Experimental Study on the formation of ripples on
an erodible bed
Ray Goldstein, Adriana Pesci, Juan Restrepo
Principal Investigators
Sarah ***, Galen ***, Joe Robles
Research Assistants
Introduction
The experimental work proposed here is designed
to help uncover fundamental granular dynamics and fluid mechanics underlying
the formation of periodic structures. Striking sedimentary structures
are found on the continental shelf, within river beds, at the beach, indeed,
wherever granular materials are driven by fluids. Two commonly occurring
patterns perpendicular to the fluid flow, known as sand ripples and sand
ridges, have intrigued researchers for nearly 200 years. Besides their
striking shape, there are more fundamental as well as practical reasons
why patterns in granular materials are the subject of significant research
efforts. At their most basic level, these patterns give clues to
the underlying dynamical properties of materials with features intermediate
between the fluid and solid states; granular matter has a finite yield
stress like a solid but may flow like a fluid. Applications range from
civil engineering studies of beach erosion to biological tracking of ocean
biota in moving sedimentary promontories to the study by geologists and
petroleum engineers of prehistoric lake and ocean beds.
At present, the general consensus among researchers
is that there is no universal agent of formation for all types of sand
structures. There is also consensus among us that our understanding of
sand formations driven by fluid flow is tentative, at best. There are many
models for the formation and evolution of oceanic sandbars, and there
is an equally long list of models for riverbed bars. None is entirely
satisfactory and most are quite difficult to test against field data. This
fact, coupled with our poor understanding of the collective dynamics of
sedimentary particles in a flow that is usually turbulent, makes this research
enterprise intriguing, challenging, and controversial.
There are five main phenomena we wish to study, as summarized below.
The onset of creeping motion:
In both the steady and oscillatory cases we wish to investigate systematically
the onset of grain motion as a function of the forcing parameters.
For oscillatory forcing, we expect to be able to investigate a resonance
phenomenon that will lower the onset conditions below that for steady forcing.
This resonance reflects dynamics at the single-particle level.
The instability to ripples:
Here the fundamental and as yet unsolved question is simply: What determines
the wavelength of the primary instability to a periodic pattern?
We wish to determine the scaling with grain size, fluid viscosity, and
buoyancy.
The nonlinear evolution of interacting ripples:
When ripples reach a finite amplitude there are nontrivial interactions
among them associated with hydrodynamic screening or "shadowing." Characterizing
the dependence of saturation amplitude on the forcing flow is one of the
key aspects of this experiment.
Drift velocity:
Informal observations of the oceanic setting and numerical studies
of models suggest that the ``drift velocity," or non-zero mean Lagrangian
flow, rather than the more convention Eulerian velocity, is the relevant
quantity to characterize large-scale forcing. We wish to investigate the
relevance of the drift velocity structure of the inviscid fluid flow, which
persists in the boundary layer, albeit with added small scale structure
and enhanced viscosity due to the turbulence present in the layer.
Vortex separation:
It is clear from direct observation that vortical structures on the
downstream side of ripples control much of the nonlinear development. Using
particle-tracking techniques we wish to study the details of the erosion
process driven by these circulating vortices.
OBSERVATIONS
One of the most reproducible quantities at any given fluid depth
is the angular frequency at which individual grains of sand become
dislodged from a flat bed and tumble on the surface for a short distance
before coming to rest again. This phenomenon, known in the literature
as surface creep, should be controlled by the shear. The shear itself
should be linear in the driving velocity, but its precise value as
a function of the height of the driving ring is difficult to determine
because it depends on the characteristics of the (highly complex) flow.
When surface creep first begins, isolated grains are dislodged from a flat
bed and travel on the order of 2 cm before coming to rest again. At higher
driving velocities, larger numbers of grains are tumbling over the surface.
At a critical driving velocity , ripples form in the surface, and the creeping
flux become larger where they occur.