Flow, deformation, and transport - Physical Processes in Earth and Environmental Sciences - page 132

The maximum horizontal orbital velocity
of a shallow water wave of surface speed

c = ( gh ) 0.5 , is u max = H /2 h ( gh) 0.5 ,

where H = wave height and h = water
depth.

c d c d c d

Fig. 4.54 The pattern of oscillatory motion under progressive surface shallow water gravity waves engenders a to-and-fro motion to any sea or
lake bed. Should this bed be a loose boundary of sand, gravel, or silt then bed defects cause net sediment transport and planes of divergence
(d) to convergence (c). These gradually develop into symmetrical ripple-like bedforms.

Forward stroke

1 m for wave periods of 10 s. At some critical junction

the increasingly 3D bed ripples are planed off and a flat
sediment bed is formed under a thick layer of suspended
sediment.

Reverse stroke

4.10.2 Transport under combined surface shallow
water surface waves and tidal currents

The observations made on transport under progressive
waves are perfectly valid for environments like lakes, but in
the shallow ocean, tidal currents of varying magnitude and
direction are invariably superimposed. These currents may
cause net transport of suspended sediment put up into the
flow by near-bed oscillatory motions. For low energy con-
ditions over smooth flow boundaries there seems to be lit-
tle overall effect of the current on near-bed values of fluid
shear stress due to the waves alone. At some critical trans-
port stage rough-bed flows show increased near-bed
vertical turbulent stresses and suspended sediment con-
centrations: it seems that some sort of interaction is set up
between the bed roughness elements, the flow, and the
oscillations.

Fig. 4.55 Once developed the forward and reverse portions of the
to-and-fro oscillatory motion develop flow separation on the ripple
lee side and a “jet” of suspended sediment upstream.

ripple forms, termed wave-formed or oscillatory ripples .
The wavelength and height of these ripples, of order
decimeters to centimeters respectively, reflects in a simple
way the decay in the magnitude of the oscillating flow cell
transmitted from wave surface to bed. The oscillatory flow
induces alternate formation of closed “roller” vortices in
the lee of either side of ripple crests during each forward
and backward stroke of the cycle. As the oscillatory flow
increases further in magnitude, the “up” part of each half-
stroke sends a plume of suspended sediment into the water
column (Fig. 4.55) and gradually an equilibrium suspen-
sion layer is formed that increases in thickness and concen-
tration with increasing wave power. Experiments also
reveal that wave ripples in shallow water have an inherent
“wave-drift” landward (Fig. 4.56). The ripples themselves
continuously adjust to changing wave period during
storms (Fig. 4.57) and may reach wavelengths of up to

4.10.3 Transport and mixing under internal
progressive gravity waves

Internal progressive gravity waves have important roles in
ocean water mixing and the transport and erosion of sub-
strates (Section 6.4.4). Vertical mixing occurs as internal