous velocity and density profiles, and two examples of such flows are studied.One of the flows that is studied is the stratified Couette flow with the buoyancy frequency equal to Qy2, where Q is a constant and y the vertical co-ordinate. The nonlinear amplitude equation is studied for various values of Q.For the Garcia flow the nonlinear amplitude equation for the long-wave modes is evaluated, and it is compared with the corresponding equation in the Kelvin–Helmholtz flow, which has been found previously.
On the oblique interaction of a large and a small solitary wave
Authors: Johnson R. S. 
Published: April 2006

The steady oblique interaction of two solitary waves on the surface of water of constant depth is considered. One wave is taken to be of arbitrary (large) amplitude and the other is small with a (non-dimensional) amplitude measured by the parameter ε. A solution is sought as an asymptotic expansion, based on ε, that assumes that in some region the solution is the sum of the two waves plus interaction terms. It is shown that this expansion is not uniformly valid close to a critical angle. This angle varies from zero (parallel waves) up to about 63°, as the amplitude of the larger wave increases from infinitesimally small to the largest-possible solitary wave. I n the limit of two small waves, the details agree precisely with the results obtained by Miles (1977a).When the angle between the two waves is dose to the critical angle, for a given large wave, an alternative asymptotic expansion is required. In this strong-interaction case, the dominant term is just the large wave but with a phase shift that is an arbitrary function of the characteristic variable associated with the small wave. This function is determined by matching to an appropriate far field, and it turns out to be proportional to the logarithm of a hypergeometric function (which itself can be expressed in terms of the associated Legendre function Pv−μ). The phase shift is then well-defined (finite, real) provided the angle is not very close to the critical value. When this occurs the phase shift can be infinite at a specific angle (which corresponds to the case |μ| = v > 0), and even closer to the critical angle (|μ| < v) the phase shift is undefined (no longer real). A real solution for the wave profile is still possible if negative amplitudes are allowed, but the resulting solution is unacceptable since the surface is then not undis- turbed at infinity. It is shown that the criterion |μ| < v matches exactly (for two small waves) with Miles’ criterion for the non-existence of a regular reflection.For the strong interaction (and |μ| ≥ v i t is argued that the small wave cannot penetrate the large wave unchanged. The large wave suffers significant distortion (bending) in the interaction, but the small wave, if it penetrates at all, must have an amplitude O(ε). This is the main aspect of the problem which cannot be completely determined using the present methods. The difficulty can be traced to the large solitary wave which is not known in closed form: only the exponential behaviour in the ‘tail’ is used explicitly in this work.
Reflection properties of internal gravity waves incident upon a hyperbolic tangent shear layer
Authors: Duin Cornelis A. Van , Kelder Hennie 
Published: April 2006

The properties of reflection and transmission of internal gravity waves incident upon a shear layer containing a critical level are investigated. The shear layer is modelled by a hyperbolic tangent profile. In the Boussinesq approximation, the differential equation governing the propagation of these waves can then be transformed into Heun's equation. For large Richardson numbers this equation can be approximated by an equation that has solutions in terms of hypergeometric functions. For these values of the Richardson number the reflection coefficient proves to be strongly dependent on the place of the critical level in the shear flow. If the Doppler-shifted frequency is an odd function of the height difference with respect to the critical level, the reflection and transmission coefficients can be evaluated in closed form.Over-reflection is possible for sufficiently small wavenumbers and Richardson numbers. It is pointed out that over-reflection and over-transmission cannot occur in a stable flow and that resonant over-reflection is not possible in our model.
General stability conditions for zonal flows in a one-layer model on the β-plane or the sphere
Authors: Ripa P. 
Published: April 2006

Sufficient stability conditions are derived for a zonal flow on the β-plane or the sphere. Two conditions guarantee both shear stability (to perturbations with vanishing zonal average) and inertial stability (to longitude-independent perturbations). These conditions are not restricted to normal-mode disturbances, and are derived without making use of the quasi-geostrophic approximation. The main limitation of the model is to have only one layer.On the β-plane, the conditions are: (i) that the product of the meridional gradient of potential vorticity and the difference between an arbitrary constant and the zonal velocity be everywhere non-negative; and (ii) that the absolute value of this difference be nowhere larger than the local phase speed of long gravity waves. Inertial stability is independently assured if the Cariolis parameter and the potential vorticity are everywhere of the same sign (this well-known condition can be easily violated near the equator, but the flow may nonetheless be stable).If the meridional gradient of potential vorticity has everywhere the same sign, then conditions (i) and (ii) can be shown to be consequences of the conservation of a total pseudo-energy E0 and pseudomomentum P0, defined so that their lowest-order contribution is quadratic in the deviation from the fundamental state (even in the case that the perturbation is longitude-independent). Thus, if there exists a value of α such that the integral of E0 − αP0 is positive-definite, then the flow is stable. In this case, the stability conditions are valid for small, rather than infinitesimal, perturbations.The parameters of stable flows, as guaranteed by these conditions, are investigated for the family of Gaussian jets centred at the equator; both the cases of an unbounded ocean and a semi-infinite ocean, poleward from a zonal wall, are considered. Easterlies with the width of a Kelvin wave and westerlies with that width or wider may be unstable, even though the gradient of potential vorticity is positive for any strength of the jet.
Tests of subgrid models in the near-wall region using represented velocity fields
Authors: Kaneda Y. , Leslie D. C. 
Published: April 2006

The 2.5-dimensional model of the turbulent field near a wall, proposed by Hatziavramidis & Hanratty (1979) and modified by Chapman & Kuhn (1981), has been used to test the subgrid models of Schumann (1973, 1975) and Moin & Kim (1982). The results are disquieting, both trends and orders of magnitude sometimes being seriously in error. It also appears that the contribution of the subgrid energy to the pseudopressure calculated in large-eddy simulations can be large, although this contribution is usually neglected. On the positive side, Leonard's model for the Leonard stress is extremely good, and Schumann's synthetic boundary condition is also found to be reliable.These results must be taken with a grain of salt, since the tests reported in §5 show that the 2.5-dimensional model cannot reproduce important characteristics of the turbulence in the neighbourhood of y+ = 40.
The structure of the large eddies in fully developed turbulent shear flows. Part 2. The plane wake
Authors: Mumford J. C. 
Published: April 2006

A set of measurements using arrays of hot-wire anemometers has been performed in the fully developed turbulent wake of a circular cylinder. The data were digitized, recorded on magnetic tape, and processed using the pattern recognition technique described in Part 1 (Mumford 1982), to yield ensemble averages of the streamwise component of the velocity fields of the large eddies in the flow.The results indicate that the large-scale structures in the turbulent wake are predominantly the inclined ‘double-roller’ vortices described by Grant (1958). These eddies consist of two contrarotating roller-like vortices with parallel axes displaced in the spanwise direction and approximately aligned with the direction of the strain associated with the mean velocity gradient. It was found that the structures are often confined to either side of the wake centreplane, rather than extending over the entire thickness of the turbulent region. In addition, eddies of similar type tended to occur in pairs or longer groups with their centres separated in the stream direction.
Scalar diffusion in simulated helical turbulence with molecular diffusivity
Authors: Drummond I. T. , Duane S. , Horgan R. R. 
Published: April 2006

We extend the simulation techniques of Kraichnan (1970, 1976) to study the effective diffusivity of a scalar field in a turbulent fluid. In our model we have introduced an adjustable helicity parameter and a technique for simulating molecular diffusivity. The results show that for non-helical turbulence the self-consistent perturbation theory of Phythian & Curtis (1978) gives excellent values for the effective diffusivity over a wide range of values for both the molecular diffusivity and the parameters describing the turbulence.This ceases to be the case immediately the helicity is given a non-zero value. Wide departures are observed between the theoretical calculation and the simulation. Our conclusion is that non-perturbative effects are very important in the presence of helicity.
Contaminant dispersion in some time-dependent laminar flows
Authors: Jimenez C. , Sullivan P. J. 
Published: April 2006

Time-dependent flows occur naturally as in pulsatile blood flow and in tidal estuaries and comprise many of the man-made flows of practical importance. A knowledge of the rate of mixing of a contaminant substance in such time-dependent flows is of paramount interest in, for example, the injection of a chemical substance in blood flow, the discharge of outfalls in estuaries, and the mutual contamination length of two feed fluids when switching from one feed line to another as part of a manufacturing process. This paper presents a study of contaminant spread in two specific and well-defined flows and provides a basis for the interpretation of contaminant mixing in the more complex flow situations that normally prevail.An extension of the probabilistic formulation of the streamwise dispersion of contaminant molecules given in Dewey & Sullivan (1982) is used to study time-dependent laminar flows between parallel plates and in tubes wherein the flows are homogeneous in the streamwise direction. The two flows considered in detail are oscillating flows and impulsively started flows. In impulsively started flows it is shown that, although the basic dispersive mechanism acts in much the same way as described by Taylor (1953), the start-up effects on the dispersion can be quite prolonged and very significantly reduce the streamwise spread of contaminant over that which is observed in the fully developed flow. In oscillatory flows, unlike the situation presented by Taylor (1953) in which a diminished value of molecular diffusivity κ increases the contaminant cloud axial growth rate in a tube of radius a, it is found that optimal streamwise contaminant spread results from a value of κ that depends upon kinematic viscosity v and frequency ω. The streamwise cloud-variance growth rate is explored over the full range of the two parameters γ2 = ωa2/κ and λ2 = ωa2/2v for all time, and it is shown that a global maximum results when γ ≈ 2π and λ ≈ 2.
On the use of an annulus to study mixed-layer entrainment
Authors: Deardorff J. W. , Yoon S.-C. 
Published: April 2006

An annulus covered by a rotating screen (or surface) which imparts stress and turbulence to the upper of two fluid layers has been shown by Scranton & Lindberg (1983) and Jones & Mulhearn (1983) to produce mixed-layer entrainment that is dependent on annulus curvature and geometry. This general result is confirmed here, where photographs of the mixed-layer interface indicate that turbulent entrainment rapidly diminishes away from the outer wall. The problem is explained as a damping of the turbulence within the bulk of the mixed layer by inertial stability associated with angular momentum increasing rapidly with radius except very close to the outer wall. Through hot-film-anemometer measurements, a shallow turbulent Ekman layer is found to exist immediately underneath the rotating screen, having a depth of order $ 0.4u_{*}r/\overline{v}$, where u* is the friction velocity, $\overline{v}$ is the mean circumferential flow speed within the layer and r is the radius. For r of order 1 m, this depth is typically only a small fraction of the mixed-layer depth determined from the density profile.When the stress input is placed near the inner wall, the mean-flow radial profile is much more nearly irrotational and the turbulence-damping problem becomes minimal. The entrainment is then much more uniform with radius, and local interfacial scaling can be used to relate the entrainment rate to one or more local Richardson numbers containing a turbulent velocity scale rather than u* or $\Delta\overline{v}$, where Δ signifies the change across the interface. Although u* and $\Delta\overline{v}$ are proper ‘external’ scales for entrainment in a horizontally homogeneous mixed layer that is turbulent throughout, a local internal turbulent velocity scale can alternatively be used. Entrainment rates thus scaled are presented and compared with Turner's (1973) locally scaled entrainment.
Stresses developed by dry cohesionless granular materials sheared in an annular shear cell
Authors: Savage S. B. , Sayed M. 
Published: April 2006

Experimental results obtained during rapid shearing of several dry, coarse, granular materials in an annular shear cell are described. The main purpose of the tests was to obtain information that could be used to guide the theoretical development of constitutive equations suitable for the rapid flow of cohesionless bulk solids at low stress levels. The shear-cell apparatus consists of two concentric disk assemblies mounted on a fixed shaft. Granular material was contained in an annular trough in the bottom disk and capped by a lipped annular ring on the top disk. The bottom disk can be rotated at specified rates, while the top disk is loaded vertically and is restrained from rotating by a torque arm connected to a force transducer. The apparatus was thus designed to determine the shear and normal stresses as functions of solids volume fraction and shear rate.Tests were performed with spherical glass and polystyrene beads of nearly uniform diameters, spherical polystyrene beads having a bimodal size distribution and with angular particles of crushed walnut shells. The particles ranged from about ½ to 2 mm in size. At the lower concentrations and high shear rates the stresses are generated primarily by collisional transfer of momentum and energy. Under these conditions, both normal and shear stresses were found to be proportional to the particle density, and the squares of the shear rate and particle diameter. At higher concentrations and lower shear rates, dry friction between particles becomes increasingly important, and the stresses are proportional to the shear rate raised to a power less than two. All tests showed strong increases in stresses with increases in solids concentrations. The ratio of shear to normal stresses showed only a weak dependence upon shear rate, but it increased with decreasing concentration. At the very highest concentrations with narrow shear gaps, finite-particle-size effects became dominant and differences in stresses of as much as an order of magnitude were observed for the same shear rate and solids concentration.
Numerical calculation of decaying isotropic turbulence using the LET theory
Authors: Mccomb W. D. , Shanmugasundaram V. 
Published: April 2006

The local-energy-transfer (LET) theory (McComb 1978) was used to calculate freely decaying turbulence for four different initial spectra at low-to-moderate values of microscale Reynolds numbers (Rλ up to about 40). The results for energy, dissipation and energy-transfer spectra and for skewness factor all agreed quite closely with the predictions of the well-known direct-interaction approximation (DIA: Kraichnan 1964). However, LET gave higher values of energy transfer and of evolved skewness factor than DIA. This may be related to the fact that LET yields the k−5/3 law for the energy spectrum at infinite Reynolds number.The LET equations were then integrated numerically for decaying isotropic turbulence at high Reynolds number. Values were obtained for the wavenumber spectra of energy, dissipation rate and inertial-transfer rate, along with the associated integral parameters, at an evolved microscale Reynolds number Rλ of 533. The predictions of LET agreed well with experimental results and with the Lagrangian-history theories (Herring & Kraichnan 1979). In particular, the purely Eulerian LET theory was found to agree rather closely with the strain-based Lagrangian-history approximation; and further comparisons suggested that this agreement extended to low Reynolds numbers as well.
Lunate-tail swimming propulsion as a problem of curved lifting line in unsteady flow. Part 1. Asymptotic theory
Authors: Cheng H. K. , Murillo Luis E. 
Published: April 2006

The asymptotic theory of a high-aspect-ratio wing in an incompressible flow is generalized to an oscillating lifting surface with a curved centreline in the domain where the reduced frequency based on the half-span is of order unity. The formulation allows applications to lightly loaded models of lunate-tail swimming and ornithopter flight, provided that the heaving displacement does not far exceed the mean wing chord. The analysis include the quasi-steady limit, in which the crescent-moon wing problem considered earlier by Thurber (1965) is solved and several aerodynamic properties of swept wings are explained.Among the important three-dimensional and unsteady effects are corrections for the centreline curvature and for the spanwise components of the locally shed vortices. Comparison of the lift distributions obtained for model lunate tails with data computed from the doublet-lattice method (Albano & Rodden 1969) lends support to the asymptotic theory.