Thick Shear Layer Research Articles

Analysis of the effect of turbulent inflow on the flow-field and noise of supersonic jet flow using large eddy simulation

The impact of inflow flow state on the flow-field and far-field noise of supersonic jet flow has been studied. A new turbulent inflow boundary condition based on the synthetic eddy method is implemented in an in-house LES code. The implementation was validated using a turbulent channel flow. Simulation results of an under-expanded supersonic jet with a converging nozzle have shown that turbulent inflow leads to thicker and turbulent initial shear layer with rich vortical structures. The thick initial shear layer hinders the growth of flow instability and break the acoustic feedback loop, which is vital to the generation of screech tone. The alternation of the flow-field by the turbulent inflow also leads to changes in the far-field noise radiation. The screech tone is eliminated, the noise in the downstream direction is considerably suppressed, and the noise radiates in the upstream direction is slightly amplified.

Vortex-induced vibration characteristics of two open girders: A comparison of experimental and numerical investigation

Open girder sections are vulnerable to vortex-induced vibrations (VIV) because of their bluff aerodynamic characteristics. A comparative investigation was conducted by wind tunnel tests and numerical simulation. Firstly, based on sectional model wind tunnel tests, the VIV performance of semi-open girder and separated edge-boxes open girder was studied with consideration of the influence of the equivalent mass, wind attack angle and damping ratio. The aerodynamic parameters Scruton number ( S c) and Strouhal number ( S t) of two girders were analyzed contrastively. In addition, VIV amplitudes corresponding to the real bridge girders were calculated by the linear and nonlinear theories. Then, flow fields around two semi-open girder sections were investigated on the basis of computational fluid dynamics. The results show that vertical and torsional VIVs of two open girders are observed, at +3°and +5° wind attack angles. There were two vertical VIV regions and the maximum amplitude in the second vertical VIV region is significantly larger than that in the first one. For the semi-open girder and separated edged-box open girder, the vertical VIV amplitudes at +5° wind attack angle is 115% and 75% larger than at +3° wind attack angle, respectively. The damping ratio could obviously mitigate the VIV of two girders and VIV amplitudes are decreased linearly with the S C number increases. There are vortexes above the girder deck at the opening position of the semi-open girder and the separated edge-boxes open girder. The oblique web and wind faring may break the large vortex into several smaller vortexes at the opening position, thus optimizing the vortex vibration performance of the girder. A thicker shear layer is formed at separated open-girder during the development of airflow towards backward of bridge deck, due to the effect of railings and the blunt boxes on the lower surface.

Impact of a jet orifice on the hydrodynamics and the oil droplet size distribution

Experiments were performed to understand the impact of the orifice on droplet size in the shear breakup region. Oil jet was released vertically from two orifice types: a pipe and a converging nozzle. The roll-up vortices were observed clearly near the edge of the jet with nozzle orifice while elongated oil ligaments in the jet direction were mostly observed near the edge of the jet with pipe orifice. The size of the droplets shed from the near field shear layer increased along the jet direction for both orifice types. At different distances from the orifice, the characteristic shed droplet size (d50) was up to 40% larger with pipe orifice. Multiphase, large-eddy simulations (LES) with two orifice types were conducted to interpret the droplet size distribution (DSD) observed in the experiments. A thicker boundary layer that was initially formed inside the pipe dominated the near field of the jet with the pipe. The turbulent kinetic energy dissipation rate (ε) was higher with pipe orifice and the peak values of ε were found closer to the jet centerline with the pipe where oil holdup is larger. The viscous shear stress with the nozzle was higher than that of the pipe orifice within the initial two diameters from the orifice and slightly lower or higher at the following distances studied. The Reynolds shear stress was significantly larger with the nozzle at different distances from the orifice. The tangential vorticity within one diameter from the orifice was also dramatically higher with the nozzle. The key parameter in the shed droplet size of a liquid jet in liquid was found to be the shear layer thickness at the orifice, similar to prior works of a liquid jet in gas. A thicker shear layer at the pipe orifice induced a larger droplet size. The increase in the instabilities and shear layer thickness in the jet direction increased the droplet size in the jet direction.

The gravity-driven migration of a drop in an unsteady Stokes flow

The motion of a spherical droplet through a fluid driven by gravity is revisited theoretically. Analytical expressions for the translational velocity of the droplet as well as its internal and external flows coupled at their interface and described by the unsteady Stokes equations are derived combining two-point Padé and Padé-type approximants with the Laplace transform. These expressions, involving scaled complementary error functions, are fast and globally convergent to the exact solutions of the equations. The migration of the droplet depends on three non-dimensional parameters, two of which determine the flow patterns inside and outside, and the last is related to the timescale. The analytical solutions reveal that there is a diffusive shear layer of thickness O(t) on either side of the interface in the early stage. Several plots are made to compare migration velocities of the droplet for different parameter sets and changes in the flow field with time.

Aerodynamics of two-dimensional bristled wings in low-Reynolds-number flow

The smallest flying insects commonly possess bristled wings and use drag to provide flight forces. A bristled wing, with a wing area about 10% of that of a flat-plate wing, operating at the relevant Reynolds number of 5–15, produces a drag close to the plate wing. How this is done is not well understood. Here, detailed flows around each of the bristles are investigated numerically using simple model wings, and the following results are shown. (1) The drag production mechanism of the bristled wing is different from that of the plate wing: For the plate wing, the flow is blocked by the wing, giving a small positive pressure on the windward surface, and there exists a pair of weak vortices on the wing back, giving a small negative pressure on the leeward surface; the drag is due to the pressure forces (the frictional stress has almost no contribution). For the bristled wing, each bristle operates in a creeping flow and produces thick and strong shear layers. Strong viscous force generates a very large pressure difference between the windward and leeward surfaces of each bristle and very large frictional stress on the bristle surface, resulting in a large drag on each bristle, and the drag is equally contributed by the pressure and frictional forces. (2) Due to the flow-interference effect, when the bristle number reaches a certain value, a further increase in bristles has little effect on force production but has the disadvantage of increasing wing mass; this means that for a bristled wing of miniature insects, the distribution density of the bristles will not be too large, which agrees with observations.

Onset of Cavity Oscillation From Transverse to Longitudinal Mode in a Supersonic Flow

Abstract Experiments are carried out in supersonic flow past cavities (L/D = 1–3) to comprehend cavity oscillation from transverse to longitudinal mode. To characterize this, time-resolved schlieren images and unsteady pressure measurements are carried out. For L/D = 1, the cavity oscillation is in the transverse direction which is characterized by a single vortex along with low frequency oscillations. In the present studies, for the given length and depth, the L/D = 2 cavity shows both transverse and longitudinal mode of oscillations. This dual nature is ascertained through high-speed schlieren images and large rise in the fluctuating pressure. For L/D = 3, the cavity oscillation is in the longitudinal direction accompanied by low values of fluctuating pressure component and number of discrete modes/tones. Hence, it is believed that the transverse to longitudinal mode of cavity oscillation in the present studies occurs between L/D = 2 and 3. These cavities are driven by a thick shear layer where the vortex convection is found to be nonlinear. The comparison of dominant modes/tones with modified Rossiter and Handa relations indicates the necessity to develop a suitable model for transitional cavities. In-depth analyzes in terms of cross-correlation as well as wavelet transform divulge the basis that generates cavity modes/tones and mode switching phenomena, respectively.

Experimental investigation on gliding arc discharge plasma ignition and flame stabilization in scramjet combustor

Ignition and flame stability in supersonic flow have always been the key problems of research in scramjet. In addition, ignition is difficult and the cavity flameholder is susceptible to support the flame stability under extreme conditions such as low equivalent ratio. In recent years, gliding arc plasma is recognized to expand ignition and extinction limit with lower energy consumption in the field of plasma assisted ignition due to its heating and chemical effects. In this paper, a gliding arc igniter has been designed and compared with the traditional spark plug in order to quantify the ignition ability. The igniter has the same size with the spark plug, using low-power AC gliding arc to carry out ethylene ignition test in Ma = 2.52 Ma supersonic flow. The average power of gliding arc discharge is 1199 W. A high-speed camera and CH⁎ chemiluminescence were used to make combustion diagnosis. Founded in the same discharge period, the lean ignition limit of the gliding arc is lower than the ignition limit of the spark. The average expansion of ethylene ignition limit is 17%. The ignition process is that gliding arc continues to generate the initial flame kernels during the discharge period, but it is extinguished continuously due to the strong convection. Until generating an initial flame kernel which can successfully propagate the flame. The ignition process can be divided into four stages. It continues to generate new flame kernels in flame propagation process. Gliding arc reignites the fuel and generates the new flame kernels after forming a stable flame, appearing intermittent ignition in the cavity. The high equivalent ratio can make ignition delay time shorter, generating initial flame kernels more frequently. The heating effect of the gliding arc and reignition character make the thermal product and ethylene occur intermittent combustion more often in the cavity, increasing the area of the combustion reaction. Gliding arc plasma can achieve combustion enhancement during the flame stabilization process. The shear layer of flame thickness increased by the average of 2 mm on S-B-1 and G-B-1 conditions. Compared with the traditional spark ignition, gliding arc broaden the lean blow-off limit in different stages may be the significant reason for broadening lean ignition limit. It concludes that gliding arc makes the flame's ignition limit closer to the flame's blow-off limit.

RANS and LES analysis of a separation region in front of a backward-facing step

Turbulent characteristics of a reattached flow separated from a rib ahead of a backward-facing step in a flat air channel were numerically analyzed by RANS and LES methods. The separation region ended just before the step edge. The both methods showed low pressure regions in corners, formed by the rib and the channel walls that caused a vorticity tube forming along the rib. Nevertheless in RANS, a separated flow was identified as two-dimensional with a thicker shear layer at the step edge. In LES, the low pressure regions caused both redistributions between velocity components, Reynolds stresses, and a thicker shear layer at the step edge. The flow structure behind the rib has been, thus, identified as three-dimensional.

Very near-nozzle shear-layer turbulence and jet noise

One of the principal challenges in the prediction and design of low-noise nozzles is accounting for the near-nozzle turbulent mixing layers at the high Reynolds numbers of engineering conditions. Even large-eddy simulation is a challenge because the locally largest scales are so small relative to the nozzle diameter. Model-scale experiments likewise typically have relatively thick near-nozzle shear layers, which potentially hampers their applicability to high-Reynolds-number design. To quantify the sensitivity of the far-field sound to nozzle turbulent-shear-layer conditions, a family of diameter $D$ nozzles is studied in which the exit turbulent boundary layer momentum thickness is varied from $0.0042D$ up to $0.021D$ for otherwise identical flow conditions. Measurements include particle image velocimetry (PIV) to within $0.04D$ of the exit plane and far-field acoustic spectra. The influence of the initial turbulent-shear-layer thickness is pronounced, though it is less significant than the well-known sensitivity of the far-field sound to laminar versus turbulent shear-layer exit conditions. For thicker shear layers, the nominally missing region, where the corresponding thinner shear layer would develop, leads to the noise difference. The nozzle-exit momentum thickness successfully scales the high-frequency radiated sound for nozzles of different sizes and exhaust conditions. Yet, despite this success, the detailed turbulence statistics show distinct signatures of the different nozzle boundary layers from the different nozzles. Still, the different nozzle shear-layer thicknesses and shapes have a similar downstream development, which is consistent with a linear stability analysis of the measured velocity profiles.

Investigation of Hypersonic Intakes Using Reynolds Stress Modeling and Wavelet-Based Adaptation

The simulation of hypersonic flows is computationally demanding due to the large gradients of the flow variables at hand, caused both by strong shock waves and thick boundary or shear layers. The resolution of those gradients imposes the use of extremely small cells in the respective regions. Taking turbulence into account intensifies the variation in scales even more. Furthermore, hypersonic flows have been shown to be extremely grid sensitive. For the simulation of fully three-dimensional configurations of engineering applications, this results in a huge amount of cells and, as a consequence, prohibitive computational time. Therefore, modern adaptive techniques can provide a gain with respect to both computational costs and accuracy, allowing the generation of locally highly resolved flow regions where they are needed and retaining an otherwise smooth distribution. In this paper, an -adaptive technique based on wavelets is employed for the solution of hypersonic flows. The compressible Reynolds-averaged Navier–Stokes equations are solved using a differential Reynolds stress turbulence model, well suited to predict shock-wave/boundary-layer interactions in high-enthalpy flows. Two test cases are considered: a compression corner at 15 deg and a scramjet intake. The compression corner is a classical test case in hypersonic flow investigations because it poses a shock-wave/turbulent-boundary-layer interaction problem. The adaptive procedure is applied to a two-dimensional configuration as validation. The scramjet intake is first computed in two dimensions. Subsequently, a three-dimensional geometry is considered. Both test cases are validated with experimental data and compared to nonadaptive computations. The results show that the use of an adaptive technique for hypersonic turbulent flows at high-enthalpy conditions can strongly improve the performance in terms of memory and CPU time while at the same time maintaining the required accuracy of the results.

Passively controlled supersonic cavity flow using a spanwise cylinder

An experimental investigation of a passively controlled open cavity with a length to depth ratio of six and freestream Mach number of 1.4 was conducted to investigate the mechanisms responsible for the observed surface pressure reductions. The passive control comes from placing a spanwise aligned cylinder in the boundary layer near the leading edge of the cavity. The two control configurations were isolated from previous experiments of the fluctuating surface pressure and correspond to a larger diameter rod near the top of the boundary layer and a smaller diameter rod placed near the wall. These were further analyzed using particle image velocimetry in an attempt to elicit the responsible mechanism for the flow control. The use of two-point statistics revealed the wall normal turbulent velocity correlation’s evolution became elongated in the wall normal direction. This suggests that the shear layer may be less-organized and consists of smaller-scale structures. The disturbance of the feedback receptivity loop is clearly demonstrated for the controlled configurations evidenced by weakened correlation signals between the aft wall sensor and positions on the cavity floor. The presence of the rod is shown to decrease the mean shear gradient, more effectively for the large rod placed at the top of the boundary layer, throughout the shear layer. The efficacy of the control leads to an initially thicker shear layer which spreads more rapidly and is clearly demonstrated by vorticity growth rates, mean, and turbulent flowfield statistics.

The crystallization morphology evolution of polyoxymethylene/poly(ethylene oxide) blend micropart prepared under microinjection molding conditions

ABSTRACTThis article is the first study on the microinjection molding and the effects of the microprocessing parameters on the crystallization and orientation of polyoxymethylene/poly(ethylene oxide) (POM/PEO) blend, which has better toughness and self‐lubricity compared with the neat POM and therefore is a better candidate material for making microparts like microgears with higher performances. The crystalline and phase morphologies were investigated by polarized light microscope (PLM), differential scanning calorimeter (DSC) and scanning electron microscope (SEM). The crystalline orientation of the microparts was evaluated by two‐dimensional wide‐angle X‐ray diffraction (2D‐WAXD) and Herman's orientation function. The experimental results showed that both POM and POM/PEO microparts prepared by microinjection molding exhibited three distinct layers, i.e., skin layer, shear layer and core layer, while the latter had thicker shear layer but thinner skin layer and core layer. PEO was well dispersed in POM matrix. The spherulite size, the melting point as well as the crystallinity of POM in the POM/PEO blend decreased due to the interference of PEO in the crystallization of POM. A shish‐kebab structure was observed in the shear layers of the POM/PEO microparts. The effects of processing parameters on the thicknesses of different layers of the POM/PEO microparts were investigated. With increase of the injection speed or decrease of the mold temperature, the skin layer and the core layer became thicker, while the shear layer and the oriented region became thinner. However, the influence of the injection pressure was not obvious. Also, the processing parameters affected the crystalline orientation of the POM/PEO microparts. With increase of the injection speed or decrease of the mold temperature, the orientation function f decreased, indicating a lower degree of orientation. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014, 131, 40538.

Direct numerical simulation of forced circular jets: Effect of varicose perturbation

Abstract Free circular jets at low and intermediate Reynolds numbers evolve through discrete transitions accompanied by the formation of large-scale structures. Understanding dynamics of coherent structures in free jets suggests control strategies that can be used to achieve enhanced spreading and mixing of the jet with the surrounding fluid. In the present work, an active control technique that alters the vortex dynamics in the jet is implemented close to the nozzle resulting in an effect over the entire flow field. Among techniques available for control, the one based on (axisymmetric) varicose perturbation has been considered. The effect of perturbation on jet evolution and flow structures is examined via a computational approach. Direct numerical simulation (DNS) of incompressible, spatially developing circular jets is reported for a Reynolds number of 1000. The three-dimensional unsteady Navier–Stokes equations are solved by a high order spatial and temporal discretization scheme. For small-scale perturbation using Gaussian white noise, the jet undergoes transition in conformity with experiments. With varicose perturbation, excitation frequencies play a significant role in the evolution of circular jets. Excitation frequencies of 0.1 and 0.2 show the formation of a trailing jet. For a frequency of 0.2, the circular jet shows pairing of the shed vortices. With further increase in the excitation frequency, formation of strong secondary hairpin vortices at the far field is to be seen. Largest influence of excitation is seen for frequencies around the preferred mode value of 0.32. For A thick shear layer helps in formation of vortex ring that undergoes tearing while a thinner shear layer develops a stronger vortex ring.

Numerical validation of shear flow corrections for beamforming acoustic source localisation in open wind-tunnels

The beamforming technique has become a common method to localise aeroacoustic sources. However, in the case of anechoic wind tunnel experiments, some shear flow corrections have to be taken into account in order to estimate accurately the position and power of the source. This study deals with the efficiency of such corrections. Several correction methods are presented. The first one is based on the convected wave equation and predicts that, if no flow model is used, the source is localised with an apparent source shift, that is approximately equal to the product of the Mach number by the mean flow thickness. Two other shear flow corrections, based on acoustic ray theory, are considered. They allow the modelling of both the effective source–receiver propagation time and pressure amplitude. The efficiency of such corrections is assessed by using a numerical simulation of the acoustic pressure measurement with a linear microphone array in an anechoic wind-tunnel. The simulation, based on a programme solving the linearised Euler equations, is first validated at a low Mach number (0.11) by a careful comparison, in terms of source localisation, with experimental data for several array positions. The efficiency of the shear flow corrections is then investigated numerically for a set of flow parameters. The apparent source shift is shown to be independent of the ratio of the shear flow thickness to the sound wavelength, and the shear flow corrections perform well, at low Mach numbers for thin and thick shear layers. Conversely, the mean flow thickness and the Mach number are shown to be the two main parameters having an influence on the apparent source shift. The estimate of this shift by the product of the Mach number with the mean flow thickness is shown to be a good approximation, and can be used for a posteriori corrections up to Mach number 0.4. For higher subsonic Mach numbers, the ray-based shear flow correction models associated to beamforming processing are shown to be robust enough to localise the source position in a flow, and to avoid significant source power under-estimation.

The structure of the absolutely unstable regions in the near field of low-density jets

AbstractThe viscous spatiotemporal stability properties of low-density laminar round jets emerging from circular nozzles or tubes are investigated numerically providing, for the first time, a separate treatment of the two particular cases typically studied in experiments: a hot gas jet discharging into a quiescent cold ambient of the same species, and an isothermal jet consisting of a mixture of two gases with different molecular weight, discharging into a stagnant ambient of the heavier species. To that end, use is made of a realistic representation for the base velocity and density profiles based on boundary-layer theory, with account taken of the effect of variable transport properties. Our results show significant quantitative differences with respect to previous parametric studies, and reveal that hot jets are generically more unstable than light jets, in the sense that they have larger associated critical density ratios for values of the Reynolds number and momentum thickness typically used in experiments. In addition, for several values of the jet-to-ambient density ratio, $S$, the downstream evolution of the local stability properties of the jet is computed as a function of the two main control parameters governing the jet, namely the Reynolds number, $\mathit{Re}$, and the momentum thickness of the initial velocity profile, ${\theta }_{0} / D$. It is shown that, for a given value of $S$, the $(\mathit{Re}, {\theta }_{0} / D)$ parameter plane can be divided in three regions. In the first region, defined by low values of $\mathit{Re}$ or very thick shear layers, the flow is locally convectively unstable everywhere. In the second region, with moderately large values of $\mathit{Re}$ and thin shear layers, the jet exhibits a localized pocket of absolute instability, away from boundaries. Finally, in the third region, that prevails in most of the $(\mathit{Re}, {\theta }_{0} / D)$ parameter plane, the absolutely unstable domain is bounded by the jet outlet. All the experiments available in the literature are shown to lie in the latter region, and the global transition observed in experiments is demonstrated to take place when the absolutely unstable domain becomes sufficiently large. The marginal frequency of the resulting global self-excited oscillations is shown to be fairly well described by the absolute frequency evaluated at the jet outlet, in agreement with the numerical results obtained by Lesshafft et al. (J. Fluid Mech., vol. 554, 2006, pp. 393–409) for synthetic jets.

Modelling rock avalanche propagation onto glaciers

Ice-rock avalanches which occur in glacial environments are controlled by the presence of snow and ice in the moving material and by possible propagation onto icy basal surfaces. All these factors contribute to enhancing the flow mobility. Mixing with ice and snow hampers block collisions and favours dense flow behaviour. Ice melting reduces granular friction by saturation of the basal material and fluidization effects. Propagating onto glaciers offers a smooth surface with low shear resistance.This work is a review of the best documented ice-rock avalanches and focuses on evaluating their mobility for hazard analysis purposes by providing a set of calibrated cases. The rock avalanches have volumes ranging from 5*106 m3 to 25*106 m3. We replicate these events by using SPH and FEM numerical methods, assuming frictional and Voellmy basal rheologies. The Voellmy rheology best performs at replicating the landslide propagation. Among the back analyzed cases, the frictional coefficient ranges in the interval 0.03–0.1, the turbulent coefficient within 1000 m s−2–2000 m s−2. The bulk basal friction angle ranges within 2.75° and 14° with values inversely related to event volumes. Forward selection of the basal friction angle based on event volume, allows the replication of the Mount Cook ice-rock avalanche predicting a maximum runout which is less than 4% larger than observed. In the perspective of forward modelling, large uncertainty is related to the reconstruction of the post-event topographies, particularly for the sliding surface.Mixing with ice and snow reduces basal friction proportionally to ice and snow content. Pure ice has a basal friction which is reduced by about 75% than basal friction of pure rock. Melting of ice during rock avalanche propagation has been evaluated for the Sherman event. The frictional heat generated at the glacier surface results in the melting of 86.2 ± 5.9 kg m−2, which could have contributed to a minimum 20–35% (±10%) reduction of the material friction angle through the sole pore pressure generation within a 40 and 20 cm thick shear layer, respectively. The largest uncertainty is related to the area of contact between rock and ice.

Texturing in Earth’s inner core due to preferential growth in its equatorial belt

We propose an extension of the model by Yoshida et al., 1996 where deformation in the inner core is forced by preferential growth in the equatorial belt, by taking into account the presence of a stable compositional stratification. Stratification inhibits vertical motion, imposes a flow parallel to isodensity surfaces, and concentrates most deformation in a shallow shear layer of thickness ∼ B −1/5, where B is the dimensionless buoyancy number. The localization of the flow results in large strain rates and enables the development of a strong alignment of iron crystals in the upper inner core. We couple our dynamical model with a numerical model of texture development and compute the time evolution of the lattice preferred orientation of different samples in the inner core. With sufficient stratification, texturing is significant in the uppermost inner core. In contrast, the deeper inner core is unaffected by any flow and may preserve a fossil texture. We investigate the effect of an initial texture resulting from solidification texturing at the ICB. In the present inner core, the deformation rate in the shallow shear layer is large and can significantly alter the solidification texturing, but the solidification texture acquired early in the inner core history can be preserved in the deeper part. Using elastic constants from ab initio calculations, we predict different maps of anisotropy in the modern inner core. A model with both solidification texturing and subsequent deformation in a stratified inner core produces a global anisotropy in reasonable agreement with seismological observations.

An analytic interface dynamo over a shear layer of finite depth

Parker's analytic Cartesian interface dynamo is generalized to the case of a shear layer of finite thickness and low resistivity (“tachocline”), bounded by a perfect conductor (“radiative zone”) on the one side, and by a highly diffusive medium (“convective zone”) supporting an α-effect on the other side. In the limit of high diffusivity contrast between the shear layer and the diffusive medium, thought to be relevant for the Sun, a pair of exact dispersion relations for the growth rate and frequency of dynamo modes is analytically derived. Graphic solution of the dispersion relations displays a somewhat unexpected, non-monotonic behavior, the mathematical origin of which is elucidated. The dependence of the results on the parameter values (dynamo number and shear layer thickness) is investigated. The implications of this result for the solar dynamo problem are discussed.

The effect of confinement on the stability of viscous planar jets and wakes

This theoretical study examines confined viscous planar jet/wake flows with continuous velocity profiles. These flows are characterized by the shear, confinement, Reynolds number and shear-layer thickness. The primary aim of this paper is to determine the effect of confinement on viscous jets and wakes and to compare these results with corresponding inviscid results. The secondary aim is to consider the effect of viscosity and shear-layer thickness. A spatio-temporal analysis is performed in order to determine absolute/convective instability criteria. This analysis is carried out numerically by solving the Orr–Sommerfeld equation using a Chebyshev collocation method. Results are produced over a large range of parameter space, including both co-flow and counter-flow domains and confinements corresponding to 0.1 < h2/h1 < 10, where the subscripts 1 and 2 refer to the inner and outer streams, respectively. The Reynolds number, which is defined using the channel width, takes values between 10 and 1000. Different velocity profiles are used so that the shear layers occupy between 1/2 and 1/24 of the channel width. Results indicate that confinement has a destabilizing effect on both inviscid and viscous flows. Viscosity is found always to be stabilizing, although its effect can safely be neglected above Re = 1000. Thick shear layers are found to have a stabilizing effect on the flow, but infinitely thin shear layers are not the most unstable; having shear layers of a small, but finite, thickness gives rise to the strongest instability.

Numerical simulation of viscous, nonlinear and progressive water waves

A numerical simulation is performed to study the velocity, streamlines, vorticity and shear stress distributions in viscous water waves with different wave steepness in intermediate and deep water depth when the average wind velocity is zero. The numerical results present evidence of ‘clockwise’ and ‘anticlockwise’ rotation of the fluid at the trough and crest of the water waves. These results show thicker vorticity layers near the surface of water wave than that predicted by the theories of inviscid rotational flow and the low Reynolds number viscous flow. Moreover, the magnitude of vorticity near the free surface is much larger than that predicted by these theories. The analysis of the shear stress under water waves show a thick shear layer near the water surface where large shear stress exists. Negative and positive shear stresses are observed near the surface below the crest and trough of the waves, while the maximum positive shear stress is inside the water and below the crest of the water wave. Comparison of wave energy decay rate in intermediate depth and deep water waves with laboratory and theoretical results are also presented.