## OUCC Proceedings 11 (1983)## An Estimate of the Palaeodischarge of Cueva Culiembro, Asturias, Northern Spain |
OUCC Proceedings 11 Contents |

*Steven Gale*

The conditions under which scallops develop has been investigated by numerous
workers (see, for example, Allen, 1971; Goodchild and Ford, 1971; Blumberg and
Curl, 1974), a number of whom have demonstrated that scallop form is
hydraulically-controlled. Under conditions of uniform, steady-state flow, it
appears that scallops develop at a stable scallop Reynolds number (*Re**),
where

(1)

in which
=
mean boundary-shear velocity, λ = mean scallop wavelength; ρ_{f} = fluid
density; and μ = fluid dynamic viscosity. Published estimates of mean* Re**
range between 1000 and 3180 (Blumberg and Curl, 1974, 742; Thomas, 1979; Gale,
1984, Hsu et al., 1979), and all these values fall within the expected
laminar-turbulent transition phase of ca. 1000-3000. Consequently, Blumberg and
Curl's (1974, 742) estimate of *Re** = 2220 will be used in subsequent
calculations, since this lies approximately in the middle of the
laminar-turbulent transition range, and since it is perhaps the most reliable
estimate of the stable value of *Re**
.

was
established in Cueva Culiembro by measuring scallop wavelength along the maximum
length in a streamwise direction, taking the mean of 26 values. Having obtained
,
from which
may
be calculated using equation (1), assuming the conduit fluid to be pure water at
10°C,
the mean flow velocity (
)
in the conduit may be computed by use of Prandtl's universal
velocity-distribution equation (as modified by Curl (1974, 3) for use in
parallel-walled conduits):

(2)

in which *d *= distance between conduit walls; and B_{L} =
Prandtl's bed-roughness constant =9.4 for scalloped surfaces (Blumberg and Curl,
1974, 742-744).

Having obtained
,
and having estimated the conduit cross-section area (a) at the point of
measurement to be 15.3 m^{2}, conduit discharge (Q) may be calculated
from:

(3)

The results of these calculations are given below:

=
0.325 m (s
= 0.1074 m)

n = 26

a = 15.3 m^{2}

=
8.9x10~^{3} m s^{-1}
=
9.4x10^{-2 }m s^{-1}

Q = 1.4 ms^{-1}

The estimated discharge is of the expected order of magnitude and may be
compared with the measured discharge of 0.7 m^{3} s^{-1} under
low-flow conditions at the modern analogue of the cave, Fuente Culiembro.

**References**

* Sediment. Geol.* **5**,
165-388.

* J. Fluid Mech.* **65**, 735-751.

*Bull. Natn. Speleol. Soc.* **36**, 1-5.

*
J. Hydrol.* **70**, 309-327.

*. J. Geol. ***79**,
52-62.

*Rep. Iowa Inst. Hydraul.
Res. *

*Nature. Lond.* **277**, 281-283.