Showing papers on "Open-channel flow published in 2002"

Open Channel Flow Resistance

Abstract: In 1965, Rouse critically reviewed hydraulic resistance in open channels on the basis of fluid mechanics. He pointed out the effects of cross-sectional shape, boundary nonuniformity, and flow unsteadiness, in addition to viscosity and wall roughness that are commonly considered. This paper extends that study by discussing the differences between momentum and energy resistances, between point, cross-sectional and reach resistance coefficients, as well as compound/composite channel resistance. Certain resistance phenomena can be explained with the inner and outer laws of boundary layer theory. The issue of linear-separation approach versus nonlinear approach to alluvial channel resistances also is discussed. This review indicates the need for extensive further research on the subject.

Force evaluation in the lattice Boltzmann method involving curved geometry

Abstract: The present work investigates two approaches for force evaluation in the lattice Boltzmann equation: the momentum-exchange method and the stress-integration method on the surface of a body. The boundary condition for the particle distribution functions on curved geometries is handled with second-order accuracy based on our recent works [Mei et al., J. Comput. Phys. 155, 307 (1999); ibid. 161, 680 (2000)]. The stress-integration method is computationally laborious for two-dimensional flows and in general difficult to implement for three-dimensional flows, while the momentum-exchange method is reliable, accurate, and easy to implement for both two-dimensional and three-dimensional flows. Several test cases are selected to evaluate the present methods, including: (i) two-dimensional pressure-driven channel flow; (ii) two-dimensional uniform flow past a column of cylinders; (iii) two-dimensional flow past a cylinder asymmetrically placed in a channel (with vortex shedding); (iv) three-dimensional pressure-driven flow in a circular pipe; and (v) three-dimensional flow past a sphere. The drag evaluated by using the momentum-exchange method agrees well with the exact or other published results.

Hydraulic resistance of flow in channels with cylindrical roughness

Abstract: A laboratory study on the hydraulics of flow in an open channel with circular cylindrical roughness is presented. The laboratory study consists of an extensive set of flume experiments for flows with emergent and submerged cylindrical stems of various sizes and concentrations. The results show that the flow resistance varies with flow depth, stem concentration, stem length, and stem diameter. The stem resistance experienced by the flow through the vegetation is best expressed in terms of the maximum depth-averaged velocity between the stems. Physically based formulas for flow resistance, the apparent channel velocity, and flow velocities in the roughness and surface layers are developed. The formulas are validated with the flume data from the present study as well as those from past studies. A method for calculating channel hydraulic conditions using these formulas is presented.

Application of lattice Boltzmann method to simulate microchannel flows

Abstract: Microflow has become a popular field of interest due to the advent of microelectromechanical systems. In this work, the lattice Boltzmann method, a particle-based approach, is applied to simulate the two-dimensional isothermal pressure driven microchannel flow. Two boundary treatment schemes are incorporated to investigate their impacts to the entire flow field. We pay particular attention to the pressure and the slip velocity distributions along the channel in our simulation. We also look at the mass flow rate which is constant throughout the channel and the overall average velocity for the pressure-driven flow. In addition, we include a simulation of shear-driven flow in our results for verification. Our numerical results compare well with those obtained analytically and experimentally. From this study, we may conclude that the lattice Boltzmann method is an efficient approach for simulation of microflows.

Measurements and modeling of two-phase flow in microchannels with nearly constant heat flux boundary conditions

Abstract: Two-phase forced convective flow in microchannels is promising for the cooling of integrated circuits. There has been limited research on boiling flow in channels with dimensions below 100 /spl mu/m, in which bubble formation and flow regimes can differ from those in larger channels. This work develops single and multi-channel experimental structures using plasma-etched silicon with pyrex glass cover, which allow uniform heating and spatially-resolved thermometry and provide optical access for visualization of boiling regimes. Boiling was observed with less than 5/spl deg/C of super-heating in rectangular channels with hydraulic diameters between 25 and 60 /spl mu/m. The channel wall widths are below 350 /spl mu/m, which minimizes solid conduction and reduces variations in the heat flux boundary condition. Pressure drop and wall temperature distribution data are consistent with predictions accounting for solid conduction and homogeneous two-phase convection.

Flow Velocity Measurements in Vegetated Channels

Abstract: Understanding of the hydraulics of flow over vegetation is very important to support the management of fluvial processes. In this paper the flow over flexible bottom vegetation is experimentally studied. A two-dimensional-acoustic doppler velocimeter is used to measure the local flow velocities for different vegetation concentrations, discharges, and flume slopes. The influence of vegetation concentration and the depth/vegetation height ratio on the measured velocity profiles is analyzed. All measured velocity distributions are S-shaped and exhibit a three-zone profile. The relationship between the velocity distribution and the turbulence intensity distribution is also analyzed. The characteristics ~inflection point, maximum value, asymptotes ! of the measured velocity distributions and the results of the previous investigators are used to select an analytical expression for the shape of the velocity profile. A theoretical velocity profile is deduced using the classical Prandtl's mixing length approach with a new expression for the mixing length. The deduced four-coefficient profile allows description of the flow both inside and above the vegetation. The physical and geometrical meaning of the four coefficients are also shown. DOI: 10.1061/~ASCE!0733-9429~2002!128:7~664! CE Database keywords: Velocity profile; Vegetation; Channel flow.

An investigation of stably stratified turbulent channel flow using large-eddy simulation

Abstract: Boundary-forced stratified turbulence is studied in the prototypical case of turbulent channel flow subject to stable stratification. The large-eddy simulation approach is used with a mixed subgrid model that involves a dynamic eddy viscosity component and a scale-similarity component. After an initial transient, the flow reaches a new balanced state corresponding to active wall-bounded turbulence with reduced vertical transport which, for the cases in our study with moderate-to-large levels of stratification, coexists with internal wave activity in the core of the channel. A systematic reduction of turbulence levels, density fluctuations and associated vertical transport with increasing stratification is observed. Countergradient buoyancy flux is observed in the outer region for sufficiently high stratification. Mixing of the density field in stratified channel flow results from turbulent events generated near the boundaries that couple with the outer, more stable flow. The vertical density structure is thus of interest for analogous boundary-forced mixing situations in geophysical flows. It is found that, with increasing stratification, the mean density profile becomes sharper in the central region between the two turbulent layers at the upper and lower walls, similar to observations in field measurements as well as laboratory experiments with analogous density-mixing situations. Channel flow is strongly inhomogeneous with alternative choices for the Richardson number. In spite of these complications, the gradient Richardson number, Ri g , appears to be the important local determinant of buoyancy effects. All simulated cases show that correlation coefficients associated with vertical transport collapse from their nominal unstratified values over a narrow range, 0.15 Ri g < 0.25. The vertical turbulent Froude number, Fr w , has an O (1) value across most of the channel. It is remarkable that stratified channel flow, with such a large variation of overall density difference (factor of 26) between cases, shows a relatively universal behaviour of correlation coefficients and vertical Froude number when plotted as a function of Ri g . The visualizations show wavy motion in the core region where the gradient Richardson number, Ri g , is large and low-speed streaks in the near-wall region, typical of unstratified channel flow, where Ri g is small. It appears from the visualizations that, with increasing stratification, the region with wavy motion progressively encroaches into the zone with active turbulence; the location of Ri g ≃ 0.2 roughly corresponds to the boundary between the two zones.

Interaction of metamorphism, deformation and exhumation in large convergent orogens

Abstract: Coupled thermal-mechanical models are used to investigate interactions between metamorphism, deformation and exhumation in large convergent orogens, and the implications of coupling and feedback between these processes for observed structural and metamorphic styles. The models involve subduction of suborogenic mantle lithosphere, large amounts of convergence (≥ 450 km) at 1 cm yr−1, and a slope-dependent erosion rate. The model crust is layered with respect to thermal and rheological properties — the upper crust (0–20 km) follows a wet quartzite flow law, with heat production of 2.0 μW m−3, and the lower crust (20–35 km) follows a modified dry diabase flow law, with heat production of 0.75 μW m−3. After 45 Myr, the model orogens develop crustal thicknesses of the order of 60 km, with lower crustal temperatures in excess of 700 °C. In some models, an additional increment of weakening is introduced so that the effective viscosity decreases to 1019 Pa.s at 700 °C in the upper crust and 900 °C in the lower crust. In these models, a narrow zone of outward channel flow develops at the base of the weak upper crustal layer where T≥600 °C. The channel flow zone is characterised by a reversal in velocity direction on the pro-side of the system, and is driven by a depth-dependent pressure gradient that is facilitated by the development of a temperature-dependent low viscosity horizon in the mid-crust. Different exhumation styles produce contrasting effects on models with channel flow zones. Post-convergent crustal extension leads to thinning in the orogenic core and a corresponding zone of shortening and thrust-related exhumation on the flanks. Velocities in the pro-side channel flow zone are enhanced but the channel itself is not exhumed. In contrast, exhumation resulting from erosion that is focused on the pro-side flank of the plateau leads to ‘ductile extrusion’ of the channel flow zone. The exhumed channel displays apparent normal-sense offset at its upper boundary, reverse-sense offset at its lower boundary, and an ‘inverted’ metamorphic sequence across the zone. The different styles of exhumation produce contrasting peak grade profiles across the model surfaces. However, P–T–t paths in both cases are loops where Pmax precedes Tmax, typical of regional metamorphism; individual paths are not diagnostic of either the thickening or the exhumation mechanism. Possible natural examples of the channel flow zones produced in these models include the Main Central Thrust zone of the Himalayas and the Muskoka domain of the western Grenville orogen.

Effect of free rotation on the motion of a solid sphere in linear shear flow at moderate Re

Abstract: The effect of free rotation on the drag and lift forces on a solid sphere in unbounded linear shear flow is investigated. The sphere Reynolds number, Re=|ur|d/ν, is in the range 0.5–200, where ur is the slip velocity. Direct numerical simulations of three-dimensional flow past an isolated sphere are performed using spectral methods. The sphere is allowed to rotate and translate freely in the shear flow in response to the hydrodynamic forces and torque acting on it. The effect of free rotation is studied in a systematic way by considering three sets of simulations. In the first set of simulations, we study how fast a pure rotational or translational motion of the sphere approaches steady state. The “history” effect of rotational and translational motions are compared. Results at high Re are found to be significantly different from the analytical prediction based on low Re theory. In steady simulations, the sphere is allowed to rotate in a torque-free condition. The torque-free rotation rate and the drag an...

Experimental studies on particle behaviour and turbulence modification in horizontal channel flow with different wall roughness

Abstract: Detailed measurements in a developed particle-laden horizontal channel flow (length 6 m, height 35 mm, the length is about 170 channel heights) are presented using phase-Doppler anemometry for simultaneous determination of air and particle velocity. The particles were spherical glass beads with mean diameters in the range of 60 µm–1 mm. The conveying velocity could be varied between about 10 m/s and 25 m/s, and the particle mass loading could reach values of about 2 (the mass loading is defined as the ratio of particle to gas phase mass flow rates), depending on particle size. For the first time, the degree of wall roughness could be modified by exchanging the wall plates. The influence of these parameters and the effect of inter-particle collisions on the profiles of particle mean and fluctuating velocities and the normalised concentration in the developed flow were examined. It was shown that wall roughness decreases the particle mean velocity and enhances fluctuating velocities due to irregular wall bouncing and an increase in wall collision frequency, i.e. reduction in mean free path. Thereby, the larger particles are mainly more uniformly distributed across the channel, and gravitational settling is reduced. Both components of the particle velocity fluctuation were reduced with increasing mass loading due to inter-particle collisions and the momentum loss involved. Moreover, the effect of the particles on the air flow and the turbulent fluctuations was studied on the basis of profiles in the developed flow and turbulence spectra determined for the streamwise velocity component. In addition to the effect of particle size and mass loading on turbulence modulation, the influence of wall roughness was analysed. It was clearly shown that increasing wall roughness also results in a stronger turbulence dissipation due to two-way coupling.

Fluid flow through nanometer-scale channels.

Abstract: We describe studies of the pressure driven flow of several classical fluids through lithographically produced channels in which one dimension, the channel height h, is in the micron or nanometer size range. The measured flow rates are compared with theoretical predictions assuming no-slip boundary conditions at the walls of the channel. The results for water agree well with this prediction for h as small as 40 nm (our smallest channels). However, for hexane, decane, hexadecane, and silicone oil we find deviations from this theory when h is reduced below about 100 nm. The observed flow rates for small h are larger than theoretical expectations, implying significant slip at the walls, and values of the slip length are estimated. The results are compared with previous experimental and theoretical work.

Multi-channel microfluidic system design with balanced fluid flow distribution

Abstract: Methods and apparatus are presented for controlling fluid flow with pressure gradient fluid control. Passive fluid flow barriers may be used to act as valves, thereby allowing the flow of fluids through flow paths to be regulated so as to allow fluids to be introduced via a single channel (50) and subsequently split into multiple channels (58, 60). Flow through flow paths can be regulated to allow a series of sister wells (51-53) or chambers to all fill prior to the fluid flowing beyond any one of the sister wells (51-53) or chambers. Each flow path may have multiple segments (66-69), at least one of which is designed to balance the pressure drops of the flow paths to provide uniform flow of fluids through the flow paths. The configurations of the wells (51-53) may be modified by adding vents or flow dividers to enhance fluid flushing and gas removal capability.

Three-Dimensional Numerical Study of Flows in Open-Channel Junctions

Abstract: An open-channel junction flow is encountered in many hydraulic structures ranging from wastewater treatment facilities to fish passage conveyance structures. An extensive number of experimental studies have been conducted but a comprehensive three-dimensional numerical study of junction flow characteristics has not been performed and reported. In this paper, a three-dimensional numerical model is developed to investigate the open-channel junction flow. The main objective is to present the validation of a three-dimensional numerical model with high-quality experimental data and compare additional simulations with classical one-dimensional water surface calculations. The three-dimensional model is first validated using the experimental data of a 90° junction flow under two flow conditions. Good agreement is obtained between the model simulation and the experimental measurements. The model is then applied to investigate the effect of the junction angle on the flow characteristics and a discussion of the results is presented.

Lattice Boltzmann simulations of binary fluid flow through porous media.

Abstract: The lattice Boltzmann equation is often advocated as a simulation tool that is particularly effective for complex fluids such as multiphase and multicomponent flows through porous media. We construct a three-dimensional 19 velocity lattice Boltzmann model for immiscible binary fluids with variable viscosities and density ratio based on the model proposed by Gunstensen. The model is tested for the following binary fluid flow problems: a stationary planar interface among two fluids; channel flow of immiscible binary fluids; the Laplace problem; and a rising bubble. The results agree well with semi-analytic results in a range of the Eotvos, Morton and Reynolds number. We also present preliminary simulation results for two large-scale realistic applications: the flow of an air-water mixture in a waste-water batch reactor and the saturation hysteresis effect in soil flow. We discuss some limitations of the lattice Boltzmann method in the simulation of realistic and difficult multiphase problems.

Transition of streamwise streaks in zero-pressure-gradient boundary layers

Abstract: Transition from laminar to turbulent flow has beentraditionally studied in terms of exponentially growingeigensolutions to the linearized disturbance equations.However, experimental findings show that transition may occuralso for parameters combinations such that these eigensolutionsare damped. An alternative non-modal growth mechanism has beenrecently identified, also based on the linear approximation.This consists of the transient growth of streamwise elongateddisturbances, mainly in the streamwise velocity component,called streaks. If the streak amplitude reaches a thresholdvalue, secondary instabilities can take place and provoketransition. This scenario is most likely to occur in boundarylayer flows subject to high levels of free-stream turbulenceand is the object of this thesis. Different stages of theprocess are isolated and studied with different approaches,considering the boundary layer flow over a flat plate. Thereceptivity to free-stream disturbances has been studiedthrough a weakly non-linear model which allows to disentanglethe features involved in the generation of streaks. It is shownthat the non-linear interaction of oblique waves in thefree-stream is able to induce strong streamwise vortices insidethe boundary layer, which, in turn, generate streaks by thelift-up effect. The growth of steady streaks is followed bymeans of Direct Numerical Simulation. After the streaks havereached a finite amplitude, they saturate and a new laminarflow, characterized by a strong spanwise modulation isestablished. Using Floquet theory, the instability of thesestreaks is studied to determine the features of theirbreakdown. The streak critical amplitude, beyond which unstablewaves are excited, is 26% of the free-stream velocity. Theinstability appears as spanwise (sinuous-type) oscillations ofthe streak. The late stages of the transition, originating fromthis type of secondary instability, are also studied. We foundthat the main structures observed during the transition processconsist of elongated quasi-streamwise vortices located on theflanks of the low speed streak. Vortices of alternating signare overlapping in the streamwise direction in a staggeredpattern. Descriptors:Fluid mechanics, laminar-turbulenttransition, boundary layer flow, transient growth, streamwisestreaks, lift-up effect, receptivity, free-stream turbulence,nonlinear mechanism, streak instability, secondary instability,Direct Numerical Simulation.

Sand screen with active flow control and associated method of use

Abstract: Apparatus and methods are disclosed for actively controlling the flow of hydrocarbon fluids from a producing formation at the downhole sand screen. A preferred embodiment of the invention provides a fluid flow annulus within the production tube inside of the screen. In a first flow control configuration, fluid passing through the screen is required to flow along the annulus to find a flow aperture into an interior flow bore. A static flow control device within the annulus between the sand screen and a first flow aperture dissipates flow energy by forcing the flow through a restricted area that helically winds about the flow annulus. Dissipation of the flow energy increases the pressure reduction from the screen into the production bore and reduces the flow velocity. In a second flow control configuration, flow control structure within the flow annulus obstructs all flow along the annulus. A third flow control configuration removes all flow restrictions within the flow annulus.

Nanostructured surfaces for dramatic reduction of flow resistance in droplet-based microfluidics

Abstract: This paper reports a dramatic reduction of liquid droplet flow resistance by engineering the surfaces into nanomechanical hydrophobic structures that show a contact angle over 175/spl deg/. Flow resistances of droplets on open surfaces as well as in confined microchannels (between surfaces) have been measured with significant reduction of flow resistance (over 99% and over 95%, respectively) compared with a surface of the same material.

Suspension and turbulence modification effects of solid particulates on a horizontal turbulent channel flow

Abstract: Experimental measurements detailing the turbulence modification and suspension mechanism of particulates within a horizontal solid/liquid channel flow are presented. The measurement technique utilized a simultaneous two-phase particle image velocimetry method to examine the instantaneous particle-fluid structure, and to acquire correlated particle-fluid statistics to describe the two-way coupling between the phases. The results show that the presence of the particles distinctly alters the mean fluid motion, even though the bulk mass loadings are only on the order of 10−4. The carrier phase turbulence properties are also altered, showing an effective increase in the wall friction velocity of approximately 7%, and an increase of the normal and shear Reynolds stress by approximately 8-10% in the outer flow (y/h > 0.1). The particles in the flow exhibited a lag in the mean streamwise velocity, while the local streamwise slip velocity in the vicinity of the particle was found to be near negligible levels. In c...

Maximum Velocity and Regularities in Open-Channel Flow

Abstract: Maximum velocity in a channel section often occurs below the water surface. Its location is linked to the ratio of the mean and maximum velocities, velocity distribution parameter, location of mean velocity, energy and momentum coefficients, and probability density function underpinning a velocity distribution equation derived by applying the probability and entropy concepts. The mean value of the ratio of the mean and maximum velocities at a given channel section is stable and constant, and invariant with time and discharge. Its relationship with the others in turn leads to formation of a network of related constants that represent regularities in open-channel flows and can be used to ease discharge measurements and other tasks in hydraulic engineering. Under the probability concept, the ratio of mean and maximum velocities being constant means that the probability distribution underpinning the velocity distribution and other related variables is resilient, and that the same probability distribution is governing various phenomena observable at a channel section and explains the regularities in open-channel flows.

Nonlinear electrokinetic ejection and entrainment due to polarization at nearly insulated wedges

Abstract: We examine a singular electrokinetic flow around a corner or a wedge in micro-channels constructed from dielectric materials whose permittivity is small but finite compared to that of the electrolyte When the wedge angle is less than 180°, the applied electric field, which is tangential far from the corner, develops a normal surface component that becomes singular at the corner This normal field leakage causes opposite polarization at the two sides of the wedge and produces a converging singular tangential electrokinetic flow that ejects liquid from the tip By expanding in cylindrical harmonics, we estimate this ejecting flow as a function of the permittivity ratio, applied electric field, angle of the wedge and the microscopic corner curvature that suppresses the singularity The ejecting flow entrains tangential flow on the front side of the wedge and produces a vortex on the downstream side This entrainment offers a long-range attractive hydrodynamic force that complements short-range electrostatic DLVO (Derjaguin–Landau–Verwey–Overbeek) and dielectrophoretic forces to enhance corner deposition and aggregation of colloids and proteins during electrophoresis/electro-osmosis

Heat Transfer Enhancement by Delta-Wing-Generated Tip Vortices in Flat-Plate and Developing Channel Flows

Abstract: Using delta wings placed at the leading edge of a flat plate, streamwise vortices are generated that modify the flow; the same wings are also used to modify a developing channel flow. Local and average measurements of convection coefficients are obtained using naphthalene sublimation, and the structure of the vortices is studied using flow visualisation and vortex strength measurements. The pressure drop penalty associated with the heat transfer enhancement of the channel flow is also investigated. In regions where a vortex induces a surface-normal inflow, the local heat transfer coefficients are found to increase by as much as 300 percent over the baseline flow, depending on vortex strength and location relative to the boundary layer Vortex strength increases with Reynolds number, wing aspect ratio, and wing attack angle, and the vortex strength decays as the vortex is carried downstream. Considering the complete channel. surface, the largest spatially averaged heat average heat transfer enhancement is 55 percent: it is accompanied by a 100 percent increase in the pressure drop relative to the same channel flow with no delta-wing vortex generator.

Micro-channel filling flow considering surface tension effect

Abstract: Understanding filling flow into micro-channels is important in designing micro-injection molding, micro-fluidic devices and an MIMIC (micromolding in capillaries) process. In this paper, we investigated, both experimentally and numerically, 'transient filling' flow into micro-channels, which differs from steady-state completely 'filled' flow in micro-channels. An experimental flow visualization system was devised to facilitate observation of flow characteristics in filling into micro-channels. Three sets of micro-channels of various widths of different thicknesses (20, 30, and 40 μm) were fabricated using SU-8 on the silicon substrate to find a geometric effect with regard to pressure gradient, viscous force and, in particular, surface tension. A numerical analysis system has also been developed taking into account the surface tension effect with a contact angle concept. Experimental observations indicate that surface tension significantly affects the filling flow to such an extent that even a flow blockage phenomenon was observed at channels of small width and thickness. A numerical analysis system also confirms that the flow blockage phenomenon could take place due to the flow hindrance effect of surface tension, which is consistent with experimental observation. For proper numerical simulations, two correction factors have also been proposed to correct the conventional hydraulic radius for the filling flow in rectangular cross-sectioned channels.

Direct simulations of a rough-wall channel flow

Abstract: In this study, we performed simulations of turbulent flow over rectangular ribs transversely mounted on one side of a plane in a channel, with the other side being smooth. The separation between ribs is large enough to avoid forming stable vortices in the spacing, which exhibits k-type, or sand-grain roughness. The Reynolds number Reτ of our representative direct numerical simulation case is 460 based on the smooth-wall friction velocity and the channel half-width. The roughness height h is estimated as 110 wall units based on the rough-wall friction velocity. The velocity profile and kinetic energy budget verify the presence of an equilibrium, logarithmic layer at y≳2h. In the roughness sublayer, however, a significant turbulent energy flux was observed. A high-energy region is formed by the irregular motions just above the roughness. Visualizations of vortical streaks, disrupted in all three directions in the roughness sublayer, indicate that the three-dimensional flow structure of sand-grain roughness is replicated by the two-dimensional roughness, and that this vortical structure is responsible for the high energy production. The difference in turbulence structure between smooth- and rough-wall layers can also be seen in other flow properties, such as anisotropy and turbulence length scales.

A linear approach for the evolution of coherent structures in shallow mixing layers

Abstract: The development of large coherent structures in a shallow mixing layer is analyzed. The results are validated with experimental data obtained from particle tracking velocimetry. The mean flow field is modeled using the self-similarity of the velocity profiles. The characteristic features of the down-stream development of a shallow mixing layer flow, like the decrease of the velocity difference over the mixing layer, the decreasing growth of the mixing layer width, and the transverse shift of the center of the mixing layer layer are fairly well represented. It turned out that the entrainment coefficient could be taken constant, equal to a value obtained for unbounded mixing layers: ? = 0.085. Linearization of the shallow water equations leads to a modified Orr–Sommerfeld equation, with turbulence viscosity and bottom friction as dissipative terms. Growth rates are obtained for each position downstream, using the model for the mean flow field. For a given energy density spectrum at the inflow boundary, integration of the growth rates along the downstream direction yields the spectra at various downstream positions. These spectra provide a measure for the intensity and the length scale of the coherent structures (the dominant mode). The length scales found are in good agreement with the measured ones. The length scale of the most unstable mode appears much larger than the length scale of the dominant mode. Obviously, the longevity of the coherent structures plays a significant role. Three growth regimes can be distinguished: in the first regime the dominant mode is growing, in the second regime the dominant mode is dissipating, but other modes are still growing, and in the third regime all modes are dissipating. It is concluded that the development of the coherent structures in a shallow mixing layer can fairly well be described and interpreted by the proposed linear analysis.