3.3 Reynolds shear stress

The distribution of the Reynolds shear stress in outer variables for flow over both smooth and rough beds is shown in Figure 8. Magnitude of the Reynolds shear stress reaches to the maximum at the location very close to the bed (y/d < 0.2) irrespective of the bed condition as one can note from Figure 8a. Effect of roughness on the Reynolds shear stress is very evident for lower two third of the depth of flow with the effect tapered off at the location closer to the surface. The peak for the flow over rough surfaces varies with the different type of roughness. As one can

Figure 8. Reynolds shear stress distribution for flow over different bed condition.

roughness can be seen for lower two third of the depth of flow with the effect tapered off at the location closer to the surface. Comparing the effect of various type of bed roughness on the vertical component of the turbulence intensity as one can see from Figure 7a that distributed roughness profile has the biggest deviation from smooth bed profile with continuous roughness and natural sand bed shows identical deviation for most the depth of the flow. For the location closer to the surface, the flow over natural sand bed shows higher magnitude of the vertical component of the turbulence intensity compared to any other surfaces. The variation of the vertical component of the turbulence intensity for flow with respect to the lower Reynolds number is shown in Figure 7b. The profile characteristics are very similar for the lower Reynolds number flow compared to the flow for higher Reynolds

Vertical turbulence intensity for flow over different bed condition.

Boundary Layer Flows - Theory, Applications and Numerical Methods

Figure 7.

60

note from Figure 8a that the flow over natural sand bed shows the highest peak compared to the similar peak for flow over continuous roughness and flow over distributed roughness. Immediately after reaching the peak the Reynolds shear stress for flow over both smooth and rough beds reduces but the trend of reduction is very different for the flow over smooth bed compared to the flow over rough surfaces. There is a sharp drop of the magnitude of the Reynolds shear stress for the rough beds compared to the smooth bed before a more constant drop towards the free surface. For the region further away from the near bed (y/d > 0.2), flow over distributed roughness shows generation of higher Reynolds shear compared to the other two rough beds where the generation of the Reynolds shear stress is very similar. As one can see in Figure 8a that the Reynolds shear stress falls below zero and becomes negative in the location close to the free surface for flow over both smooth and rough beds. The location of zero Reynolds shear stress is different for flow over smooth bed (at y/d � 0.5) compared to the flow over rough beds (y/d � 0.7). The location of negative Reynolds shear stress for different bed conditions are on the same location where dU/d∂y is negative as one can see in Figure 4. Few other researchers [25, 6, 26] found the visible effect of roughness on Reynolds shear stress for the depth of flow y/d ≈ 0.2–0.3 but the distinct effect of roughness for the present study can be seen penetrating deep into the flow y/d ≈ 0.7. In case of the study by [3] where the researcher did not find any effect of roughness (2 mm sand and 9 mm pebbles) on Reynolds shear stress compared to the flow over smooth bed. The sample size used for the tests by [3] were rather very small rendered to the unexpected conclusion. The variation of the Reynolds shear stress for flow with respect to the lower Reynolds number is shown in Figure 8b. The profile characteristics are very similar for the lower Reynolds number flow compared to the flow for higher Reynolds number with one of the exception is that the flow over continuous roughness and flow over distributed roughness shows the similar highest peak compared to the flow over natural sand bed. Another exception can be seen as much higher generation of Reynolds shear stress for the flow over distributed roughness for the region further away from the near bed (y/d > 0.2) followed by flow over natural sand bed and continuous roughness.

#### 3.4 Shear stress correlation coefficient

The distribution of the correlation coefficient of the Reynolds shear stress <sup>R</sup> <sup>¼</sup> �uv u � v for flow over both smooth and rough beds is shown in Figure 9. One can state that R is the expression of a normalized covariance where degree of similarity between the streamwise component of the turbulence intensity and the vertical component of the turbulence intensity is established. The range of the R as �1 ≤ R ≤ 1 where the value of R = 1 is the indication that the linear relationship between the streamwise component and the vertical component of the turbulence intensity is increasing. The value of R = �1 is the indication that the linear relationship between the streamwise component and the vertical component of the turbulence intensity is decreasing. Local statistics of R at a particular location can be an indication of the presence or absence of any flow structures. The effect of roughness on the variation of R is mixed compared to the smooth bed flow. As one can see from Figure 9a that at the location close to the bed (y < 0.3d) the magnitude of R is very similar for flow over smooth bed compared to the flow over distributed roughness with much higher value of R for the flow over continuous roughness and natural sand bed. The effect of roughness for the outer layer (y > 0.3d) is very clear with value of R is consistently higher for the flow over all three rough beds compared to the flow over smooth bed. One can also see from Figure 9a that the value

of R increases with the increasing distance from the bed and the trend reverses for the outer layer (y > 0.3d), indicating the changes of flow structure characteristics between the near-bed region and outer region. This observation is clearly different than the characteristics of R noted by [7, 5–6] where [7] called the distribution of R universal as they did not find any effect of roughness on the value of R. In Ref. [7] noted an existence of equilibrium region for 0.1 ≤ y/d ≤ 0.6 with a value of R = 0.4–0.5 in open-channels, pipes, and boundary layers, irrespective of whether the wall bed is smooth or rough. In the inner region and for the flow over smooth bed, [6] found a much lower value of R and noted indifference of R value for the flow over rough and smooth bed for y > 0.15d with the peak values floating to 0.35 0.02 range. Comparing the effect of various type of bed roughness on the correlation coefficient as one can see from Figure 9a that distributed roughness has

Distribution of correlation coefficient for flow over different bed condition.

Roughness Effects on Turbulence Characteristics in an Open Channel Flow

DOI: http://dx.doi.org/10.5772/intechopen.85990

Figure 9.

63

Roughness Effects on Turbulence Characteristics in an Open Channel Flow DOI: http://dx.doi.org/10.5772/intechopen.85990

Figure 9. Distribution of correlation coefficient for flow over different bed condition.

of R increases with the increasing distance from the bed and the trend reverses for the outer layer (y > 0.3d), indicating the changes of flow structure characteristics between the near-bed region and outer region. This observation is clearly different than the characteristics of R noted by [7, 5–6] where [7] called the distribution of R universal as they did not find any effect of roughness on the value of R. In Ref. [7] noted an existence of equilibrium region for 0.1 ≤ y/d ≤ 0.6 with a value of R = 0.4–0.5 in open-channels, pipes, and boundary layers, irrespective of whether the wall bed is smooth or rough. In the inner region and for the flow over smooth bed, [6] found a much lower value of R and noted indifference of R value for the flow over rough and smooth bed for y > 0.15d with the peak values floating to 0.35 0.02 range. Comparing the effect of various type of bed roughness on the correlation coefficient as one can see from Figure 9a that distributed roughness has

note from Figure 8a that the flow over natural sand bed shows the highest peak compared to the similar peak for flow over continuous roughness and flow over distributed roughness. Immediately after reaching the peak the Reynolds shear stress for flow over both smooth and rough beds reduces but the trend of reduction is very different for the flow over smooth bed compared to the flow over rough surfaces. There is a sharp drop of the magnitude of the Reynolds shear stress for the rough beds compared to the smooth bed before a more constant drop towards the free surface. For the region further away from the near bed (y/d > 0.2), flow over distributed roughness shows generation of higher Reynolds shear compared to the other two rough beds where the generation of the Reynolds shear stress is very similar. As one can see in Figure 8a that the Reynolds shear stress falls below zero and becomes negative in the location close to the free surface for flow over both smooth and rough beds. The location of zero Reynolds shear stress is different for flow over smooth bed (at y/d � 0.5) compared to the flow over rough beds (y/d � 0.7). The location of negative Reynolds shear stress for different bed conditions are on the same location where dU/d∂y is negative as one can see in Figure 4. Few other researchers [25, 6, 26] found the visible effect of roughness on Reynolds shear stress for the depth of flow y/d ≈ 0.2–0.3 but the distinct effect of roughness for the present study can be seen penetrating deep into the flow y/d ≈ 0.7. In case of the study by [3] where the researcher did not find any effect of roughness (2 mm sand and 9 mm pebbles) on Reynolds shear stress compared to the flow over smooth bed. The sample size used for the tests by [3] were rather very small rendered to the unexpected conclusion. The variation of the Reynolds shear stress for flow with respect to the lower Reynolds number is shown in Figure 8b. The profile characteristics are very similar for the lower Reynolds number flow compared to the flow for higher Reynolds number with one of the exception is that the flow over continuous roughness and flow over distributed roughness shows the similar highest peak compared to the flow over natural sand bed. Another exception can be seen as much higher generation of Reynolds shear stress for the flow over distributed roughness for the region further away from the near bed (y/d > 0.2) followed by flow over natural sand bed and

Boundary Layer Flows - Theory, Applications and Numerical Methods

The distribution of the correlation coefficient of the Reynolds shear stress

 for flow over both smooth and rough beds is shown in Figure 9. One can state that R is the expression of a normalized covariance where degree of similarity between the streamwise component of the turbulence intensity and the vertical component of the turbulence intensity is established. The range of the R as �1 ≤ R ≤ 1 where the value of R = 1 is the indication that the linear relationship between the streamwise component and the vertical component of the turbulence intensity is increasing. The value of R = �1 is the indication that the linear relationship between the streamwise component and the vertical component of the turbulence intensity is decreasing. Local statistics of R at a particular location can be an indication of the presence or absence of any flow structures. The effect of roughness on the variation of R is mixed compared to the smooth bed flow. As one can see from Figure 9a that at the location close to the bed (y < 0.3d) the magnitude of R is very similar for flow over smooth bed compared to the flow over distributed roughness with much higher value of R for the flow over continuous roughness and natural sand bed. The effect of roughness for the outer layer (y > 0.3d) is very clear with value of R is consistently higher for the flow over all three rough beds compared to the flow over smooth bed. One can also see from Figure 9a that the value

continuous roughness.

<sup>R</sup> <sup>¼</sup> �uv u � v

62

3.4 Shear stress correlation coefficient

the higher absolute value of R followed by continuous roughness and natural sand bed for the upper third of the flow. One can also note from Figure 9a that the value of R changes sign and become negative for flow over both smooth and rough bed surfaces at the locations where the Reynolds shear stress and dU/dy is negative. In the reference [6] also report similar observation. The value of R for the present study ranges from 0.25 < R < 0.5 and can be considered as small to medium correlation between the streamwise component and the vertical component of the turbulence intensity for all bed conditions and full depth of flow. The variation of the correlation coefficient of the Reynolds shear stress for flow over various bed surfaces with respect to the lower Reynolds number is shown in Figure 9b. The profile characteristics are very similar for the lower Reynolds number flow compared to the flow for higher Reynolds number with the exception that the profiles are more or less flatter for all bed conditions and bottom third of the flow. Another difference is that for the outer layer (y > 0.3d) flow the magnitude of R is higher for flow over natural sand bed compared to the flow over continuous roughness.

### 3.5 Higher-order moments

Velocity triple products u<sup>3</sup> , u<sup>2</sup>v, v<sup>3</sup> and v<sup>2</sup>u are very useful tools used by the researchers to extract valuable information of the flow structures and the distribution of different normalized velocity triple products are shown in Figure 10. To avoid any additional uncertainties by using computed quantities in relation to the scaling parameters, directly measured parameters of the maximum velocity (Ue) and the maximum flow depth (d) are used for normalizing all four velocity triple products. Streamwise flux of the turbulent kinetic energy u<sup>2</sup> and v2 is defined by u<sup>3</sup> and v<sup>2</sup>u respectively whereas vertical transport/diffusion of the turbulent kinetic energy u<sup>2</sup> and v2 is defined by u<sup>2</sup>v and v<sup>3</sup> respectively. Transportation in the direction normal to the bed for the Reynolds shear stress is also defined by v<sup>2</sup>u. Ejection-sweep cycle is considered to be the main turbulent motion contributing to the turbulent transport and velocity triple products are the tools used by the researchers to explain the ejection-sweep events effectively. Various bed conditions affect the variation of the different velocity triple products eventually provide insight about causing turbulent transport mechanisms change/modification.

For the flow condition over the smooth bed and very close to the bed, the magnitude of u<sup>3</sup> is negative and u<sup>2</sup>v is positive as one can note from Figure 10a and b indicating a fluid parcel slowly moving upward causing transportation of u momentum away from the bed representing an motion of ejection type. For the flow condition over the rough beds and very close to the bed, the magnitude of u<sup>3</sup> is positive with very high comparable value and u<sup>2</sup>v is negative as one can note from Figure 10a and b indicating a fast moving fluid parcel acting downwards causing transportation of u momentum towards the bed representing an motion of sweep type. Both triple products parameters of u<sup>3</sup> and u<sup>2</sup>v changes sign as one moves away from bed towards the free surface rendered changes of ejection-sweep cycle. The change of ejection-sweep cycle as one moving away from the bed is also observed by [27] and they had related this characteristic to the accompanying streaks of lowspeed produced by the rough bed conditions and modification of the longitudinal vortices. The magnitude of u<sup>3</sup> becomes more negative as one moves further away from the bed (y/d > 0.08) causing the sweeping events reduced substantially with the value of u<sup>3</sup> fluctuates but stays negative for the depth throughout. The effect of roughness is also very evident for the value of u3when compared with flow over smooth bed. The above mentioned differences between the flow over smooth bed

and rough beds are in complete opposite to the observation of [27–28] who did not observe much variation at distance y/d > 0.2. For flows over transverse rod roughness, large differences in the variation of u<sup>3</sup> were observed by [29] upto to the edge of the boundary layer. This difference as related by [3] is related to the lack of formation of long streamwise vortices near the rough wall. Comparing flow over rough bed conditions with flow over smooth bed, the mechanics of the entrainment of low momentum fluid at the wall differed as noted by [3]. The variation trend for of v<sup>3</sup> (Figure 10c) and u<sup>2</sup>v (Figure 10b) are very similar but there are exception in

Distribution of different velocity triple products for flow over different bed condition at Re 47,500.

Roughness Effects on Turbulence Characteristics in an Open Channel Flow

DOI: http://dx.doi.org/10.5772/intechopen.85990

Figure 10.

65

Roughness Effects on Turbulence Characteristics in an Open Channel Flow DOI: http://dx.doi.org/10.5772/intechopen.85990

Figure 10. Distribution of different velocity triple products for flow over different bed condition at Re 47,500.

and rough beds are in complete opposite to the observation of [27–28] who did not observe much variation at distance y/d > 0.2. For flows over transverse rod roughness, large differences in the variation of u<sup>3</sup> were observed by [29] upto to the edge of the boundary layer. This difference as related by [3] is related to the lack of formation of long streamwise vortices near the rough wall. Comparing flow over rough bed conditions with flow over smooth bed, the mechanics of the entrainment of low momentum fluid at the wall differed as noted by [3]. The variation trend for of v<sup>3</sup> (Figure 10c) and u<sup>2</sup>v (Figure 10b) are very similar but there are exception in

the higher absolute value of R followed by continuous roughness and natural sand bed for the upper third of the flow. One can also note from Figure 9a that the value of R changes sign and become negative for flow over both smooth and rough bed surfaces at the locations where the Reynolds shear stress and dU/dy is negative. In the reference [6] also report similar observation. The value of R for the present study ranges from 0.25 < R < 0.5 and can be considered as small to medium correlation between the streamwise component and the vertical component of the turbulence intensity for all bed conditions and full depth of flow. The variation of the correlation coefficient of the Reynolds shear stress for flow over various bed surfaces with respect to the lower Reynolds number is shown in Figure 9b. The profile characteristics are very similar for the lower Reynolds number flow compared to the flow for higher Reynolds number with the exception that the profiles are more or less flatter for all bed conditions and bottom third of the flow. Another difference is that for the outer layer (y > 0.3d) flow the magnitude of R is higher for flow over natural sand bed compared to the flow over continuous roughness.

Boundary Layer Flows - Theory, Applications and Numerical Methods

Velocity triple products u<sup>3</sup> , u<sup>2</sup>v, v<sup>3</sup> and v<sup>2</sup>u are very useful tools used by the researchers to extract valuable information of the flow structures and the distribution of different normalized velocity triple products are shown in Figure 10. To avoid any additional uncertainties by using computed quantities in relation to the scaling parameters, directly measured parameters of the maximum velocity (Ue) and the maximum flow depth (d) are used for normalizing all four velocity triple products. Streamwise flux of the turbulent kinetic energy u<sup>2</sup> and v2 is defined by u<sup>3</sup> and v<sup>2</sup>u respectively whereas vertical transport/diffusion of the turbulent kinetic energy u<sup>2</sup> and v2 is defined by u<sup>2</sup>v and v<sup>3</sup> respectively. Transportation in the direction normal to the bed for the Reynolds shear stress is also defined by v<sup>2</sup>u. Ejection-sweep cycle is considered to be the main turbulent motion contributing to the turbulent transport and velocity triple products are the tools used by the researchers to explain the ejection-sweep events effectively. Various bed conditions affect the variation of the different velocity triple products eventually provide insight about causing turbulent transport mechanisms change/modification. For the flow condition over the smooth bed and very close to the bed, the magnitude of u<sup>3</sup> is negative and u<sup>2</sup>v is positive as one can note from Figure 10a and b indicating a fluid parcel slowly moving upward causing transportation of u momentum away from the bed representing an motion of ejection type. For the flow condition over the rough beds and very close to the bed, the magnitude of u<sup>3</sup> is positive with very high comparable value and u<sup>2</sup>v is negative as one can note from Figure 10a and b indicating a fast moving fluid parcel acting downwards causing transportation of u momentum towards the bed representing an motion of sweep type. Both triple products parameters of u<sup>3</sup> and u<sup>2</sup>v changes sign as one moves away from bed towards the free surface rendered changes of ejection-sweep cycle. The change of ejection-sweep cycle as one moving away from the bed is also observed by [27] and they had related this characteristic to the accompanying streaks of lowspeed produced by the rough bed conditions and modification of the longitudinal vortices. The magnitude of u<sup>3</sup> becomes more negative as one moves further away from the bed (y/d > 0.08) causing the sweeping events reduced substantially with the value of u<sup>3</sup> fluctuates but stays negative for the depth throughout. The effect of roughness is also very evident for the value of u3when compared with flow over smooth bed. The above mentioned differences between the flow over smooth bed

3.5 Higher-order moments

64

sign that throughout the depth the v<sup>3</sup> is positive and much smaller magnitude (60%) than u2v. The trend is qualitatively similar if one compare v2u (Figure 10d) with u<sup>3</sup> (Figure 10a) with the exception that the magnitude of v<sup>3</sup> is about 60% less than that of u2v but the magnitude of v2u is much lower (about 20– 25%) comparing magnitude of u<sup>3</sup> . In Refs. [6, 8] in their open channel flow experiments and [27–28] in their turbulent boundary layer experiments had also noted a similar reduction. The lower turbulent intensity in vertical direction is mainly the reason for the differences between v<sup>3</sup> and u2v and v2u and u<sup>3</sup> . Comparing the magnitude of different velocity triple products for the open channel flow with the turbulent boundary layer flow, one can see the similarity as well as differences for magnitude and extent of the depth of the flow affected mainly in the outer layer by the roughness. As one can see from the Figure 10 that the local peak (maxima/ minima) for all normalized velocity triple products are in very similar location for the flow over smooth wall (≈0.26d). But the location of the peak (maxima/minima) for all normalized velocity triple products does not vary much with different type of roughness and occurs at a location of y/d ≈ 0.33 for different rough beds. The magnitude of various velocity triple products changes in the range of 200–300% as one can note it from Figure 10 when comparing the flow over the smooth bed to the flow over rough beds. The similar significant decrease/increase of the magnitude of various velocity triple products in the range of 300% was also noticed by [8] when comparing the flow over the smooth bed to the flow over dunes. With the exception of the magnitude of u<sup>3</sup> for the flow over distributed roughness, the magnitudes of the various velocity triple products approach zero for all smooth and rough surfaces as one moves from the location where the local maximum/minimum level achieved towards the free surface at y/d > 0.85.

The magnitude of various velocity triple product reaches near-zero at the location very close to the free surface irrespective of the bed surface conditions as one can note from Figure 10 which is a clear indication of significant reduction of turbulent activity at near free surface. There is another significant finding one can note from the same figure that the type of bed roughness does not affect the location of maximum/minimum of various velocity triple product although there is clear effect of roughness on the magnitude of various velocity triple products. Flow over distributed roughness shows higher magnitude of various velocity triple product comparing with flow over other rough beds followed by very similar magnitude for flow over continuous roughness and natural sand bed. Turbulent activity at the near bed (y/d < 0.1) location also seen to be dependent on bed surface conditions. Flow over smooth bed shows the ejection type activity near bed location whereas the flow over rough beds show the sweep type activity at the location close to the bed. Interpolating this scenario to the real life stream or river flow, one can clearly note the influence of strong ejection/sweeping motion of the fluid parcels to the resuspension/transport of the bed particles. Ejection type events are very evident throughout the depth of flow with the exception of the location very close to the bed with flow over smooth bed only where one can observe some sweeping type of event. Bed surface conditions clearly affect the strength of the ejection like events with distributed roughness again shows the highest strength compared to similar strength from continuous bed roughness and natural sand bed. Figure 11 shows the variation of same velocity triple products for the flow with respect to lower Reynolds number. The profile characteristics of all velocity triple products are very similar for flow with respect to lower Reynolds number compared to the flow with respect to higher Reynolds number. The differences in magnitude of various velocity triple products are seen to be reduced in the case of lower Reynolds number flow comparing the flow over smooth bed to the flow over continuous bed roughness and

natural sand bed. The value of u<sup>3</sup> is also reaches near-zero close to the free surfaces irrespective of the bed conditions representing a vanishing turbulent activity at that

Distribution of different velocity triple products for flow over different bed condition at Re � 31,000.

Roughness Effects on Turbulence Characteristics in an Open Channel Flow

DOI: http://dx.doi.org/10.5772/intechopen.85990

The distribution of the vertical flux of the turbulent kinetic energy described as

for a two-dimensional flow [8]

3.6 Vertical flux of the turbulent kinetic energy

Fkv and which is normally measured as 0:5 v<sup>3</sup> þ vu<sup>2</sup>

location.

67

Figure 11.

Roughness Effects on Turbulence Characteristics in an Open Channel Flow DOI: http://dx.doi.org/10.5772/intechopen.85990

Figure 11. Distribution of different velocity triple products for flow over different bed condition at Re � 31,000.

natural sand bed. The value of u<sup>3</sup> is also reaches near-zero close to the free surfaces irrespective of the bed conditions representing a vanishing turbulent activity at that location.

#### 3.6 Vertical flux of the turbulent kinetic energy

The distribution of the vertical flux of the turbulent kinetic energy described as Fkv and which is normally measured as 0:5 v<sup>3</sup> þ vu<sup>2</sup> for a two-dimensional flow [8]

sign that throughout the depth the v<sup>3</sup> is positive and much smaller magnitude

(Figure 10d) with u<sup>3</sup> (Figure 10a) with the exception that the magnitude of v<sup>3</sup> is about 60% less than that of u2v but the magnitude of v2u is much lower (about 20– 25%) comparing magnitude of u<sup>3</sup> . In Refs. [6, 8] in their open channel flow experiments and [27–28] in their turbulent boundary layer experiments had also noted a similar reduction. The lower turbulent intensity in vertical direction is mainly the reason for the differences between v<sup>3</sup> and u2v and v2u and u<sup>3</sup> . Comparing the magnitude of different velocity triple products for the open channel flow with the turbulent boundary layer flow, one can see the similarity as well as differences for magnitude and extent of the depth of the flow affected mainly in the outer layer by the roughness. As one can see from the Figure 10 that the local peak (maxima/ minima) for all normalized velocity triple products are in very similar location for the flow over smooth wall (≈0.26d). But the location of the peak (maxima/minima) for all normalized velocity triple products does not vary much with different type of roughness and occurs at a location of y/d ≈ 0.33 for different rough beds. The magnitude of various velocity triple products changes in the range of 200–300% as one can note it from Figure 10 when comparing the flow over the smooth bed to the flow over rough beds. The similar significant decrease/increase of the magnitude of various velocity triple products in the range of 300% was also noticed by [8] when comparing the flow over the smooth bed to the flow over dunes. With the exception of the magnitude of u<sup>3</sup> for the flow over distributed roughness, the magnitudes of the various velocity triple products approach zero for all smooth and rough surfaces as one moves from the location where the local maximum/minimum level achieved

The magnitude of various velocity triple product reaches near-zero at the location very close to the free surface irrespective of the bed surface conditions as one can note from Figure 10 which is a clear indication of significant reduction of turbulent activity at near free surface. There is another significant finding one can note from the same figure that the type of bed roughness does not affect the location of maximum/minimum of various velocity triple product although there is clear effect of roughness on the magnitude of various velocity triple products. Flow over distributed roughness shows higher magnitude of various velocity triple product comparing with flow over other rough beds followed by very similar magnitude for flow over continuous roughness and natural sand bed. Turbulent activity at the near bed (y/d < 0.1) location also seen to be dependent on bed surface conditions. Flow over smooth bed shows the ejection type activity near bed location whereas the flow over rough beds show the sweep type activity at the location close to the bed. Interpolating this scenario to the real life stream or river flow, one can clearly note the influence of strong ejection/sweeping motion of the fluid parcels to the resuspension/transport of the bed particles. Ejection type events are very evident throughout the depth of flow with the exception of the location very close to the bed with flow over smooth bed only where one can observe some sweeping type of event. Bed surface conditions clearly affect the strength of the ejection like events with distributed roughness again shows the highest strength compared to similar strength from continuous bed roughness and natural sand bed. Figure 11 shows the variation of same velocity triple products for the flow with respect to lower Reynolds number. The profile characteristics of all velocity triple products are very similar for flow with respect to lower Reynolds number compared to the flow with respect to higher Reynolds number. The differences in magnitude of various velocity triple products are seen to be reduced in the case of lower Reynolds number flow comparing the flow over smooth bed to the flow over continuous bed roughness and

(60%) than u2v. The trend is qualitatively similar if one compare v2u

Boundary Layer Flows - Theory, Applications and Numerical Methods

towards the free surface at y/d > 0.85.

66

is shown in Figure 12 in outer variables for the flow over both smooth and rough beds. The LDA used to measure the velocity component is two-dimensional and not possible to measure the third component of turbulent intensity. An approximate method as proposed by [30] is used to overcome this shortcoming and the coefficient is changed from 0.75 to 0.5. The effect of roughness is very evident for the transport of the turbulent kinetic energy in the vertical direction as one can see from Figure 12. The effect of roughness is not only confined for near bed but can be seen throughout the depth of flow. This observation is in direct conflict with the observation of [8] who in their tests with large-bottomed roughness did not visualize notable differences in profile for the vertical flux of the turbulent kinetic energy when comparing open channel flow over smooth bed and rough bed conditions.

In Ref. [6] noted that the location of the outer (larger) peak of Fkv is closer to the wall (albeit slightly) as the roughness effect increases. The maximum value of Fkv is also noted in Ref. [8] where they found it occurred near the bed for the flow over rib roughness. As one can note from Figure 12 that there are obvious effect of roughness on the variation of the vertical flux of the turbulent kinetic energy with the magnitude of the peak is very different for different type of rough surfaces but the location of the peak for all rough beds are more or less at around y/d 0.3. The differences in magnitude of the vertical flux of the turbulent kinetic energy when comparing between smooth bed flow and flow over rough beds is a clear indication that the strength of the vertical flux of the turbulent kinetic energy is very different for flow over different surfaces. The slope of the variation of Fkv is different between smooth and rough beds representing difference in loss or gain of turbulent kinetic energy resulted from turbulent diffusion. Flow over distributed roughness shows the highest deviation compared to the flow over smooth bed. The vertical flux of the turbulent kinetic energy approaches near zero value after a peak value around y/d = 1 at the location near free surface for all bed conditions. Location of reaching zero value for the vertical flux of the turbulent kinetic energy also varies with the bed surface condition with flow over different rough beds show zero values closer to the free surface compared to the flow over smooth bed. Figure 12b shows the variation of the vertical flux of the turbulent kinetic energy for the flow with respect to lower Reynolds number. The profile characteristics are very similar for flow with respect to lower Reynolds number compared to the flow with respect to higher Reynolds number. The differences in magnitude of Fkv is seen to be reduced in the case of lower Reynolds number flow comparing the flow over smooth bed to the flow over continuous bed roughness and natural sand bed.

Roughness Effects on Turbulence Characteristics in an Open Channel Flow

DOI: http://dx.doi.org/10.5772/intechopen.85990

In order to extract the magnitude of the Reynolds shear stress related to turbulent bursting events researchers often use quadrant decomposition as a convenient tool. A hydro dynamically unstable low-speed fluid particle lifted up from the surface because of the turbulent flow over a fixed bed can be swept away by comparatively high-speed fluid from the outer layer moving towards the bed surface. All different type of turbulent flow events that eventually contributed in the four different very important turbulent characteristics closer to the wall can be described by coupling streamwise and vertical fluctuating velocity components u and v based on their sign. Four different quadrants formed by using u and v with proper sign are related to four very important turbulent bursting events. Quadrant 1 represents the bursting effect called as outward interaction where the value of u is >0 and the value of v is >0. Quadrant 2 represents the bursting effect called as ejection where the value of u is <0 and the value of v is >0. Quadrant 3 represents the bursting effect called as inward interaction where the value of u is <0 and the value of v is <0. Quadrant 4 represents the bursting effect called as sweep where

The contributions from Q2 and Q4 events for different threshold values to the

Reynolds shear stress are shown in Figure 13 with higher Reynolds number (Re = 47,500). For the flow over rough walls and inclusive of all turbulent events, it was noted higher magnitude of Q2 and Q4 contributions as shown in Figure 13a and b compared to the flow over smooth wall for H = 0. The effect of roughness is not limited to the near-bed region but well progressed into the outer layer (y/d ≈ 0.7). A local peak can be seen at y/d = 0.1–0.2 for the Q2 and Q4 contributions as one progresses from the bed towards the free surface for the flow over all rough beds. The peak magnitudes of both of the events eventually reduced

3.7 Quadrant analysis

69

the value of u is >0 and the value of v is <0.

Figure 12. Distribution of vertical flux of the turbulent kinetic energy for flow over different bed condition.

#### Roughness Effects on Turbulence Characteristics in an Open Channel Flow DOI: http://dx.doi.org/10.5772/intechopen.85990

In Ref. [6] noted that the location of the outer (larger) peak of Fkv is closer to the wall (albeit slightly) as the roughness effect increases. The maximum value of Fkv is also noted in Ref. [8] where they found it occurred near the bed for the flow over rib roughness. As one can note from Figure 12 that there are obvious effect of roughness on the variation of the vertical flux of the turbulent kinetic energy with the magnitude of the peak is very different for different type of rough surfaces but the location of the peak for all rough beds are more or less at around y/d 0.3. The differences in magnitude of the vertical flux of the turbulent kinetic energy when comparing between smooth bed flow and flow over rough beds is a clear indication that the strength of the vertical flux of the turbulent kinetic energy is very different for flow over different surfaces. The slope of the variation of Fkv is different between smooth and rough beds representing difference in loss or gain of turbulent kinetic energy resulted from turbulent diffusion. Flow over distributed roughness shows the highest deviation compared to the flow over smooth bed. The vertical flux of the turbulent kinetic energy approaches near zero value after a peak value around y/d = 1 at the location near free surface for all bed conditions. Location of reaching zero value for the vertical flux of the turbulent kinetic energy also varies with the bed surface condition with flow over different rough beds show zero values closer to the free surface compared to the flow over smooth bed. Figure 12b shows the variation of the vertical flux of the turbulent kinetic energy for the flow with respect to lower Reynolds number. The profile characteristics are very similar for flow with respect to lower Reynolds number compared to the flow with respect to higher Reynolds number. The differences in magnitude of Fkv is seen to be reduced in the case of lower Reynolds number flow comparing the flow over smooth bed to the flow over continuous bed roughness and natural sand bed.
