A model of the free surface dynamics of shallow turbulent flows

Figures & data

Figure 1 The streamwise spatial correlation function of the free surface elevation (Horoshenkov et al., 2013) for three steady flows with uniform average water depths: 40, 70 and 100 mm. Markers represent measured data; error bars show variation between three repeated measurements; solid line shows best fit according to Eq. (1)

Figure 2 Idealized free surface deformation, and a half period of the conceptualized oscillation of the surface deformation (omitting decay)

Figure 3 Schematic diagram of the effective volume of water influenced by the surface feature oscillation

Figure 4 The estimated oscillon frequency as a function of the RMS wave height, , and depth of influence factor, AAA

Figure 5 Flume overview (adapted from Horoshenkov, 2013).

Table 1 Measured hydraulic conditions for gravel bed flows

	Bed slope	Depth	Depth average velocity	Surface velocity	RMS wave height	Characteristic period	Froude number
Condition		(mm)	(m s^−1)	(m s^−1)	(mm)	(m)
1	0.004	40	0.41	0.53	0.34	0.11	0.66
2	0.004	50	0.50	0.58	0.40	0.15	0.71
3	0.004	60	0.55	0.61	0.45	0.17	0.71
4	0.004	70	0.60	0.67	0.57	0.20	0.72
5	0.004	80	0.64	0.70	0.74	0.24	0.72
6	0.004	90	0.69	0.78	0.86	0.27	0.73
7	0.004	100	0.74	0.82	0.97	0.30	0.75
8	0.003	50	0.36	0.47	0.36	0.12	0.51
9	0.003	60	0.41	0.51	0.43	0.16	0.54
10	0.003	70	0.47	0.56	0.50	0.16	0.57
11	0.003	80	0.52	0.61	0.58	0.19	0.59
12	0.003	90	0.57	0.65	0.67	0.22	0.61
13	0.002	60	0.32	0.45	0.23	0.10	0.42
14	0.002	70	0.35	0.50	0.36	0.13	0.43
15	0.002	80	0.40	0.55	0.43	0.15	0.45
16	0.001	70	0.26	0.42	0.11	0.07	0.31

Figure 6 Diagram of camera arrangements for flow visualization

Figure 7 A series of oscillatory free surface features that were observed advecting over space and time for flow conditions 1, 3, and 6. The white dashed lines indicate the surface velocity measured by the transit of a floating tracer

Figure 8 Measured data from all 16 flow conditions (markers), and modelled data (solid line) for surface oscillation frequency

Figure 9 Depth of influence factor, N, calculated for each flow condition

Figure 10 Oscillon frequency and bursting frequency (calculated according Nezu & Nakagawa, 1993) as a function of the flow depth

Horoshenkov, K. V., Nichols, A., Tait, S. J., & Maximov, G. A. (2013). The pattern of surface waves in a shallow free surface flow. Journal of Geophysical Research: Earth Surface, 118(3), 1864–1876. doi:10.1002/jgrf.20117

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Nezu, I., & Nakagawa, H. (1993). Turbulence in open-channel flows. Rotterdam: Balkema.

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