Helmholtz Vortices Research Articles

High-fidelity simulations of microramp-controlled shock wave/boundary layer interaction

Microvortex generators (MVGs) are a promising solution to control shock wave/turbulent boundary layer interactions (SBLIs), especially in supersonic inlets. In this study, we examine the effects of a microramp vortex generator on an SBLI generated by an oblique shock wave and a turbulent boundary layer using direct numerical simulations (DNSs). Two cases, with and without the presence of a microramp, are compared in terms of their mean and unsteady flow features at free-stream Mach number equal to 2 and friction Reynolds number at the inviscid shock impingement equal to 600. The long integration period allows us to assess how microramps affect the typical low-frequency unsteadiness observed in SBLIs, and the data generated may serve as a reference for simulations of lower fidelity or reduced order models. The analysis shows that the three-dimensional microramp wake alters the interaction region dramatically, inducing a significant spanwise modulation and topology change of the separation. For example, tornado-like structures redistribute the flow in both the spanwise and wall-normal directions inside the recirculation region. The increase in momentum close to the wall by the ramp vortices effectively delays the onset of the separation and, thus, the separation length, but at the same time leads to a significant increase in the intensity of the wall-pressure fluctuations. We then characterise the mutual interaction between the arch-like vortices around the ramp wake and the SBLI. The specific spanwise vorticity shows that these vortices follow the edge of the separation and their intensity, apart from mean compressibility effects, is not affected by the shocks. The shocks, instead, are deformed in shape by the periodic impingement of the vortices, although the spectral analysis did not reveal any significant trace of their shedding frequency in the separation region. These Kelvin–Helmholtz vortices, however, may be relevant in the closure of the separation bubble. Fourier analysis also shows a constant increase, in both value and magnitude, in the low-frequency peak all along the span, suggesting that the motion of the separation shock remains coherent while being disturbed by the arch-like vortices and oscillating at a higher frequency in absolute terms.

Time-resolved tomographic particle image velocimetry of flow structures in non-circular orifice impinging jets

In this study, time-resolved tomographic particle image velocimetry (Tomo-PIV) was implemented on two different non-circular orifice impinging jets, i.e., elliptical and square orifices, and the circular one was employed as a reference for comparison, with the same equivalent diameter De=20 mm, impinging distance-to-diameter H/D = 3.0, and the Reynolds number (Re) at 1.6×103. A particular concern was placed on examining the coherent structure dynamics and turbulence dissipation of these impinging jets. The dominant Strouhal number (St) of all three jets has the component of 0.53, representing the large-scale Kelvin–Helmholtz (K–H) vortex ring, particularly for the square orifice, the dominant St is 0.70 at the central axis and 0.18 at the diagonal axis near the impinging surface. In free jet region, the streamwise velocity profile of the square orifice jet always maintains a rhombic development with a 45° difference relative to the outlet shape. In the impingement region, the circular orifice jet has the strongest K–H structure, with two opposite wall jets generated inside and outside, while in elliptical jet impinging, the upturned short axis of the vortex ring after axis-switching invariably contacts the impinging surface first, and then the wall jet vortex ring re-stretches to a circular shape due to the higher velocity of the wall jets generated from the upturned short axis, and the square orifice impinging jet contains no obvious wall K–H vortex rings but undergoes an irregular merging with the vortex ring downstream and stagnation. The time-averaged flow field statistics show that the circular orifice impinging jets have stronger wall jets, while the square orifice is the weakest, due to the strongest turbulent dissipation generated by the more fragmented flow upstream.

Quantifying wake dynamics subjected to stream vegetation patch elongation: The influence of patch-edge vortices

Vortices are generated across a wide range of scales due to the interaction between in-stream vegetation and surrounding flows, significantly influencing hydro-geomorphodynamics in earth surface water systems. Recent advance in vegetation patch hydrodynamics has revealed that the elongation of the middle channel patch can generate complex wake flow patterns by adjusting the bleed flow from the patch and triggering the patch-edge Kelvin–Helmholtz (KH) vortices. With a broader range of experimental configurations, this study reveals how the patch wake mixing is apparently strengthened by the presence of KH vortices, indicated by a larger steady wake velocity, a shorter steady wake length, and a damped energy of wake von Karman vortex. Furthermore, we quantify these characteristic metrics of patch wake behavior with and without the influence of KH vortices. Our findings provide insights into the role of vegetation-induced vortex interactions in regulating mixing processes, thereby promoting informed practices in environmental flows.

Small-scale Field-aligned Currents in the Magnetopause Boundary Layer

Based on high-resolution measurements from the Magnetospheric Multiscale mission from 2015 May to 2018 June, we statistically investigate the properties of small-scale field-aligned currents (SFACs) in the magnetopause boundary layer. A total of 2235 SFACs are successfully identified. The durations of SFACs mainly fall between 0.2 and 0.3 s. Over 90% of SFACs have a width of less than 1 ion inertia length and are primarily distributed from 5 to 25 electron inertia lengths, implying that the SFACs belong to the kinetic-scale current layer. The main carriers of SFACs are electrons, and over 70% of SFACs exhibit net energy dissipation (i.e., J · E ′ > 0) with the majority of energy dissipation taking place in the parallel direction. SFACs are widely distributed spatially, and the occurrence rate of SFACs is higher in the boundary layer closer to the magnetosphere. Additionally, less than half of the total SFACs are identified in well-known structures, including the magnetic reconnection region, flux transfer event, Kelvin–Helmholtz vortex, and exhaust region, and 54% of the SFACs are in the “others” unknown structures. These results improve our comprehension of the current system at the magnetopause and the roles of SFACs in the coupling between the solar wind and magnetosphere.

Formation and propagation characteristics of a weak shock wave in maglev tube

The propagation of the weak shock wave (WSW) to the tunnel exits and their radiation as micro-pressure waves (MPWs) may cause sonic booms or structural resonance of buildings, posing potential hazards to humans, animals, and buildings in the exit's environment. The characteristics of the WSW and sonic booms of a maglev train/tube coupling model were studied based on the two-dimensional axisymmetric unsteady Reynolds average Navier–Stokes turbulence model. In the later stage of a MPW, the formation mechanism, geometry, and kinematic characteristics of compressible vortex rings (CVRs) were systematically analyzed. The inertial effect causes the initial wavefront to gradually transition from a Gaussian-shape waveform to a triangular waveform during its propagation, eventually coalescing into a WSW. The overpressure, density jump, and shock Mach number at the WSW location all increase with the increasing train speed, while the WSW thickness decreases accordingly. The formation distance of the WSW is inversely proportional to the amplitude of the initial wavefront gradient, and the WSW directly causes the occurrence of the exit sonic boom. The MPW amplitude has significant directionality with a largest value in the axial direction. Within the speed range of 450–700 km/h, the sound pressure level of the MPW exceeds the hearing threshold and even reaches the feeling threshold. The evolution of CVRs includes primary CVR, secondary CVR, and Kelvin–Helmholtz vortices. Primary CVR has the greatest impact on the axial MPW among them. The occurrence of CVRs will cause a second small noise level other than the sonic boom.

Vortex dynamics and boundary layer transition in flow around a rectangular cylinder with different aspect ratios at medium Reynolds number

The numerical investigation focuses on the flow patterns around a rectangular cylinder with three aspect ratios ( $L/D=5$ , $10$ , $15$ ) at a Reynolds number of $1000$ . The study delves into the dynamics of vortices, their associated frequencies, the evolution of the boundary layer and the decay of the wake. Kelvin–Helmholtz (KH) vortices originate from the leading edge (LE) shear layer and transform into hairpin vortices. Specifically, at $L/D=5$ , three KH vortices merge into a single LE vortex. However, at $L/D=10$ and $15$ , two KH vortices combine to form a LE vortex, with the rapid formation of hairpin vortex packets. A fractional harmonic arises due to feedback from the split LE shear layer moving upstream, triggering interaction with the reverse flow. Trailing edge (TE) vortices shed, creating a Kármán-like street in the wake. The intensity of wake oscillation at $L/D=5$ surpasses that in the other two cases. Boundary layer transition occurs after the saturation of disturbance energy for $L/D=10$ and $15$ , but not for $L/D=5$ . The low-frequency disturbances are selected to generate streaks inside the boundary layer. The TE vortex shedding induces the formation of a favourable pressure gradient, accelerating the flow and fostering boundary layer relaminarization. The self-similarity of the velocity defect is observed in all three wakes, accompanied by the decay of disturbance energy. Importantly, the decrease in the shedding frequency of LE (TE) vortices significantly contributes to the overall decay of disturbance energy. This comprehensive exploration provides insights into complex flow phenomena and their underlying dynamics.

On the dynamics of the turbulent flow past a three-element wing

A comprehensive analysis of the unsteady flow dynamics past the 30P30N three-element high lift wing is performed by means of large eddy simulations at different angles of attack (α = 5°, 9°, and 23°) and at a Reynolds number of Rec=750 000 (based on the nested chord). Results are compared with experimental and numerical investigations, showing a quantitatively good agreement and, thus, proving the reliability and accuracy of the present simulations. Within the slat and main coves, large recirculation bubbles are bounded by shear layers, where the onset of turbulence is triggered by Kelvin–Helmholtz instabilities. In the energy spectrum of the velocity fluctuations, the footprint of these instabilities is detected as a broadband peak; its frequency being moved toward lower values as the angle of attack increases. Kelvin–Helmholtz vortices roll-up and break down into small scales that eventually impinge into the slat and main coves lower surfaces. The slat impingement shows to be more prominent, and hence, larger velocity and pressure fluctuations are observed. The impingement strength diminishes with the angle of attack in both coves, while higher fluctuations are originated on the slat and main respective suction sides, leading to larger boundary layers. This is associated with the displacement of the stagnation point with the angle of attack. Another salient feature observed is the laminar-to-turbulent flow transition in the main and flap leading edges although the average location of this transition seems to not be affected by the angle of attack. Tollmien–Schlichting instabilities precede this transition, with the disturbances amplified by the inviscid mode at low angles of attack, while at α=23°, the local Reynolds number on the main suction side is incremented and the viscous mode becomes important. The analysis shows that the turbulent wake formed at the trailing edge of all elements dominates the dynamics downstream. This is especially true at the higher angle of attack, where a large region of velocity deficit above the flap is observed, thus indicating the onset of stall conditions.

Flow velocity adjustment in a channel with a floating vegetation canopy

Floating vegetation with unanchored and connected roots can completely cover the water surface of rivers, ditches, and streams. Eichhornia crassipes is a typical macrophyte with a stable network of roots that is present in aquatic environments, forming a complicated flow velocity adjustment. This study constructed model floating canopies and real E. crassipes canopies to investigate flow velocity adjustment and verify a new proposed velocity model. Laboratory experiments showed that flow velocity was modified in both the streamwise (x) and vertical (z) directions and impacted by the mean channel velocity, canopy density, and relative flow depth. The penetration distance δe of the Kelvin–Helmholtz vortices penetrating into the floating canopy increased to its maximum beyond the flow adjustment distance XD, where XD was the distance from the canopy leading edge to the position at which the flow was fully developed. The thickness of the bed boundary layer δb was related to the vegetation drag (FD(x)), the bed shear stress (τb(x)), and the height of the free-flow region below the canopy hg. New estimators for δe and δb were proposed and validated for floating canopies. Combined with the new estimators (δe and δb), flow continuity equation, momentum equation and four-layer divided method, a new analytical model was proposed to predict vertical profiles of velocity within and below a floating canopy in both the flow adjustment region (XD > x > 0) and fully developed flow region (x > XD). Fourteen groups of velocity data from this study and published literature were used to verify the proposed model. The predicted vertical profiles of velocity in flow adjustment and fully developed flow regions agreed with measurements under a wide range of vegetation and flow conditions, suggesting that the proposed model was capable of accurately predicting velocity profiles in a channel with a floating canopy. Finally, the model was validated in a channel with a real E. crassipes canopy. A comparison between predicted and measured velocities confirmed that the new model is valid for application in a channel with real floating macrophytes.

Direct numerical simulation of supersonic boundary layers over a microramp: effect of the Reynolds number

Microvortex generators are passive control devices smaller than the boundary layer thickness that energise the boundary layer to prevent flow separation with limited induced drag. In this work, we use direct numerical simulations (DNS) to investigate the effect of the Reynolds number in a supersonic turbulent boundary layer over a microramp vortex generator. Three friction Reynolds numbers are considered, up to $Re_\tau = 2000$ , for fixed free stream Mach number $M_\infty =2$ and fixed relative height of the ramp with respect to the boundary layer thickness. The high-fidelity data set sheds light on the instantaneous and highly three-dimensional organisation of both the wake and the shock waves induced by the microramp. The full access to the flow field provided by DNS allows us to develop a qualitative model of the near wake, explaining the internal convolution of the Kelvin–Helmholtz vortices around the low-momentum region behind the ramp. The overall analysis shows that numerical results agree excellently with recent experimental measurements in similar operating conditions and confirms that microramps effectively induce a significantly fuller boundary layer even far downstream of the ramp. Moreover, results highlight significant Reynolds number effects, which in general do not scale with the ramp height. Increasing Reynolds number leads to enhanced coherence of the typical vortical structures in the field, faster and stronger development of the momentum deficit region, increased upwash between the primary vortices from the sides of the ramp – and thus increased lift-up of the wake – and faster transfer of momentum towards the wall.

DIFFUSION COMBUSTION OF A HYDROGEN MICROJET, OUTFLOWING FROM A CURVLINEAR CHANNEL

The presented work examines the combustion of a hydrogen microjet flowing from a curved channel with a round micronozzle. Jet flows that are generated using rectilinear and curved channels differ in that in the second case, Dean vortices make a noticeable contribution to the formation of the jet and its combustion. The interaction of the latter with Kelvin–Helmholtz vortices, the formation of which is typical for flows with a velocity shift, causes changes in combustion characteristics. They include spatial distortions of the laminar flame zone near the nozzle exit, the area of turbulent combustion downstream, as well as the turbulent flame in the conditions of its separation from the nozzle exit and the cessation of laminar combustion in the initial section of the flow. The results of these studies provide an opportunity to better understand the combustion features of hydrogen microjets under conditions of their hydrodynamic instability.

Effects of Submerged Flexible Vegetation on Scalar Transport in an Open‐Channel Flow

AbstractScalar transport in vegetated flow plays an important role in natural river ecology. In this study, a scalar transport model for the flow with flexible submerged vegetation is developed. The turbulent structure and scalar transport characteristics in the flow without vegetation, and with rigid and flexible vegetation are compared. The results show that the scalar diffusion in the flow is mainly governed by the turbulent diffusion outside the diffusion boundary layer. The wake flow downstream of rigid vegetation and the small‐scale Kelvin–Helmholtz (KH) vortices near the top of the canopy are the main reasons to enhance the turbulence intensity in the flow and to significantly increase the turbulence diffusion of scalars. However, the flexible vegetation movement induces the large‐scale KH vortices near the top of the canopy. It also causes to increase the turbulence intensity in the flow, to redistribute the scalar concentration in a wide range, to increase the scalar concentration across the flow depth, and to increase the scalar turbulence diffusion intensity. In the flow with rigid vegetation, the values of the turbulent Schmidt number vary from 0.72 to 1.93 below the top of the canopy, while in the flow with flexible vegetation, they vary from 0.58 to 1.99 only near the top of the canopy. Above the top of the canopy, the Schmidt number ranges from 0.48 to 0.84. The results are useful for the parameterization of scalar transport in natural vegetated rivers.

Flows past cylinders confined within ducts. Effects of the duct width

We present direct numerical simulations (DNS) of the flow past a circular cylinder confined in a rectangular duct at a Reynolds number of Re=630, based on the bulk velocity and the cylinder diameter. The blockage ratio, defined as the ratio of the cylinder diameter to the duct height, is set at β=0.6. We find the topology of the wake is highly sensitive to the duct width, and suggest that care needs to be taken comparing results with experimental data sets. This is unlike the flow past an unconfined or lowly confined cylinder where the general topology remains relatively similar with duct width. Ducts of width 4.44, 10, and 20 times the cylinder diameter have been considered along with an infinite channel. For the smallest duct of 4.44 cylinder diameters, the effects of the side walls of the duct, or the end walls from the perspective of the cylinder, extend into the core region, where there are strong interactions between the influence from opposing sides. The wake formed is much more chaotic, with Kelvin–Helmholtz vortices observed to form in the shear layers off the cylinder. Hence leading to a shorter wake. With increases in the duct width to 10 cylinder diameters, the separation of the side walls lessens the interactions within the centre of the duct. The shear layers off the cylinder are less destabilised as a result, leading to the formation of a more classical Kármán vortex street. The wake was also found to be longer as a result. However, the blockage effect was still evident at such a duct width. It was only for widths of 20 cylinder diameters or greater, a flow structurally similar to that in an infinite channel could be obtained, with asymmetric structures modulated along the span. Furthermore, the increases in the duct width beyond 10 cylinder diameters lead to decreases in the wake length.

Modelling the response of a turbulent jet flame to acoustic forcing in a linearized framework using an active flame approach

This study performs a linear mean field analysis of a turbulent reacting methane-air jet flame, with the goal of predicting the response of the reacting flow to upstream acoustic actuation. Unlike previous studies, this work develops and applies an active flame approach by taking the heat release oscillations of the flame resulting from the acoustic fluctuations into account. For an active flame approach in the linear mean field analysis, a linearized combustion model is necessary. Linearizing Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS) combustion models leads to closure problems, making their application in this context troublesome, whereas Reynolds-averaged Navier Stokes (RANS) combustion models prove to circumvent this problem making them suitable candidates for this purpose. The RANS combustion models are linearized around the temporal mean state variables of the turbulent jet flame, which is obtained by LES. An a priori analysis shows that a linearized RANS–Eddy Break Up (EBU) model is the best suited among all investigated combustion models for the investigated set-up and reproduces with high accuracy the fluctuations in reaction rate obtained in the LES. Furthermore, the linearized governing equations of the flow including the linearized EBU model for the reaction rate are solved for incoming acoustic perturbations. The response modes show that the reaction rate oscillations are caused by Kelvin–Helmholtz vortex rings, which perturb the jet flame. The results are in good agreement with the LES simulations in terms of the mode shapes of both reaction rate and velocity fluctuations. This study represents a basis for linear mean field analysis of turbulent flames and monolithic modelling approaches for thermoacoustic instabilities in gas turbine combustors.

Experimental study on the combined effects of patch density and elongation on wake structure behind a rectangular porous patch

This paper presents an experimental study on how both variable solid volume fractions and aspect ratios (length/width) of a centre-channel rectangular porous patch under aligned configuration of rigid and emergent stems impact the flow behaviour and wake structure. This study forms an essential extension to the existing fundamentals and knowledge on this topic. Through rigorous experimental tests by velocity measurement and dye visualization, the aspect ratio, rarely addressed before, is confirmed to play a critical role. Vortex street, unable to be triggered under a low solid volume fraction, however, can be generated by elongating the patch (increasing the aspect ratio). The key reason is that patch elongation promotes the generation of the wake vortex street by producing a relatively high transverse velocity gradient in the wake region. Meanwhile, Kelvin–Helmholtz vortex streets are triggered along the two patch lateral edges, re-increasing the in-patch velocity and imposing contributions to the wake vortex streets generation. By scaling the characteristic velocity (at the wake vortex initiation position and patch trailing edge) and solid volume fraction with the patch aspect ratio, three non-dimensional threshold maps can be established to express the combined effects of the solid volume fraction and aspect ratio on the initiation of the wake vortex street. They could be alternatively used for theoretical analysis and implementation on wake formation and structure subject to parameter availability.

Experimental investigation on the cavitation modulation mechanism in submerged self-sustained oscillating jets

To investigate the cavitation evolution states in chamber and its modulation on the self-sustained oscillation, experimental research is conducted in the nozzles with three different chamber lengths using high-speed photography and high frequency sensors. The experiment results indicate that with the increase of the chamber length of Helmholtz nozzles utilized in this study, the intensity of cavitation gradually decreases and the complex congestion cavitation state will switch to the periodic shedding annular cavitation cloud and even discrete free cavitation. With the increase of inlet pressure, the self-maintenance of Helmholtz vortex ring in the jet shear layer enhances, making the random components in the shear layer and the chaotic degree of the flow field reduce. For the submerged self-sustained oscillating jets, the cavitation structure in the nozzle can be regarded as an accumulator, which shrinks and expands periodically to determine the release and aggregation of energy and modulates the pulsation frequency and intensity of the pulsed jet induced by Helmholtz nozzles. The amplitude of pressure pulsation is positively correlated with the cavitation intensity, which means that the pulsation performance of the self-sustained oscillating pulsed jet gets better with the increase of the cavitation intensity.

Suppression mechanism of Richtmyer–Meshkov instability by transverse magnetic field with different strengths

The Richtmyer–Meshkov instability (RMI) is caused by an incident planar shock wave impinging on the heavy-gas-density interface. We have numerically investigated the RMI controlled by different transverse magnetic-field strengths based on the ideal compressible magnetohydrodynamics (MHD) equations. The MHD equations are solved by the corner transport upwind + constrained transport algorithm, which guarantees a divergence-free constraint on the magnetic field. We discuss the flow characteristics and shock patterns in both classical hydrodynamic and MHD situations and verify our conclusions by comparing the experimental results with the numerical results. The results show that the magnetic field modifies the pressure-gradient distribution, and the baroclinic vorticity splits and attaches to the MHD shock waves. In addition, the results indicate that the interaction of shock wave and density interface changes the distribution of magnetic-field energy and distorts the magnetic induction line in the region of magnetic-field energy accumulation. The distortion of the magnetic induction lines alters the magnetic field gradient and creates a magnetic tension that produces a torque opposing that generated by the shear force on the vorticity layer, so the Kelvin–Helmholtz instability is effectively suppressed and no Kelvin–Helmholtz vortex appears on the vorticity layer. The result is that the interface instability is suppressed.

A study on the effect of driver section length on the flow field inside a two-dimensional closed-ended viscous shock tube: A numerical investigation

The interaction of a reflected shock wave with the boundary layer inside a closed-ended shock tube is studied by many researchers using different numerical schemes. However, the interaction of a reflected shock wave having a decaying pressure profile ahead of the reflected shock is lacking in the literature. It is essential to quantify the deviation in flow characteristics experienced in tests performed inside the shock tube compared to field tests while studying blast wave attenuation and mitigation. In the present study, the effect of transient upstream pressure on the shock wave reflecting from a solid wall and the associated flow separation inside the boundary layer is examined in detail through numerical simulations using the viscous shock tube problem for Re = 1000. Simulations were performed using an in-house 13th-order high-resolution hybrid solver with 50 million grid points. The transient pressure profile behind the incident shock wave is achieved by varying the non-dimensional driver section length from 0.5 to 0.02 while keeping the overall shock tube length as 1. The flow field is scrutinized through numerical schlieren and vorticity plots. It is observed that the decaying pressure profiles behind the incident shock wave have an immense impact on the dynamics of shockwave-boundary layer interaction and the vortices emanating from the shear layer due to Kelvin–Helmholtz Instability. The secondary vortices inside the boundary layer, vortices at the shear layer, and compression waves in the separated boundary layer region reduce with a decrease in driver section length. The triple point height increases as driver section length decreases due to the weakening of upstream velocity. The Kelvin–Helmholtz vortices originating from the triple point moves back into the separated boundary layer rather than interacting with the end wall. It suggests that the decaying pressure behind the incident shock wave minimizes the secondary effects on the solid wall during shock wave impingement.

Shallow mixing interfaces between parallel streams of unequal densities

As opposed to the case of shallow mixing layers forming between parallel streams of unequal velocities and equal densities, the spatial development of the mixing interface (MI) between two parallel streams of unequal velocities and sufficiently large density contrast is controlled by the formation of a spatially developing, lock-exchange-like flow in transverse planes. Buoyancy effects are driven by the presence of a vertical density interface near the splitter plate. Eddy-resolving numerical simulations conducted in a wide and very long channel are used to investigate the mean flow structure and the effects of the lock-exchange-like flow and the associated coherent structures on mixing and the capacity of the flow to entrain sediment from the channel bed. When the two streams have unequal densities, quasi-two-dimensional Kelvin–Helmholtz (KH) vortices still form near the MI origin, but their coherence is lost over a much shorter distance compared with the case with no density contrast, and their cores are severely stretched in the transverse direction. A main cell of recirculating (cross-) flow forms in the mean flow, in between the fronts of the near-bed intrusion of heavier fluid and the free-surface intrusion of lighter fluid. The instantaneous flow fields contain streamwise-oriented vortical cells along the interface separating the regions containing heavier and lighter fluids. These vortical cells play an important role in enhancing mixing, similar to the KH billows forming in a classical lock-exchange flow. The regions of highest turbulence amplification are situated next to the boundaries of the main recirculating cell. Once the oscillating fronts of the intrusions get sufficiently close to the channel sidewalls, streamwise cells of secondary flow form near the channel boundaries. For cases with a strong density contrast, the free-surface mixing pattern is not a good indicator of mixing between the two streams. For the same flow velocities in the incoming channels, the two streams mix faster with increasing density difference between the two streams. This is because, as opposed to the KH vortices, coherent structures induced by the formation of the lock-exchange-like flow maintain their coherence and capacity to induce mixing at very large distances from the splitter plate. Meanwhile, the redistribution of the streamwise momentum leading to uniform, fully developed flow over the whole cross-section is delayed by buoyancy effects. Away from the splitter plate, the region with the highest sediment entrainment potential is situated next to the edge of the main recirculation cell on the high-speed side of the channel. For the same flow velocities in the incoming channels, the sediment entrainment capacity of the flow is much larger in the simulations conducted with density contrast between the incoming streams and peaks for the case when the faster stream contains the denser fluid.

Analytical model for predicting the lateral profiles of velocities through a partially vegetated channel

In an open channel, an emergent canopy of vegetation enhances local resistance, producing a complicated velocity distribution within and around the canopy. Laboratory experiments were performed to understand the flow velocity variations in a partially vegetated channel, revealing both streamwise and lateral velocity variations as the flow entered the canopy. An analytical model was proposed to predict the lateral velocity profiles across the vegetated region and bare channel in both the flow adjustment region and the fully developed flow region. The flow velocity variations in the streamwise and lateral directions were parameterized and included in the new proposed model, allowing the model to capture both the streamwise and the lateral velocity variations. Twenty sets of experimental data from our experiments and data from published studies were used to verify the new model. The predicted velocity profiles exhibited good agreement with the measurements under a wide range of vegetation and flow conditions, suggesting that the proposed model is capable of accurately predicting the velocity profiles in a partially vegetated channel. Finally, the proposed model was applied to evaluate the critical frontal area per canopy volume at which Kelvin–Helmholtz vortices form along the emergent canopy side edge. With the same spatially averaged velocity, the critical frontal area exhibited no dependence on stem diameter.

Local stability analysis of homogeneous and stratified Kelvin–Helmholtz vortices

We perform a three-dimensional short-wavelength linear stability analysis of numerically simulated two-dimensional Kelvin–Helmholtz vortices in homogeneous and stratified environments at a fixed Reynolds number of $Re = 300$ . For the homogeneous case, the elliptic instability at the vortex core dominates at early times, before being taken over by the hyperbolic instability at the vortex edge. For the stratified case of Richardson number $ Ri = 0.08$ , the early-time instabilities comprise a dominant elliptic instability at the core and a hyperbolic instability influenced strongly by stratification at the vortex edge. At intermediate times, the local approach shows a new branch of (convective) instability that emerges at the vortex core and subsequently moves towards the vortex edge. A few more convective instability bands appear at the vortex core and move away, before coalescing to form the most unstable region inside the vortex periphery at large times. In addition, the stagnation point instability is also recovered outside the periphery of the vortex at intermediate times. The dominant instability characteristics from the local approach are shown to be in good qualitative agreement with the results based on global instability studies for both homogeneous and stratified cases. A systematic study of the dependence of the dominant instability characteristics on $ Ri $ is then presented. While $ Ri = 0.1$ is identified as most unstable (with convective instability being dominant), another growth rate maximum at $ Ri = 0.025$ is not far behind (with the hyperbolic instability influenced by stratification being dominant). Finally, the local stability approach is shown to predict the potential orientation of the flow structures that would result from hyperbolic and convective instabilities, which is found to be consistent with three-dimensional numerical simulations reported previously.