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.