# Turbulence Measurement of Vertical Dense Jets in Crossflow

^{*}

## Abstract

**:**

## 1. Introduction

_{r}F, where u

_{r}is the ratio of ambient to jet velocity and F is the jet densimetric Froude number. These complex phenomena make the jet difficult to numerically manage. Thanks to the extensive jet-concentration measurements, the authors obtained a detailed three-dimensional picture of the jet structure within the surrounding environmental flow. They indicated that, at low speeds (u

_{r}F < 0.5), the jet descending flow is strongly asymmetric and of complex hydrodynamic structure, experiencing a sharp curvature at its terminal rise height. At u

_{r}F = 0.9, a slight asymmetry occurs in the ascending region, whereas, an almost vertical symmetry of the jet was observed in the descending region. Recently, Ben Meftah et al. [18], analyzing the same data of the present study but focusing on the vortical structure of the jet, definitely confirmed the formation of counter-rotating vortex pair (CRVP) through both the ascending and descending jet regions, a topic of conjecture in many previous studies without any experimental demonstration.

_{r}F > 2), the jet undergoes rapid dispersion in the receiving water body by the effect of the ambient flow-turbulence. This significantly reduces the negative-buoyancy effect of the jet, leading to the disappearance of the descending region. At u

_{r}F > 2, the dense jet almost behaves as a momentum jet discharged into a crossflow [5,14,20,21].

## 2. Theoretical Analysis

_{r}, the jet is only weakly affected near the exit, penetrating uprightly into the crossflow before bending over. During the descent phase, the jet changes to a kind of negatively buoyant jet/plume; its velocity significantly reduces, the downward buoyant forces cause the discharge to gradually fall back and its trajectory impacts the bottom at a downstream distance x

_{i}. Near the bottom, the discharge laterally spreads in all directions, forming a bottom layer of spreading density current of thickness z

_{L}.

_{0}, which releases effluent of an initial density ρ

_{0}into a channel crossflow of fluid density ρ

_{a}, with ρ

_{a}< ρ

_{0}. The jet discharges at an initial velocity U

_{0}in a uniform channel/ambient flow of mean velocity U

_{a}. The effluent consists of saltwater solution of initial conductivity c

_{0}and that of the ambient flow is c

_{a}, c

_{a}< c

_{0}. Figure 2 also shows the jet trajectory. In Figure 2, z

_{t}indicates the maximum rise height of the jet trajectory occurred at the downstream distance x

_{t}. All the basic symbols and the system of coordinates are clearly indicated in Figure 2.

_{i}(=U, V, W) are the mean velocity components in the x

_{i}(=x, y, z) directions, in which x, y and z are the streamwise, the spanwise and the vertical directions, respectively, t is the time, μ is the dynamic viscosity, τ

_{ij}= −ρU

_{i}’U’

_{j}is the time-averaged stress of u’

_{i}u’

_{j}(t) over the length of the time series, p is the fluid pressure, g’ = [(ρ

_{0}− ρ)/ρ]g is the reduced gravity, g is the gravity acceleration, C is the mean fluid concentration, U’C’ is the time-averaged concentration transport by turbulent velocity fluctuations u’

_{i}c(t) over the length of the time series and K

_{i}(=K

_{x}, K

_{y}, K

_{z}) is the dispersion coefficient in the x

_{i}(=x, y, z) directions, respectively. The instantaneous velocity and concentration are defined as u

_{i}(t) = U

_{i}+ u

_{i}’(t) and c(t) = C + c’(t), where u

_{i}= (u, v, w) in the x, y and z directions, respectively, and u

_{i}’ = (u’, v’, w’) is its fluctuation, while c’ is the concentration fluctuation. The second member of the left-hand side of Equation (3) describe the advection of the solute in the three directions. The dispersion coefficient in the right-hand side of Equation (3) aggregate all the turbulent diffusion in the three directions.

_{i}’U

_{i}’ is the time-averaged turbulent kinetic energy of 1/2u

_{i}’u

_{i}’(t) over the length of the time series, U

_{i}’P’ is the time-averaged pressure diffusion of u

_{i}’p’(t), U

_{i}’k’ is the time-averaged turbulent transport of 1/2u

_{i}’u

_{i}’u

_{i}’(t) and D

_{i}is the turbulent diffusion coefficient.

_{i}, and the turbulent diffusion coefficients, D

_{i}, are strongly flow dependent, varying with the flow field, especially in the case of a dense jet discharged into a flowing current. These coefficients are properties of the flow. Therefore, the obvious question that arises for any numerical simulation of the dense jet is: what are the values of these coefficients in any particular situation and positions within the jet/ambient flows and how do they depend on the measured mean properties of the flow.

_{i}must be length squared per time, lending to a product of a velocity scale and a length scale, a physical meaningful expression of D

_{i}can be obtained as:

_{i}is a characteristic eddy length scale and (k)

^{1/2}is a turbulent velocity scale.

_{0}, its momentum flux M

_{0}and its buoyancy flux B

_{0}, defined as:

_{0}= πD

^{2}/4 is the jet source area. These fluxes can be combined with the ambient velocity, U

_{a}, to provide some relevant length scales, such as:

_{M}is the jet-to-plume length and measures the relative importance of the initial momentum flux against the buoyancy flux, differentiating the region of jet-like mixing dominance from the region of buoyancy dominance (for z/L

_{m}<< 1, as an example, the initial momentum effect will be dominant over the bouncy effec), l

_{m}is the jet-to-crossflow length scale and measures the relative importance of the initial excess momentum flux to the ambient flow-velocity (for z/l

_{m}<< 1, the jet velocity is so much higher than the ambient velocity and then a momentum jet will be vertically grown within the ambient flow), and l

_{Q}is the discharge length scale and indicates the distance over which the volume flux of the entrained ambient fluid becomes approximately equal to the initial volume flux (for z/l

_{Q}< 10, the jet diameter will have a direct effect on the flow characteristics) [19,32].

_{M}/l

_{Q}in Equation (10) is proportional to the jet densimetric Froude Number F as:

_{a}/U

_{c}, which is also equal to l

_{M}/l

_{m}. For round jet nozzle this ratio can be expressed as:

_{t}, x

_{i}, z

_{t}can therefore be written as:

_{M}is proportional to DF.

_{Q}<< l

_{M}(F >> 1), the dynamic effect of the source volume flux becomes negligible, and then F does not appear as an individual variable. After these assumptions Equation (13) becomes:

## 3. Experimental Method

^{3}, is used. The tank is equipped with four compressed air jets, installed on two levels at opposite positions, to mix the salt with the fresh water. The saltwater is pumped through a pipeline to the jet nozzle. This pipeline is equipped with a regulating valve and a magnetic flow meter to provide a well-defined flow discharge. The jet nozzle is of diameter D = 10 mm, vertically mounted in the flume center at a port height z

_{0}= 10 mm above the flume bottom.

_{r}F, are also illustrated.

## 4. Results and Discussion

#### 4.1. Jet Velocity Fields

_{a}. All of them were obtained in the plane of flow symmetry (y = 0). On Figure 4 and Figure 5, the jet axis positions, location of maximum jet velocity (velocity resultant of U and W), are indicated by horizontal arrows. Note that, due to the flow symmetry, the spainwise velocity, V, is theoretically expected to be null and therefore it has not any physical significance in this plane.

_{t}(Figure 2) and then it inclines downward, showing two distinct characteristic regions: an ascending region followed by a descending one [18]. Figure 4a and Figure 5a show that the trend of the vertical profile of U/U

_{a}gradually changes with the increase of x/D. In the ascending region (x/D < 12 and 15, respectively for R1 and R2), the U/U

_{a}-profiles show two characteristic maxima: an absolute maximum, located within the jet flow-field slightly above the jet axis, and a local maximum, appeared in the jet wake-like region.

_{a}, in the jet flow-field, always appears slightly above the jet axis. The magnitudes of both maxima gradually decrease as x/D increases, as clearly shown by the profiles of run R2. In the wake region, close to the jet source, the jet velocity U/U

_{a}experiences very small and negative values. At x/D = 3, as an example, U/U

_{a}≈ 0.05 and −0.1 with R1 and R2, respectively. This confirms the wake vortices formation at the inner part of the jet, as also mentioned in the previous study by Fric and Roshko [40]. For all the profiles at any position x/D, U/U

_{a}shows an almost constant value of order 1.2U

_{a}, over the flow depth starting from the jet outer-boundary up to the free-surface flow. These results are in complete agreement with those obtained by Ben Meftah et al. [14] and Sherif and Pletcher [39], reflecting simply the vertical distribution of U/U

_{a}in the ambient current without the jet effects. In the descending region, the two velocity-maxima are less pronounced, and the U/U

_{a}-profiles, at x/D > 30, resemble a classical vertical profile of mean velocity in an open channel flow.

_{a}-profiles are differently developed over the flow depth. They always experience a single peak below the jet axis. In the ascending region, W/U

_{a}shows positive values which gradually decrease as going further away from the jet source, similar to what happens with momentum jets in crossflows [14,39]. At the downstream distance x

_{t}(Figure 2), where the jet flow practically becomes horizontal, W/U

_{a}significantly reduces. In the descending region, W/U

_{a}shows negative values, indicating that the jet bends downward.

_{r}, leading to a simple power-law in the form of u

_{r}z/D = α(u

_{r}x/D)

^{β}, where α and β are coefficient determined experimentally.

_{r}and plotted in log-log scales. It is important to note here that these trajectories refer to the jet axis, as above defined. In addition to the data of the present study, the jet centerlines (as above defined) obtained by Gungor and Roberts [19] for a dense jet of five different values of u

_{r}F are also plotted. On Figure 6 we also plot some predicted and experimental trajectories obtained in previous studies [41,42,43] for momentum jets.

_{r}does not show similarity between the different runs. On the other hand, the examination of Figure 6b, indicates that the trajectories are not randomly scattered between them, but they show a kind of systematic gaps. The jet trajectories show a “manure fork-shape” of inclined “root”, following the power-law (dashed line on the figure) proposed by Margason [41], and parallel “tines”, as shown by the different trajectories. The distance between the “tines” seems proportional to u

_{r}F. When u

_{r}F increases, the jet trajectory linearly translates (along almost the dashed line on the figure) to the right. For comparable values of u

_{r}F, such as the case in runs R1 to R4 of the present study and in run DJV03 of Gungor and Roberts [19] (Table 1), the jet trajectories collapse onto an almost single curve. The absence of similarity between the jet trajectories at different values of u

_{r}F is related to the choice of the scaling mode, where the scaling with D/u

_{r}is not appropriate to represent all the trajectories by a typical profile.

_{r}F, as also observed in Figure 6b scaling the jet trajectory by D/u

_{r}. Once again, it can be noted that the scaling of the jet trajectories by DF is also not appropriate to represent the trajectories of different u

_{r}F-values by a typical profile.

_{r}F < 2, it was observed that the dense jet is characterized by an ascending and a descending regions [14,19] and its trajectory is fundamentally described by three characteristic length scales (Figure 2) x

_{i}, x

_{t}and z

_{t}(Table 1). In the present study, we will try to rescale the jet trajectory as z/z

_{t}vs. x/x

_{t}, in the ascending region, and z/z

_{t}vs. [1 + (x − x

_{t})/(x

_{i}− x

_{t})], in the descending region. Figure 7a illustrates both the rescaled jet axis, for all the experimental runs illustrated in Table 1 of the present study (except that of run R5 at u

_{r}F > 2, where the jet undergoes rapid dispersion by the effect of the ambient flow-turbulence), and the jet centerline for runs R1 and R2. The results of the present study are also compared to the centerline trajectories obtained by Gungor and Roberts [19]. Figure 7a clearly shows that all the jet trajectories (axis and centerline), of the present study and those of Gungor and Roberts [19], perfectly collapse onto a single profile. In the ascending region, at x/x

_{t}< 0.03, it can be noted a slight data scattering, due to the effect of the potential core region of the jet. The rescaling of the jet trajectories by x

_{t}, x

_{i}and z

_{t}leads to a typical trajectory for all experiments with complete independence of u

_{r}F (ranging almost between 0.2 and 1.1 in the present study). This typical trajectory is predictable by the following proposed closed-form expression:

_{i}, x

_{t}and z

_{t}can be found, based on the dimensional analysis as depicted in Equation (14). Figure 7b–d show, respectively, the normalized jet characteristic lengths x

_{i}/DF, x

_{t}/DF and z

_{t}/DF plotted versus u

_{r}F. Based on the experimental data of the present study and that of Gungor and Roberts [19], x

_{i}, x

_{t}and z

_{t}, for the jet centerline, can be approximately predicted by the following semi-empirical equations:

_{t}and increasing that of x

_{i}and of z

_{t}by almost 8%, since the jet axis appears slightly above the jet centerline.

_{r}F ranging almost between 0.2 and 1.1. This approach can be extended with vertical dense jets of u

_{r}F < 2 and for inclined dense jets, which is the subject of a future study. Indeed, such approach is very useful to many engineering and environmental applications such as the brine discharge from desalination plants or dense wastewater discharge.

#### 4.2. Turbulence Intensity Associated with the Jet Flow-Field

_{a}. Hereafter, we indicate by U’/U

_{a}, V’/U

_{a}and W’/U

_{a}, the streamwise, the spanwise and the vertical flow turbulence intensities, where U’, V’ and W’ are the standard deviation of the streamwise, the spanwise and the vertical flow velocity component fluctuations, respectively.

_{a}and W’/U

_{a}, at different downstream positions x/D of runs R1 and R2. The data refer to the plane of flow symmetry (y = 0). Due to the flow symmetry, the spanwise velocity is theoretically expected to be null and therefore V’ has not any physical significance in this plane. U’/U

_{a}shows the largest values in the ascending region. In this region, U’/U

_{a}almost shows an absolute peak near the jet axis. In general, according to previous studies, this peak is a distinct off-axis peak, where the turbulence undergoes a slight decrease at the jet axis. This behavior is less pronounced with the current profiles because the vertical profiles are not perfectly orthogonal to the jet axis. Figure 8a and Figure 9a show that U’/U

_{a}significantly increases in the jet flow-field as compared to that in the ambient flow-field (upper part of profiles). Moreover, it can be noted that U’/U

_{a}gradually decays as x/D increases. It shows a maximum value equal to 0.83, 0.93, 1.05 and 1.17 at x/D = 3, and 0.45, 0.47, 0.49 and 0.61at x/D = 12, for runs R1 to R4, respectively. These values clearly indicate that U’/U

_{a}increases as u

_{r}decreases. In the descending region, U’/U

_{a}continues to decrease monotonically. Far from jet source, at x/D > 27, U’/U

_{a}shows values comparable to those of the ambient flow-field.

_{a}take place in the jet flow-field. W’/U

_{a}also shows an absolute peak below the jet axis. In the ascending region, W’/U

_{a}decreases as x/D increases, attains minimum values at the maximum rise height position, as shown at x/D = 9 and 12, and then starts to slightly increase in the descending region with the increase of x/D. Outside the jet flow-field, independently of x/D, W’/U

_{a}for both runs R1 and R2 shows almost constant values of O(0.10) over the flow depth.

_{m}/U

_{a}and W’

_{m}/U

_{a}against x/x

_{t}, where the subscribed m indicates the maximum value of U’/U

_{a}and W’/U

_{a}on the vertical profiles of Figure 8 and Figure 9. Figure 10a shows that, for all runs, U’

_{m}/U

_{a}continuously decays as a function of x/x

_{t}, regardless its appearance in the ascending (x ≤ x

_{t}) or in the descending regions (x ≥ x

_{t}). Figure 10a indicates that U’

_{m}/U

_{a}decays more rapidly in the ascending region than in the descending region. As going further downstream, the decrease-rate of U’

_{m}/U

_{a}as a function of x/x

_{t}significantly reduces.

_{m}/U

_{a}behaves in a similar way as U’

_{m}/U

_{a}. It strongly decays in the ascending region, attaining a minim value at x = x

_{t}(Figure 2). In the descending region, however, W’

_{m}/U

_{a}shows a gradual increase as x/x

_{t}increases and then starts to decrease again, as clearly shown with R1 for x/x

_{t}> 2.5. The decay and rise of W’

_{m}/U

_{a}are related to the vertical-velocity behavior, which shows a decrease of its magnitude along the ascending region as x/D increases, attains almost null values at x

_{t}and then starts to increase along the descending region, as above discussed (Figure 4 and Figure 5).

_{a}

^{2}, at different downstream positions x/D from the jet exit. The data refer to runs R1 and R2. Figure 11 clearly highlights a significant increase of k/U

_{a}

^{2}within the jet flow-field. Outside the jet flow-field, k/U

_{a}

^{2}experiences almost constant values over the ambient flow-depth. It is of O(0.02) above the jet outer-boundary, and O(0.04) below the jet inner-boundary. Figure 11 indicates that the largest values of k/U

_{a}

^{2}take place below the jet axis, as indicated by the horizontal arrows on the figure. This indicates that the jet wake-region is a location of maximum turbulent energy production.

_{a}

^{2}monotonically decreases as x/D increases, reaching values comparable to those obtained in the ambient flow at considerable downstream positions x/D, as shown on Figure 11a at x/D = 42. In Figure 12 we plot the maximum values of k/U

_{a}

^{2}versus x/x

_{t}for runs R1 to R4. Figure 12 shows that k

_{m}/U

_{a}

^{2}strongly reduces along the ascending region as x/x

_{t}increases. It is reduced by up to 65% at x = x

_{t}as compared to its value at x/x

_{t}= 0.16. In the descending region, k

_{m}/U

_{a}

^{2}shows a very slight increase until x/x

_{t}= 2.5, and then returns to decrease again, but very gradually.

#### 4.3. Turbulent Length Scales and Dispersion Coefficients

_{i}is simply calculated as the integral time scale T

_{i}times the local time-averaged velocity U

_{i}, where T

_{i}is computed integrating the autocorrelation of the measured instantaneous flow velocities.

_{x}and L

_{z}, normalized by the jet diameter D, at different downstream position x/D. The data always refer to run R1 and R2, respectively. The profiles are presented in semi-logarithmic plot for a better visualization of the data. The most important observation from Figure 13 and Figure 14 is the significant spatial-variation of L

_{x}and L

_{z}in the jet flow-field, which is more pronounced in the ascending region. In the ambient flow-region, above the jet outer-boundary or at x/D = 42 (with small jet effect) in R1, L

_{x}and L

_{z}are nearly constant over the flow depth. They are, respectively, equal to almost 10D, a value of order the channel flow depth H, and 0.5D. This seems reasonable for the ambient flow where the vertical-velocity component is very small as compared with the streamwise component.

_{x}decrease as compared to that obtained in the ambient flow-field. L

_{x}shows a typical trend over the flow depth, as represented by the profile at x/D = 9 for both runs R1 and R2. This profile shows that L

_{x}reduces from a values of O(10D), above the jet outer-boundary, to a value of O(D) in the jet upper-region, increases at the jet axis and then again decreases to a scale of O(D) in the wake-like region. Figure 13 and Figure 14 indicate that the jet wake region is the location of minimum L

_{x}-scales. As x/D increases, the typical trend of L

_{x}gradually changes and disappears at large values of x/D, resembling a profile in the ambient flow-field. Figure 13 and Figure 14 indicate that L

_{z}behaves contrary to L

_{x}. It increases in the jet upper-region, attaining values of order 3 to 5D, decreases at the jet axis and then significantly increases in the wake-like region, as clearly shown in Figure 14b at x/D = 3 to 12.

^{½}L

_{x}/U

_{a}D and k

^{½}L

_{x}/U

_{a}D, order of magnitude of the normalized dispersion coefficients K

_{x}and K

_{z}, at different downstream position x/D, for runs R1 and R2. According to previous studies [31,44], the net dispersion coefficient can be generally determined as K

_{i}= αk

^{½}L

_{i}, where the scale factor α will differ between the vertical and horizontal diffusion and differ from a location to another within the jet flow-field. Following Nepf [44], the scale factor is of O(1). Figure 15 and Figure 16 show that K

_{x}and K

_{z}roughly behave like L

_{x}and L

_{z}, respectively. These observation support the assumption that turbulent diffusion is proportional to the turbulent eddies length-scales. The change in eddy scales controls the turbulent diffusion, such that the longitudinal dispersion K

_{x}is reduced in the jet flow-field, despite the fact that the turbulence intensity is increased, as shown in Figure 8, Figure 9 and Figure 11a. This finding is in good agreement with that observed by Nepf [44] for turbulent flow dispersion in vegetated channel. The decrease of the longitudinal dispersion K

_{x}, as compared to that of the ambient flow-field, is somewhat recovered by an increase of the vertical dispersion K

_{z}, increasing the jet width, and consequently the transversal dispersion K

_{y}could be also increased. As a conclusion, the results of the present study demonstrate that the turbulent dispersion of the jet flow is an anisotropic process. It is strongly influenced by the jet hydrodynamic structure itself. In the jet flow-field, the longitudinal dispersion K

_{x}decreases enough as compared to that in the ambient flow-field, promoting an increase of the vertical dispersion K

_{z}, and consequently an increase of the jet width occurs.

## 5. Conclusions

_{r}F < 2, the measured flow velocity fields show that the dense jet is characterized by two distinct regions: a rapidly ascending region and a gradually descending region. In the ascending region, the buoyancy effect is dominated by the jet momentum flux and the mixing is jet-like, analogously to momentum jets. In the descending region, the jet flow is buoyancy-driven and the mixing is plume-like.

_{i}, x

_{t}and z

_{t}(Figure 2), is proposed. This new rescaling rule enables all the trajectories to collapse onto a typical profile, independent of the current speed parameter u

_{r}F, leading to an empirical closed-form expression as depicted in Equation (15). By proposing empirical expressions of x

_{i}, x

_{t}and z

_{t}, the new scaling approach become very practical and easily applicable to predict the trajectory of any dense jet, of u

_{r}F ranging between 0.2 and 1.1, vertically discharged into a flowing current.

_{r}-ratio. The streamwise turbulence intensity shows a rapid decay along the ascending region and very gradually decay in the descending region. The vertical turbulence intensity, however, rapidly decays in the ascending region, attains a minimum value at x = x

_{t}, gradually rises in the beginning of the descending region and then undergoes again a decay as going further downstream. The time-averaged turbulent kinetic energy also shows a significant increase in the jet flow-field. The maximum production of turbulent kinetic energy takes place in the jet wake-region.

_{x}and K

_{z}follow those of the turbulent length scales L

_{x}and L

_{z}, respectively. The change in eddy scales controls the turbulent diffusion of the jet flow. In comparison with the ambient flow-field, K

_{x}shows an enough reduction in the jet flow-field, however, an increase of the vertical dispersion K

_{z}occurs, leading to the increase of the jet width.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**Schema of a brine discharge system at a desalination plant [2].

**Figure 2.**Definition sketch of the vertical dense jet in shallow water. The jet trajectory (jet axis or centerline) is indicated by the dashed-dot curve.

**Figure 3.**General sketch of the laboratory flume with the jet flow. For the sake of simplicity, only one vertical profile is qualitatively presented to show the sampling locations, the same sampling locations are repeated at different downstream locations x/D along the plane of flow symmetry.

**Figure 4.**Normalized velocity profiles in the plane of flow symmetry (y = 0) of run R1 at u

_{r}= 0.131 and u

_{r}F = 1.006: (

**a**) U/U

_{a}; (

**b**) W/U

_{a}. The horizontal arrow on the profiles indicate the position of the jet axis.

**Figure 5.**Normalized velocity profiles in the plane of flow symmetry (y = 0) of run R2 at u

_{r}= 0.109 and u

_{r}F = 1.071: (

**a**) U/U

_{a}; (

**b**) W/U

_{a}.

**Figure 6.**Normalized jet trajectory: (

**a**) ascending region; (

**b**) descending region. R1 to R5 represent the jet axis of the present study, DJV02 to DJV09 are the jet centerlines of Gungor and Roberts [19], M [41] is a similar power-law of momentum jet trajectory proposed by Margason [41], PB [42] is a similar power-law of momentum jet trajectory proposed by Pratte and Baines [42], and C [43] are experimental data of momentum jet trajectory obtained by Chochua et al. [43].

**Figure 7.**Jet trajectory analysis: (

**a**) scaling of jet trajectories based on the characteristic length scales x

_{i}, x

_{t}and z

_{t}. The solid red curve represents the solution of Equation (15); (

**b**) x

_{i}/DF versus u

_{r}F; (

**c**) x

_{t}/DF versus u

_{r}F; (

**d**) z

_{t}/DF versus u

_{r}F. The solid regression lines on (

**b**–

**d**) refer to the data of jet concentration of the present study and that of Gungor and Roberts [19].

**Figure 8.**Vertical profiles of the flow turbulence intensity at different downstream positions x/D along the plane of flow symmetry (y = 0) of run R1: (

**a**) U’/U

_{a}; (

**b**) W’/U

_{a}. The horizontal arrow on the profiles indicate the position of the jet axis.

**Figure 9.**Vertical profiles of the flow turbulence intensity at different downstream positions x/D along the plane of flow symmetry (y = 0) of run R2: (

**a**) U’/U

_{a}; (

**b**) W’/U

_{a}.

**Figure 10.**Decay/rise of the maximum turbulence intensity as a function of the downstream position x/x

_{t}: (

**a**) U’

_{m}/U

_{a}; (

**b**) W’

_{m}/U

_{a}.

**Figure 11.**Vertical profiles of the normalized time-averaged turbulent kinetic energy at different downstream positions x/D: (

**a**) run R1; (

**b**) run R2. The horizontal arrows on the profiles indicate the position of the jet axis.

**Figure 13.**Vertical profiles of the normalized turbulent length scales at different downstream positions x/D at the plane of flow symmetry (y = 0) of run R1: (

**a**) L

_{x}/D; (

**b**) L

_{z}/D. The horizontal arrow on the profiles indicate the position of the jet axis.

**Figure 14.**Vertical profiles of the normalized turbulent length scales at different downstream positions x/D at the plane of flow symmetry (y = 0) of run R2: (

**a**) L

_{x}/D; (

**b**) L

_{z}/D.

**Figure 15.**Trend of the turbulent dispersion coefficient K

_{x}and K

_{z}at different downstream positions x/D at the plane of flow symmetry (y = 0) of run R1: (

**a**) k

_{x}~ k

^{½}L

_{x}/U

_{a}D; (

**b**) k

_{z}~ k

^{½}L

_{z}/U

_{a}D. The horizontal arrow on the profiles indicate the position of the jet axis.

**Figure 16.**Trend of the turbulent dispersion coefficient K

_{x}and K

_{z}at different downstream positions x/D at the plane of flow symmetry (y = 0) of run R2: (

**a**) k

_{x}~ k

^{½}L

_{x}/U

_{a}D; (

**b**) k

_{z}~ k

^{½}L

_{z}/U

_{a}D.

Runs | H (cm) | T (°C) | U_{a} (cm/s) | U_{0} (cm/s) | u_{r} (-) | F (-) | u_{r}F (-) | x_{t}/(DF) (-) | x_{i}/(DF) (-) | z_{t}/(DF) (-) | ||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

^{1} Sal. | ^{2} Vel. | ^{1} Sal. | ^{2} Vel. | ^{1} Sal. | ^{2} Vel. | |||||||||

Present study | R1 | 36 | 16 | 4.17 | 31.83 | 0.131 | 7.7 | 1.006 | 1.28 | 1.52 | 4.16 | 4.29 | 1.51 | 1.57 |

R2 | 36 | 16 | 4.17 | 38.20 | 0.109 | 9.8 | 1.071 | 1.48 | 1.41 | 4.07 | 4.34 | 1.46 | 1.62 | |

R3 | 36 | 14 | 4.17 | 44.56 | 0.093 | 11.4 | 1.069 | NI | 1.68 | NI | 4.25 | NI | 1.59 | |

R4 | 36 | 14 | 4.17 | 50.93 | 0.082 | 13.1 | 1.069 | NI | 1.48 | NI | 4.27 | NI | 1.60 | |

R5 | 28 | 13 | 8.93 | 31.83 | 0.280 | 8.2 | 2.287 | NI | NI | NI | NI | NI | NI | |

Gungor and Roberts [19] | DJV01 | NI | NI | NI | NI | 0.025 | 20.9 | 0.522 | NI | NI | 2.87 | NI | NI | NI |

DJV02 | NI | NI | NI | NI | 0.025 | 20.1 | 0.511 | NI | NI | 3.01 | NI | NI | NI | |

DJV03 | NI | NI | NI | NI | 0.044 | 20.7 | 0.915 | NI | NI | 6.12 | NI | NI | NI | |

DJV04 | NI | NI | NI | NI | 0.010 | 23.0 | 0.233 | NI | NI | 1.16 | NI | NI | NI | |

DJV05 | NI | NI | NI | NI | 0.010 | 22.5 | 0.232 | NI | NI | 1.49 | NI | NI | NI | |

DJV06 | NI | NI | NI | NI | 0.036 | 19.0 | 0.692 | NI | NI | 5.24 | NI | NI | NI | |

DJV07 | NI | NI | NI | NI | 0.010 | 23.7 | 0.243 | NI | NI | 1.36 | NI | NI | NI | |

DJV08 | NI | NI | NI | NI | 0.017 | 21.6 | 0.373 | NI | NI | NI | NI | NI | NI | |

DJV09 | NI | NI | NI | NI | 0.010 | 21.5 | 0.220 | NI | NI | 1.32 | NI | NI | NI | |

DJV10 | NI | NI | NI | NI | 0.010 | 20.9 | 0.213 | NI | NI | 0.75 | NI | NI | NI |

^{1}Salinity;

^{2}Velocity. NI stands for not identified.

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**MDPI and ACS Style**

Ben Meftah, M.; Mossa, M.
Turbulence Measurement of Vertical Dense Jets in Crossflow. *Water* **2018**, *10*, 286.
https://doi.org/10.3390/w10030286

**AMA Style**

Ben Meftah M, Mossa M.
Turbulence Measurement of Vertical Dense Jets in Crossflow. *Water*. 2018; 10(3):286.
https://doi.org/10.3390/w10030286

**Chicago/Turabian Style**

Ben Meftah, Mouldi, and Michele Mossa.
2018. "Turbulence Measurement of Vertical Dense Jets in Crossflow" *Water* 10, no. 3: 286.
https://doi.org/10.3390/w10030286