In this work, three parameters have been utilized in representing the flow dynamics: the Turbulent Kinetic Energy, TKE, defined by Eq. 7, the Overall Flow Velocity, OV, defined by Eq. 8, and the Froude Number, Fr, defined by Eq. 9. TKE is half of the summed squared fluctuating velocity components, u', v', w', which provides the mean kinetic energy as a result of velocity fluctuations. It means that the overall flow velocity, OV, is taken to be the square root of the squared sum of the mean velocity components; thus, it becomes a full measure of flow magnitude. The Froude Number, Fr, is a dimensionless parameter indicative of the relative significance of inertial to gravitational forces and is computed as the ratio of OV to the square root of the product of gravitational acceleration, g, by characteristic flow depth, h.
These parameters comprehensively describe flow characteristics and thus allow for an in-depth analysis of turbulence, velocity distribution, and flow regimes. In this respect, these metrics embed valuable insights into the complex hydrodynamics of the groyne structure, underpinning a nuanced appreciation of the scouring processes and resultant impacts on the system's overall performance and stability (Wilcox, 1998).
$$\text{T}\text{K}\text{E} = (1/2) \times ({\text{u}{\prime }}^{2}+ {\text{v}{\prime }}^{2} + {\text{w}{\prime }}^{2})$$
7
Where:
\(\text{T}\text{K}\text{E}\) is the turbulent kinetic energy (m²/s²), u' is the fluctuating component of the horizontal velocity (m/s), v' is the fluctuating component of the vertical velocity (m/s), w' is the fluctuating component of the transverse velocity (m/s).
$$\text{O}\text{V}= \sqrt{({\text{u}{\prime }}^{2}+ {\text{v}{\prime }}^{2} + {\text{w}{\prime }}^{2})}$$
8
where:
\(\text{O}\text{V}\) is the overall flow velocity (m/s), u is the mean horizontal velocity (m/s), v is the mean vertical velocity (m/s), w is the mean transverse velocity (m/s).
$$\text{F}\text{r}= \text{O}\text{V} / \sqrt{(\text{g} \times \text{h})}$$
9
where:
Fr is the Froude number, OV is the overall flow velocity (m/s), g is the acceleration due to gravity (9.81 m/s²), h is the characteristic flow depth (m)
Figure 5 shows a computer-generated model of the Qezil Ozan River flow patterns with velocity distribution. Color coded contours indicate various flow velocities, where the warmer colors reflect higher and cooler colors reflect lower velocities. Streamlines are also superimposed on top to indicate the direction of water flow inside the river channel. It can be seen that the highest magnitude values of velocities are still confined to the main channel of the river because water can flow freely along the middle of the channel, having a minimal frictional resistance from the banks and bed of the river. On the contrary, the flow velocities decrease towards the riverbanks because of the frictional interaction of the flowing water with the banks that leads to loss of energy and consequent reduction in velocity. Local variations in flow velocity occur around obstacles or irregularities in the bed; accordingly, swirls or eddies in the streamline pattern represent turbulence and localized disruptions in flow. Knowing the flow velocity distribution, therefore, those areas in the river channel prone to erosion can be pointed out. The flow velocities at outer bends of the river channel are concentrated and may cause scouring, resulting in sediment removal and leading to bank erosion. Furthermore, narrow sections of flow and regions that include points downstream of obstacles are equally vulnerable to erosion due to the possibility that channel narrowing or obstacle presence can be the cause of a local gaining in speed, thus enhancing the potential erosive power of the water. Similarly, eddy formation assessment is found to create eddies, represented by swirling patterns in stream lines, formed in areas of flow separation and turbulence. The reason for these eddies is mostly related to the obstacles and irregularities that the bed of the river and its banks have, which disrupt the smooth flow of water and result in a change in direction and huge variations of flow velocities, creating swirls..
Figure 6 is showing TKE distribution and velocity vectors. Color-coded contours indicate the TKE varying between different values according to their intensity. Warmer colors show the higher and cooler colors the lower TKE values. Velocity vectors are further superimposed in the view, showing the direction and magnitude of the water flow in the river channel. Analysis of the TKE distribution indicates that the largest values concentrate near the obstacles or irregularities in the riverbed. This is due to an increase in turbulence and energy dissipation through a breakdown in smooth flow patterns. Large velocity gradients across the adjacent water layers form shear zones that also illustrate high TKE values, evidenced by bands of warm colors next to the riverbanks and at the transition between the main channel and near-bank flow. Generally, the deeper pools within the river channel hold lower TKE values because they are least affected by surface turbulence and energy dissipation. Based on the TKE distribution, what may be identified as locations prone to erosion would be those areas having high TKE, since vigorous turbulence and large shear stresses can dislodge sediments and cause the erosion of riverbanks and beds. Further, swallowing currents, turbulence, and energy dissipation occur in the downstream areas of obstacles and bends with high TKE, and thus localized erosion can also be expected. Eddy formation assessment has shown that eddies form at the sites of flow separation or wherever there is turbulence, as indicated by swirling patterns in velocity vectors. Eddies are usually attached to obstacles and irregularities on a riverbed, abrupt changes in flow direction, and high-shear zones whose dissimilar velocities of interaction create localized Turbulence and a rotational flow.
Figure 7 shows Computer-aided model of Qezil Ozan River flow patterns, Froude number distribution, and velocity vectors. From the Fr distribution analysis, it can be understood that most of the areas prone to erosion in the river channel are located at the outer bends of supercritical flow regions. In these areas, high flow velocities may scour the outer banks due to the formation of secondary currents, causing bank erosion. Moreover, downstream of obstacles, hydraulic jumps or standing waves arising at the transition from supercritical to subcritical flow can locally erode and displace sediments, creating scour holes. Also, only in the case of tectonically or topographically-induced narrowing or constrictions in the river channel or due to artificial obstacles, there might be a danger of localized increases of flow velocity and the associated gain in erosive energy, which would eventually lead to erosion. The swirling patterns of velocity vectors represent the simulation of eddy formations, indicating that the eddies obviously form at the site of flow separation and turbulence. In most cases, they are attached to obstacles and irregularities of the riverbed that disrupt the smooth flow of water to eventually form localized turbulence and a rotational flow. Moreover, sharp changes in flow direction can result in eddy formation at such features as bends or confluences due to the inertia of the flowing water, which resists a sudden change in direction. In addition, transition areas from supercritical to subcritical flow, most commonly bends or near obstacles, may further foster eddy formation as a result of confused flow patterns and turbulence connected with such areas.
Figure 8 shows two various flow patterns of Qezil Ozan River in the presence and absence of longitudinal groins, which are structures installed perpendicular to the shoreline for erosion control. Figure 8 (a) – without a groin; Fig. 8 (b) – after construction of six groins along the right bank of the river.
In Fig. 8 (a), the flow velocities are typically the smallest within the main channel, evidenced through dense streamlines, and the warmer color tones. As one goes towards the river banks, the velocities are smaller, as shown through the cooler color tones and thinner streamlines. Velocity variations come up around the bends with higher velocities on the outer bends and lower on the inner bends. In this case, outer bends, downstream of obstacles, and areas of flow constriction are all prone to erosion. Eddy formations are mainly related to the presence of obstacles and irregularities in the riverbed, sudden changes in flow direction, and zones of high shear. Whereas in Fig. 8 (b) the addition of groynes fundamentally changes the flows. Groynes create localized perturbations in the flow field precipitating velocity fluctuations along the channel. In general, flow velocities normally increase on the upstream side and decrease on the downstream side of a groyne. The velocities then gradually return to their original values with decreasing groyne influence. While groynes can induce sedimentation and hence reduce erosion on the upstream side, scour holes could form on the downstream side as a result of increases in flow velocity and ensuing turbulence. Furthermore, groynes are able to alter the erosion pattern along the riverbank and may cause erosion at locations, which would otherwise be less susceptible to erosion. In terms of eddy formation, groynes themselves introduce localized eddies through the disruption of flow around them, and downstream of the groynes, increased turbulence and eddies are formed as a result of these structures' complicated flow patterns. Further, it is possible to form shear zones at greater distances around groynes and in the area between the groynes and the riverbank, possibly leading to eddy formation.
Figure 9 shows diversifying flow patterns in Qezil Ozan River with an installed number of groynes on the right bank for erosion control. Figure 9 (a) shows the condition in the case of four groynes, and Fig. 9 (b) shows the effects with seven groynes installed. For both these cases, the highest flow velocities will be limited to the main channel, as indicated by the closely spaced streamlines and warmer color tones. It is observed that the velocities in flow increase at the upstream side of the groins and decrease at the downstream side, before increasing again as the effects of the groin weaken. However, as shown in Fig. 9 (b), the more intense localized disturbances in the flow due to the added groins, result in more dramatic changes in velocity along the channel than in the other case. In all such cases, scour holes can be expected to form downstream of groynes due to localized increases in flow velocity and turbulence. Similarly, upstream of groynes, sediment aggrading may be caused, which may reduce erosion in those areas. Consequently, this causes a deflection of the erosion distribution along the riverbank and probably causes erosion in regions that would not have been strong before. This effect would be more profound with six groynes in Fig. 9 (b) than four groynes in Fig. 9 (a). The modification or breaking of flow pattern within the vicinity of the groynes is considered due to eddy turbulence formation, with eddies most highly explicit in the downstream of groynes because of the complex flow pattern. Shear zones can be created around groynes and between the groynes and riverbank, that could create eddies in both cases. Nonetheless, the presence of six groins in Figure (b) might generate more energetic eddies and long-lasting ones than those four groins in Fig. 9 (a).