Streamwise Shear Research Articles

Large-scale structures in high-Reynolds-number rotating Waleffe flow

We perform direct numerical simulations of rotating turbulent Waleffe flow, the flow between two parallel plates with a sinusoidal streamwise shear driving force, to study the formation of large-scale structures and the mechanisms for momentum transport. We simulate different cyclonic and anti-cyclonic rotations in the range of dimensionless rotation numbers (inverse Rossby numbers) $R_\Omega$ $\in$ $[-0.16, 2.21]$, and fix the Reynolds number to $Re=3.16\times 10^3$, large enough such that the shear transport is almost entirely due to Reynolds stresses and viscous transport is negligible. We find an optimum rotation in anti-cyclonic regime at $R_\Omega=0.63$, where a given streamwise momentum transport in the wall-normal direction is achieved with minimum mean energy of the streamwise flow. We link this optimal transport to the strength of large scale structures, as was done in plane Couette by Brauckmann \& Eckhardt (J. Fluid Mech., 815, 2017). Furthermore, we explore the large-scale structures and their behaviour under spanwise rotation, and find disorganized large structures at $R_\Omega =0$ but highly organized structures in the anti-cyclonic regime, similar to the rolls in rotating plane Couette and turbulent Taylor Couette flow. We compare the large scale structures of plane Couette flow and Waleffe flow, and observe that the streamwise vorticity is localized inside the cores of the rolls. We show that the rolls take energy from the mean flow at long time-scales, and relate these structures to eigenvalues of the streamfunction.

Continuously-fed gravity currents propagating over a finite porous substrate

We present the results of laboratory investigations of continuously-fed density currents that propagate first over a smooth horizontal bed and then over a porous substrate of limited length. Inflow discharge, initial excess density, and substrate porosities are varied. Density measurements, acquired through an image analysis technique, are performed above the porous layer simultaneously with quasi-instantaneous vertical velocity profiles. After a first phase in which the current sinks into the substrate, freshwater entrainment from the bed begins and, gradually, a mixing layer forms at the interface between the surface flow and the porous bed. Shear-driven and Rayleigh-Taylor instabilities rule the dynamics of this mixing layer. The porous boundary effects are observed in the vertical distributions of both density and velocity, especially in the near-bed region. Here, larger flow velocities are recorded over porous substrates. We argue that these are due to the presence of a longitudinal pressure gradient, which in turn is a consequence of the current mass loss. Its presence over the porous substrate is proved by the current interface longitudinal slope. However, other effects of the presence of the porous substrate, such as the relaxation of the no-slip boundary condition and the bed-normal momentum exchange, also affect the velocity field. The turbulent structure changes significantly over the porous substrate: while streamwise turbulence decreases, shear and bed-normal Reynolds stresses increase in large part of the current depth. Buoyancy instabilities further enhance the bed-normal momentum flux and, in the near-bed region, contribute to turbulent kinetic energy generation together with shear.

Experiments on grain size segregation in bedload transport on a steep slope

Sediment transport in mountain and gravel-bed-rivers is characterized by bedload transport of a wide range of grain sizes. When the bed is moving, dynamic void openings permit downward infiltration of the smaller particles. This process, termed here ‘kinetic sieving’, has been studied in industrial contexts, but more rarely in fluvial sediment transport. We present an experimental study of two-size mixtures of coarse spherical glass beads entrained by turbulent and supercritical steady water flows down a steep channel with a mobile bed. The particle diameters were 4 mm and 6 mm, and the channel inclination 10%. The spatial and temporal evolution of the segregating smaller 4 mm diameter particles was studied through the introduction of the smaller particles at a low constant rate into the large particle bedload flow at transport equilibrium. Particle flows were filmed from the side by a high-speed camera. Using original particle tracking algorithms, the position and velocity of both small and large particles were determined. Results include the time evolution of the layer of segregating smaller beads, assessment of segregation velocity and particle depth profiles. Segregation resulted in the progressive establishment of a quasi-continuous region of small particles reaching a steady-state penetration depth. The segregation dynamics showed a logarithmic time decreasing trend. This evolution was demonstrated to be dependent on the particle streamwise shear rate which decays downwards exponentially. This result is comparable to theories initially developed for dry granular flows.

Towards a unified shear-induced lift model for prolate spheroidal particles moving in arbitrary non-uniform flow

The paper proposes a unified shear-induced lift force model which divides the lift force into four lift components arising from the spin tensor, the volumetric and the deviatoric parts of the rate of deformation tensor, and the inertia effect of the Stokes drag. This unified model is successfully simplified into a shear-induced lift model for prolate spheroidal particles moving in arbitrary flow conditions via analogy arguments. The simplified shear-induced lift model for prolate spheroidal particles is verified by comparing it with several established lift force models via simulation of a prolate spheroidal particle moving in the Poiseuille and lid-driven cavity flows. The computational results demonstrate that the present lift force model for prolate spheroidal particles is applicable in flow cases with streamwise and non-streamwise flow shear. The implementation of the simplified lift model leads to computational results with reasonably small difference to the results of the full lift model of Cui et al. [Int. J. Multiph. Flow, 111, 232–240 (2019)], with a significantly decreased computational cost, rendering it as suitable for the implementation in large scale Lagrangian particle tracking.

A novel model for the lift force acting on a prolate spheroidal particle in arbitrary non-uniform flow. Part II. Lift force taking into account the non-streamwise flow shear

The present contribution is the second part of a two-part research work presenting a generic method to extend lift force models that were originally devised for single linear shear flow to arbitrary flow conditions. The method can be applied to the computation of lift forces exerted on prolate spheroidal particles (or fibres) in arbitrary non-uniform flows. The method proposed in the Part I calculates the lift force arising from the dominant streamwise flow shear. In Part II the influence of the non-streamwise flow shear on the lift force is also taken into account. The present method assumes that the particle slip velocity is parallel to the fluid velocity along the particle trajectory. The novelty in the presented method is the computation of the shear lift force model for prolate spheroidal particles taking into account also non-streamwise flow shear. The accuracy of the novel shear lift force model for prolate spheroidal particles is verified by comparing it with the lift force model proposed in Part I via simulating the axial migration of a prolate spheroidal particle in the Poiseuille flow. In order to validate the ability of the present method for capturing the lift component arising from non-streamwise flow shear, the lift force model is compared with established generalised Saffman-type lift models by simulating the motion of a particle in lid-driven cavity flow. The computational results demonstrate that the present lift force model for prolate spheroidal particles is applicable in flow cases with streamwise and non-streamwise flow shear, even if some (reasonably small) accuracy for the case of the streamwise-only shear is lost.

Flow characteristics of a partially-covered trapezoidal channel

Partial ice covers alter the hydraulic regime of rivers in cold regions. Border ice is a type of partial ice cover that forms on the river banks and grows toward the centre of the channel to form a full ice cover; thereby impacting freeze-up processes. Many studies have been conducted to understand flow characteristics under open channel and full ice cover conditions; however, only a few studies have focused on the effects of partial ice covers on flow characteristics in a rectangular channel. This study goes even further by investigating stream-wise velocity and shear stress distributions in a trapezoidal channel with simulated border ice. This is the very first study to investigate the effects of different border ice coverage ratios and roughness conditions on flow characteristics in a trapezoidal channel. Experiments were conducted under seven different roughness and coverage conditions. High-resolution velocity data were collected using acoustic Doppler velocimeters within the fully-developed region of the flume. The magnitude and shape of the stream-wise velocity contours were significantly altered by the presence of the partial ice and rough boundaries. Moreover, local boundary shear stress distributions were significantly impacted by the coverage and roughness conditions. Generally, stream-wise velocity and local boundary shear stress increased within the open section and decreased within the covered section. For practical purposes, depth-averaged velocity and discharge distributions were investigated for each experiment. Results from this study will improve the current knowledge of the flow in partially covered channels and can be used for design and modelling purposes.

Lateral distribution of depth average velocity & boundary shear stress in a gravel bed open channel flow

ABSTRACT Gravel bed flow is so generic condition that its study becomes fascinating as well as critical to apprehend flow characteristic. In this particular study, no bed load movement was maintained using grains of 13.5 mm (D50 value) characterised as no load condition. Depth Average Velocity (DAV) and the Boundary Shear Stress (BSS) has been experimentally estimated for five different depths for the prevailing no load condition. Furthermore, the distribution of streamwise depth-averaged velocity and boundary shear stress at different flow depths of gravel bed are also calculated using different hydraulic software packages such as CES & ANSYS FLUENT. These numerical simulation results have shown reasonably good agreement with experimental data over main channel in inbank flow. Finally, results obtained are corroborated through error analysis. The overall idea of this study was to understand flow characteristic and behaviour of gravel bed having inbank flow through experimental and numerical simulation techniques.

Application of rod vortex generators for flow separation reduction on wind turbine rotor

AbstractThis paper focuses on flow control on wind turbine blades. A rod vortex generator (RVG) is proposed. Previous experimental and numerical results obtained for channels and blade sections proved RVGs to effectively enhance the streamwise shear stresses and reduce flow separation. The benefits of application of RVGs to control and decrease the flow separation on horizontal axis wind turbine rotor blades are assessed and presented in the paper. The numerical investigation was conducted with the FINE/Turbo solver from Numeca International, which solves the 3D Reynolds‐averaged Navier‐Stokes equations. The validation of the numerical model for the clean case is based on phase VI of the Unsteady Aerodynamics Experiment. At selected operating conditions, flow control devices have proven to reattach the flow locally to the wall and improve the aerodynamic performance of the wind turbine. Additionally, the local implementation of RVGs shows strong effect on flow structure and interaction with the main flow to create a “shielding” effect, preventing further penetration of separation towards blade tip. As a consequence, the positive effect of RVGs exists outside the blade span covered by devices. The obtained aerodynamic improvement shows that RVGs may be used as an alternative to traditional flow control devices applied on wind energy turbines.

Coherent structures in the wake behind a trailing edge cutback

An experimental study was performed to investigate the influence of coolant ejection on the aerodynamic characteristics of the unsteady wake behind a trailing edge cutback. A high-resolution planar particle image velocimetry (PIV) system was emlpoyed to conduct detailed flowfield measurements at a Reynolds number of Reh=2000. The time-averaged velocity fields, the distributions of reverse-flow intermitteny and velocity deficts were comparatively studied, and contours of streamwise Reynolds stress and shear stress were examined to disclose the influence of coolant ejection on wake aerodynamic performance. Proper orthogonal decomposition (POD) ananlysis was applied to the velocity flowfileds to disclose the evolution of coherent structures and the mixing process between the cooling stream and mainstream. Large scale coherent structures shed from both the lip and lower plates were identified in low-order modes, indicating that these are the most energtic structures in the wake. Moreover, a “strip” structure was found in the unpaired third eigemode for lower blowing cases (VR = 0.5 and 0.75). By POD filtering with first six eigenmodes, the flapping motion of the separated shear layer from the upper shear layer of the lower plate was observed. Coherent strucutres were identified from the contours of swirling strength. It is speculated that the “strip” structure and the flapping of the seprarated shear layer is resuled from vortex merging, i.e., the merging of two clockwise-rotating vortical structures shed from the upper shear layers of the lip and lower plates.

Assessment of suboptimal control for turbulent skin friction reduction via resolvent analysis

This paper extends the resolvent analysis of McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382) to elucidate the drag reduction mechanisms for the suboptimal control laws proposed by Lee, Kim & Choi (J. Fluid Mech., vol. 358, 1998, pp. 245–258). Under the resolvent formulation, the turbulent velocity field is expressed as a linear superposition of propagating modes identified via a gain-based decomposition of the Navier–Stokes equations. This decomposition enables targeted analyses of the effects of suboptimal control on high-gain modes that serve as useful low-order models for dynamically important coherent structures such as the near-wall (NW) cycle or very-large-scale motions. The control laws generate blowing and suction at the wall that is proportional to the fluctuating streamwise (Case ST) or spanwise (Case SP) wall shear stress, with the magnitude of blowing and suction being a design parameter. It is shown that both Case ST and SP can suppress resolvent modes resembling the NW cycle. However, for Case ST, the analysis reveals that control leads to substantial amplification of flow structures that are long in the spanwise direction. Quantitative comparisons show that these predictions are broadly consistent with results obtained in previous direct numerical simulations. Further, the predicted changes in mode structure suggest that suboptimal control can be considered a modified version of opposition control. In addition to the study of modes resembling the NW cycle, this paper also considers modes of varying speed and wavelength to provide insight into the effects of suboptimal control across spectral space.

Condensation in Microchannels: Detailed Comparisons of Annular Laminar Flow Theory With Measurements

A relatively simple theory of annular laminar film condensation in microchannels, based on the Nusselt approximations for the condensate film and a theoretically based approximation for the vapor shear stress, has no empirical input and gives the local heat transfer coefficient and local quality for given vapor mass flux and vapor–surface temperature difference distribution along the channel. As well as streamwise vapor shear stress and gravity, the theory includes transverse (to the flow direction) surface tension-driven motion of the condensate film and gives a differential equation for the local (transverse and streamwise) condensate film thickness. As well as four transverse direction boundary conditions due to condensate surface curvature, a streamwise boundary condition is required as in the Nusselt theory. When the vapor is saturated or superheated at inlet, this is provided by the fact that the film thickness is zero around the channel perimeter at the position of onset on condensation. Most experimental investigations have been conducted with quality less than one at inlet and only approximate comparisons, discussed in earlier papers, can be made. The present paper is devoted to comparisons between theory and measurements in investigations where local heat flux and channel surface temperature were measured and the vapor at inlet was superheated. Measured and calculated heat transfer coefficients and their dependence on distance along the channel and on local quality are in surprisingly good agreement and suggest that the mode of condensation is, in fact, annular and laminar, at least where the quality is high.

Skin-friction drag reduction in turbulent channel flow based on streamwise shear control

It is known that stretching and intensification of a hairpin vortex by mean shear play an important role to create a hairpin vortex packet, which generates the large Reynolds shear stress associated with skin-friction drag in wall-bounded turbulent flows. In order to suppress the mean shear at the wall for high efficient drag reduction (DR), in the present study, we explore an active flow control concept using streamwise shear control (SSC) at the wall. The longitudinal control surface is periodically spanwise-arranged with no-control surface while varying the structural spacing, and an amplitude parameter for imposing the strength of the actuating streamwise velocity at the wall is introduced to further enhance the skin-friction DR. Significant DR is observed with an increase in the two parameters with an accompanying reduction of the Reynolds stresses and vorticity fluctuations, although a further increase in the parameters amplifies the turbulence activity in the near-wall region. In order to study the direct relationship between turbulent vortical structures and DR under the SSC, temporal evolution with initial eddies extracted by conditional averages for Reynolds-stress-maximizing Q2 events are examined. It is shown that the generation of new vortices is dramatically inhibited with an increase in the parameters throughout the flow, causing fewer vortices to be generated under the control. However, when the structural spacing is sufficiently large, the generation of new vortex is not suppressed over the no-control surface in the near-wall region, resulting in an increase of the second- and fourth-quadrant Reynolds shear stresses. Although strong actuating velocity intensifies the near-wall turbulence, the increase in the turbulence activity is attributed to the generation of counter-clockwise near-wall vortices by the increased vortex transport.

Similarity solutions for power-law and exponentially stretching plate motion with cross flow

Laminar boundary layers generated by power-law plate stretching with cross flows are studied. Only the stretching solutions of Banks [10] are considered, those being bounded by exponentially stretched plates. In one case the cross flow is generated by a uniform transverse stream far above the stretching plate or a wall moving with uniform transverse velocity. Two other cases deal with cross flows generated by transverse shearing motions of the surface. Possible two parameter solutions appear, but here we present two one-parameter families of cross flow solutions generated by transverse plate shearing motion. Streamwise and transverse shear stresses and velocity profiles are displayed in graphical form.

Reynolds Stress Structures in the Hybrid RANS/LES of a Planar Channel

The near-wall cycle of hybrid RANS/LES is studied by calculating the flow through a planar channel. Statistical results are commented on and related to instantaneous structures which are extracted from the flow field. The problematic structures in the artificial near-wall cycle, well known to be super-streaks, are identified and quantified. The calibration of such closures provides a correct mixing length argument in the logarithmic layer. However because of these overly intense streamwise streaks, it is impossible to simultaneously predict the Reynolds streamwise normal and shear stress components correctly. Further, because the location of the RANS-LES interface changes spatially and temporally, we see these structures are more free to move vertically and this further worsens statistical results.

Active control of turbulence for drag reduction based on the detection of near-wall streamwise vortices by wall information

The spatial relations between the measurable wall quantities (streamwise shear stress $$\tau _{\mathrm{w}{ x}}$$ , spanwise shear stress $$\tau _{\mathrm{w}{ z}}$$ , and pressure fluctuations $$p^\prime _\mathrm{w}$$ ) and the near-wall streamwise vortices (NWSV) are investigated via direct numerical simulation (DNS) databases of fully developed turbulent channel flow at a low Reynolds number. In the standard turbulent channel flow, the results show that all the wall measurable variables are closely associated with the NWSV. But after applying a stochastic interference, the relation based on $$\tau _{\mathrm{w}{ x}}$$ breaks down while the correlations based on $$p^\prime _\mathrm{w}$$ and $$\tau _{\mathrm{w}{ z}}$$ are still robust. Hence, two wall flow quantities based on $$p^\prime _\mathrm{w}$$ and $$\tau _{\mathrm{w}{ z}}$$ are proposed to detect the NWSV. As an application, two new control schemes are developed to suppress the near-wall vortical structures using the actuation of wall blowing/suction and obtain 16 % and 11 % drag reduction, respectively. The deformation and typical force curve of the mosquito leg when it is pressed onto a water surface.

The motion induced by the orthogonal stretching and shearing of a membrane beneath a quiescent fluid

The flow induced above an impermeable membrane undergoing orthogonal linear stretching and orthogonal linear shearing is investigated. For an exact solution of the Navier–Stokes equations, the orthogonal shearing motions must be related through the constant σ = γ δ, where γ and δ are the dimensionless streamwise and transverse shear rates, respectively. The resulting similarity reduction leads to three nonlinearly coupled ordinary differential equations governed by σ and the ratio of membrane stretch rates β. All possible solutions of these equations are found either numerically or, in special cases, analytically. Features of the σ = 0 solutions at β = 0 and asymptotically as β → ∞ are found to be in excellent agreement with numerical calculations. An aside calculation shows that orthogonal shearing in the absence of any plate stretching cannot exist. However, shearing in one coordinate direction is possible as long as the membrane stretches in at least one direction with the caveat that there exists uniform suction through a porous membrane.

Effect of upstream flow regime on street canyon flow mean turbulence statistics

The effect on the flow over a street canyon (lateral length/height, L/h $$=$$ 30) of using either 3D (cube) or 2D (rectangular block) upstream roughness arrays, of the same height as the canyon, has been studied for two streamwise canyon width to height aspect ratios (AR $$=$$ W/h) of 1 and 3, in a wind tunnel using Particle Image Velocimetry. The mean streamwise velocity, shear stress, turbulent intensities and length scales, together with shear layer boundaries and mass fluxes across the canyon opening are presented for different combinations of skimming and wake-interference regimes using different upstream roughness and canyon configurations. These results show significant trends with canyon aspect ratio and roughness array plan area packing density $$(\uplambda _{\mathrm{p}})$$ with respect to 2D and 3D configurations. The mean streamwise velocity for configurations of equal $$\uplambda _{\mathrm{p}}$$ is higher in 3D than 2D configurations, while the spatially averaged shear stress is shown to be lower in 3D than 2D configurations. The relative contribution to the total turbulent kinetic energy (TKE) demonstrates that staggered and aligned arrays or 2D and 3D arrays do not produce similar profiles of TKE. Finally, the integral length scale is larger in 2D cases than 3D cases of equal $$\uplambda _{\mathrm{p}}$$ . Urban air quality is a significant concern for human health. By investigating the influence of upstream roughness on canyon flow one can determine which cases or flow regimes in both the upstream roughness and canyon will result in decreased ventilation and negatively effect the air quality of urban areas. From the present work decreased ventilation occurs in the skimming flow regime and is lowest in the case of upstream 2D bar roughness with $$\uplambda _{\mathrm{p}} = 50~\%$$ and canyon AR $$=$$ 1.

The turbulence vorticity as a window to the physics of friction-drag reduction by oscillatory wall motion

DNS data for channel flow, subjected to spanwise (in-plane) wall oscillations at a friction Reynolds number of 1025, are used to examine the turbulence interactions that cause the observed substantial reduction in drag provoked by the forcing. Following a review of pertinent interactions between the forcing-induced unsteady Stokes strain and the Reynolds stresses, identified in previous work by the present authors, attention is focused on the equations governing the components of the enstrophy, with particular emphasis placed on the wall-normal and the spanwise components. The specific objective is to study the mechanisms by which the Stokes strain modifies the enstrophy field, and thus the turbulent stresses. As such, the present analysis sheds fresh light on the drag-reduction processes, illuminating the interactions from a different perspective than that analysed in previous work. The investigation focuses on the periodic rise and fall in the drag and phase-averaged properties during the actuation cycle at sub-optimal actuation conditions, in which case the drag oscillates by around ±2% around the time-averaged 20% drag-reduction margin. The results bring out the important role played by specific strain-related production terms in the enstrophy-component equations, and also identifies vortex tilting/stretching in regions of high skewness as being responsible for the observed strong increase in the spanwise enstrophy components during the drag-reduction phase. Simultaneously, the wall-normal enstrophy component, closely associated with near-wall streak intensity, diminishes, mainly as a result of a reduction in a production term that involves the correlation between wall-normal vorticity fluctuations and the spanwise derivative of wall-normal-velocity fluctuations, which pre-multiplies the streamwise shear strain.

Study of a stall cell using stereo particle image velocimetry

The structure of Stall Cells (SCs) on wings is analyzed on the basis of stereo particle image velocimetry measurements. All experiments regard a Reynolds number 0.87 × 106 flow around a rectangular wing with endplates and an aspect ratio of 2.0. The inherently unstable stall cell is stabilized by means of a localized spanwise disturbance. Velocity, vorticity, and Reynolds stress data above the wing and in the wake are presented and discussed, also in combination with Computational Fluid Dynamics data. The present study completes and clarifies the previously suggested models regarding the SC structure. The SC emerges in between the separation and trailing edge shear layer where three different types of vortices are identified: (a) the stall cell vortices that start normal to the wing surface and continue downstream aligned with the free stream, (b) the separation line vortex, and (c) the trailing edge line vortex that both run parallel to the wing trailing edge and grow significantly at the center of the stall cell. Analysis of the Reynolds stress data reveals high anisotropy. Concentration of high streamwise shear stress values is connected to the two shear layers and high cross shear Reynolds stresses are connected to vortex stretching. High normal Reynolds stress values are observed (a) in the separation but not in the trailing edge shear layer indicating the flapping of the former and (b) along the stall cell vortices indicating their wandering motion. The eddy viscosity based Reynolds averaged Navier-Stokes simulations are found in good qualitative agreement with the experiments in terms of the type and position of the identified vortex structures, an agreement which is linked to the correct trend in the predicted shear Reynolds stresses distributions. Quantitative deviations of the numerical results from the measurements are attributed to the isotropic definition of the turbulence model. Therefore, use of large eddy simulation is suggested for better prediction of the flow.

Numerical and experimental investigation of the near zone flow field in an array of confluent round jets

Numerical simulations, using three different turbulence models (i.e., standard k–ε, RNG k–ε and Reynolds Stress Model [RSM]) is performed in order to predict mean velocity field as well as turbulence characteristics in the near zone of a 6×6 in-line array of unconfined confluent round jets. The numerical results are compared with experimental data acquired by Particle Image Velocimetry (PIV).All the turbulence models used are able to reproduce the mean velocity field and the development of turbulent kinetic energy of the confluent round jets, but in general, the standard k–ε and RSM model show better agreement with experimental data than the RNG model. In terms of mean velocity the second-order closure model (RSM) is not found to be superior to the less advanced standard k–ε model in spite of the mean flow curvature present in the flow field. The RSM model, however, provides information on individual Reynolds stresses. RSM show satisfactory agreement of streamwise normal Reynolds stress and shear stress, but generally underpredicts the normal Reynolds stress in the spanwise direction.In comparison with plane twin jets, confluent round jets show a longer merging region. Within the merging region the maximum velocity of the confluent jets decay linearly. As the jets enter the combined region confluent jets have hardly any velocity decay, which leads to a higher maximum velocity for a combined confluent jet than a single round jet.The jet’s position within the configuration has a substantial impact on the velocity decay, length of the potential core, and the lateral displacement of the confluent jets. Side jets show faster velocity decay, shorter potential core and higher turbulence level compared to central jets. Side jets are also deformed and has a kidney shaped cross-section in the merging region. Corner jets interact less with neighboring jets compared to side jets, thereby extending the potential core and reducing the velocity decay in the merging region compared to side jets.