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Flows, Sediment and Bedforms 57
flow is subcritical and a wave can propagate upstream
because it is travelling faster than the flow. If the
Froude number is greater than one this indicates that
the flow is too fast for a wave to propagate upstream
and the flow is supercritical. In natural flows a sudden
change in the height of the surface of the flow, a
hydraulic jump, is seen at the transition from thin,
supercritical flow to thicker, subcritical flow.
Where the Froude number of a flow is close to one,
standing waves may temporarily form on the surface
of the water before steepening and breaking in an
upstream direction. Sand on the bed develops a bed-
form surface parallel to the standing wave, and as the
flow steepens sediment accumulates on the upstream
Fig. 4.19 Horizontal lamination in sandstone beds.
side of the bedform. These bedforms are called anti-
dunes, and, if preserved, antidune cross-bedding
in flow speed as the formation of flow separation is
would be stratification dipping upstream. However,
suppressed at higher velocities. These plane beds such preservation is rarely seen because as the wave
produce well-defined planar lamination with laminae breaks, the antidune bedform is often reworked, and
that are typically 5–20 grains thick (Bridge 1978) as the flow velocity subsequently drops the sediment
(Fig. 4.19). The bed surface is also marked by elongate is reworked into upper stage plane beds by subcritical
ridges a few grain diameters high separated by fur- flow. Well-documented occurrences of antidune
rows oriented parallel to the flow direction. This fea- cross-stratification are known from pyroclastic surge
ture is referred to as primary current lineation deposits (17.2.3), where high velocity flow is accom-
(often abbreviated to ‘pcl’) and it is formed by sweeps panied by very high rates of sedimentation (Schminke
within the viscous sublayer (Fig. 4.7) that push grains et al. 1973).
aside to form ridges a few grains high which lie par-
allel to the flow direction. The formation of sweeps is
subdued when the bed surface is rough and primary 4.3.6 Bedform stability diagram
current lineation is therefore less well defined in coar-
ser sands. Primary current lineation is seen on the
The relationship between the grain size of the sedi-
surfaces of planar beds as parallel lines of main grains
ment and the flow velocity is summarised on
which form very slight ridges, and may often be
Fig. 4.20. This bedform stability diagram indic-
rather indistinct.
ates the bedform that will occur for a given grain
size and velocity and has been constructed from
experimental data (modified from Southard 1991,
4.3.5 Supercritical flow and Allen 1997). It should be noted that the upper
boundary of the ripple field is sharp, but the other
Flow may be considered to be subcritical, often with boundaries between the fields are gradational and
a smooth water surface, or supercritical, with an
there is an overlap where either of two bedforms
uneven surface of wave crests and troughs. These
may be stable. Note also that the scales are logarith-
flow states relate to a parameter, the Froude number
mic on both axes. Two general flow regimes are
(Fr), which is a relationship between the flow velocity
recognised: a lower flow regime in which ripples,
(y) and the flow depth (h), with ‘g’ the acceleration
dunes and lower plane beds are stable and an upper
due to gravity:
flow regime where plane beds and antidunes form.
p Flow in the lower flow regime is always subcritical
Fr ¼ y= g h
and the change to supercritical flow lies within the
The Froude number can be considered to be a ratio of antidune field.
the flow velocity to the velocity of a wave in the flow The fields in the bedform stability diagram in
(Leeder 1999). When the value is less than one, the Fig. 4.20 are for a certain water depth (25 to 40 cm)