Introduction:

Knowledge of the turbulence characteristics in open-channel flow is of importance in hydraulic engineering. Phenomena such as the flow resistance are linked to the velocity distribution and the characteristics of the turbulence structure. Kironoto and Graf (1995) studied turbulence structure of rough, non-uniform open channel flow and measured velocity, turbulence intensity and Reynolds stress profiles. They reported that the turbulence intensities and Reynolds stress decrease in accelerating and increase in decelerating flows (compared with the ones in uniform flow). Liu et al. (2004) presented a detailed study of the turbulence characteristics of hydraulic jumps at low Froude numbers (<3.3) using ADV. They noted that the ADV underestimates the mean velocity in bubbly two-phase flows. Yang et al. (2006) investigated the interaction of the vertical velocity v and the streamwise velocity u in a gradually accelerating flow. The analytical result shows that the non-zero vertical velocity causes the Reynolds shear stress profile to deviate from the conventional linear distribution in a 2-D flow. Islam et al. (2007) studied Turbulence characteristics downstream of a forced hydraulic jump using ADV. They founded that with the longitudinal distance Reynolds’ stresses decrease linearly and turbulence kinetic energy at each section decreases gradually. the results of Dey and Sarkar (2008) study showed that the rate of decay of jet velocity in a submerged jump increases with increase in bed roughness. Jesudhas et al. (2018) revealed that the expanding shear layer interacts with the free surface resulting in intense undulations and breaking up of the free surface. Most of the aforementioned investigations focused on the turbulent structures of the free or submerged jumps on smooth or rough bed in a rectangular channel. There is a considerable dearth of understanding of the effect of bed roughness and side walls divergence on the turbulent structures in submerged jumps. The present study aims to investigate turbulent characteristics of flow in submerged hydraulic jump over rough bed of stilling basin with divergent side walls.



Methods:

The experiments were conducted in a hydraulic laboratory of the University of Tabriz in a metal-glass horizontal rectangular flume. The facility had been relatively large-size channel 0.5 m wide, 0.5 m high and 10 m long. The sidewalls had been made of glass for observational purpose with 0.5 m high and 2.1 m long. The inlet flow conditions were controlled by a vertical sluice gate. In order to create a desirable submergence factor in the flume, the tailwater depth was controlled by an adjustable tailgate located at the downstream end of the flume. The upstream gate opening was fixed (2.1 cm) in all of the conducted experiments. To investigate the effect of roughness, discontinuous dissipative elements of lozenge shape with two heights (1.4 and 2.8 cm) were installed on the horizontal bed. Three glass physical models were built with divergence ratio (B = b1/b2) of 0.4, 0.6 and 1 (where b1 and b2 are the widths of the stilling basin in upstream and downstream of the hydraulic jump, respectively). During the jump, flow depths were measured using ultrasonic sensors Data Logic US30 with operation range of 10–100 cm and accuracy of ±0.1 mm that were mounted above the channel. Submergence ratio (S) which is defined as (〖(h〗_t-h_j)⁄(h_j)), whereas h_t= tailwater depth and h_j= conjugate depth of free jump. It was important that h_t was measured at the location where the free surface profile became parallel to the bed, and h_j was estimated from the well-known formula of the conjugate depth of free jump which is 0.5b(√(1+8〖Fr〗^2 )-1). The instantaneous velocity components were extracted by a SonTek acoustic Doppler velocimeter (ADV). The ADV measurements were taken in the central vertical axis, which is along the centerline of the flume in vertical lines at different streamwise distances from the sluice gate. By computing the values of signal correlation coefficient (COR) and signal-to-noise ratio (SNR) for each of the three ADV receivers, the accuracy and the quality of the collected data were controlled.



Results:

The flow field in submerged jump on horizontal channel with gradually divergent side walls and rough bed was measured by an acoustic Doppler velocimeter. The vertical distributions of time-averaged velocity components, turbulence intensity components, and Reynolds stresses at different streamwise distances from the sluice opening and the horizontal distribution of bed-shear stress have been presented. Presented charts provide a good understanding of the process of decay of jet velocity in submerged jumps on rough beds. The bed-shear stress decreases with increase in streamwise distance and increases with increase in bed roughness. The important observations of the turbulent structures of submerged jumps on channel with gradually divergent side walls and rough bed are summarized below:

With increase in bed roughness and decrease in side walls divergence, maximum values of u ̂ occurrence depth (compared to channel bed) would be increased.

Increasing bed roughness would results increase in the growth rate of boundary layer which produces more shear stress and more energy dissipation.

Variations of u^+ is more than v^+ which is causing more jet distribution ratio in horizontal axes vs vertical axes.

Increasing bed roughness and decreasing side walls divergence would increase 〖uv〗^+Reynolds’ stress and turbulence.

The length of fully developed zone reduces with increase in bed roughness and reduce in divergence ratio.

The bed-shear stress decreases with increase in streamwise distance and increases with increase in bed roughness and decrease in side walls divergence.