Understanding fish-hydrodynamic interactions within Cylindrical Bristle Cluster arrays to improve passage over sloped weirs

Figures & data

Figure 1. Different wake overlap states, from full overlap to no overlap, for spacing (S_c) to diameter (D) ratios ranging from less than 1.2 to greater than 4 (Nicolle 2009).

Figure 2. (a) Plan and (b) section of the experimental setup used to quantify passage of roach (Rutilus rutilus) at a model gauging weir with CBC array installed. The weir and extent of the experimental area are shown (dimensions in mm).

Table 1. Configurations tested during experimentation and their diameters (D), diagonal spacings (S_d), slope (S_o), temperature (T), average water depth (y), velocity (V) and Froude number (Fr), percentage of “low” velocity area within the array (% LVA) and lateral spacing (c/c)/diameter ratio (S_c/D).

	Treatments
	High D—Low Sd	Intermediate D—Low Sd	Low D—Low Sd	High D—High Sd	Intermediate D—High Sd	Low D—High Sd
D	0.07	0.05	0.03	0.07	0.05	0.03
Sd	0.10	0.10	0.10	0.15	0.15	0.15
So	0.25	0.22	0.19	0.17	0.17	0.17
T	16.94 ± 1.02	17.94 ± 0.77	19.31 ± 0.50	19.01 ± 0.38	17.74 ± 0.73	18.26 ± 0.55
y (±SD)	0.08 ± 0.01	0.07 ± 0.005	0.07 ± 0.005	0.08 ± 0.013	0.07 ± 0.008	0.07 ± 0.010
V (±SD)	1.18 ± 0.15	1.23 ± 0.14	1.24 ± 0.19	1.20 ± 0.22	1.24 ± 0.24	1.28 ± 0.27
Fr	1.37	1.54	1.56	1.36	1.54	1.60
%LVA	57	49	29	45	32	24
Sc /D	3.4	4.2	6.1	4.6	6.0	8.3

Figure 3. Representative (Intermediate D—High S_d treatment) water velocity profile (m s⁻¹) within a CBC array from the crest (0) to the top of the hydraulic jump. Flow direction is denoted by the black arrow, while black dots and purple crosses indicate locations of the clusters (not actual size) and velocity measurements, respectively. The colour map was created by interpolating between these points.

Table 2. Metrics used to determine the influence of cluster spacing and diameter, and thus wake width and length, on passage efficiency and swimming behaviour of roach (Rutilus rutilus) when navigating through CBC arrays installed on an experimental sloped weir.

Metric	Definition
Passage efficiency	Number of fish that passed the weir as a percentage of those that attempted. An attempt occurred when the whole body length of the fish passed upstream of the hydraulic jump, located at the convergence of high velocity flow down the face and the lower velocity water at the base of the weir, forming 1.67 m from the weir crest. A pass occurred when the whole body length of the fish passed the weir crest.
Swim path length	Calculated as: ${\Sigma }_{n=1}^N\sqrt{{({\mathrm{x}}_{\mathrm{n}+1}-{\mathrm{x}}_{\mathrm{n}})}^2+{({\mathrm{y}}_{\mathrm{n}+1}-{\mathrm{y}}_{\mathrm{n}})}^2}$ where x and y are swim path co-ordinates along the x and y axes, n denotes the time step and N the number of time steps.
Time to pass	Time from when fish head first appears above the hydraulic jump to when the fish head passes over the weir crest.
Swimming behaviour	Categorised as either: 1. Zigzagging: where fish zigzagged between two lines of clusters when passing through the array 2. Wall association: where fish only used the route between the side wall and the first line of bristle clusters 3. Combinations of 1, 2 and lateral traverse: For example, where a fish traversed laterally to another cluster before returning to zigzagging, or zigzagging between more than two lines of clusters.
Use of low velocity regions	Expressed as a percentage, the duration of total time spent occupying a low velocity region that extends for one cluster width between an upstream cluster to the next one downstream.

Figure 4. Passage efficiency for each treatment tested is depicted, where passage efficiency is quantified as the number of roach that successfully passed an experimental gauging weir, expressed as a percentage of those that attempted for different array arrangements. The six alternative treatments based on characteristics of a CBC array, are High D—Low S_d (HDLS), Intermediate D—Low S_d (IDLS), Low D—Low S_d (LDLS), High D—High S_d (HDHS), Intermediate D—High S_d (IDHS), Low D—High S_d (LDHS). S_d is the diagonal spacing between clusters, S_c is the lateral spacing between clusters (c/c) and D is cluster diameter in metres. The dashed diagonal line depicts the trend line between passage efficiency and the spacing to diameter ratio.

Table 3. Numbers of roach that attempted, passed and failed, and corresponding passage efficiency for each of the treatments tested.

Treatment	High D—Low Sd	Intermediate D—Low Sd	Low D—Low Sd	High D—High Sd	Intermediate D—High Sd	Low D—High Sd
	D = 0.07 Sd = 0.10	D = 0.05 Sd = 0.10	D = 0.03 Sd = 0.10	D = 0.07 Sd = 0.15	D = 0.05 Sd = 0.15	D = 0.03 Sd = 0.15
Attempts	14	13	5	7	8	4
Pass	12	9	2	5	1	0
Fail	2	4	3	2	7	4
Passage efficiency (%)	85.7	69.2	40.0	71.4	12.5	0

Figure 5. Examples of swim paths exhibited by roach as they ascended an experimental gauging weir with CBCs installed on the face. The crosses indicate swimming behaviour paths for zigzagging (a) wall association (b) and combination including lateral traversing (c). The arrow indicates the direction of flow.

Nicolle A. 2009. Flow through and around groups of bodies [thesis]. University College London.

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