Exactly how sand moves in water is a matter that even the most complex mathematical models don't really explain. Einstein reportedly advised his son Hans not to pursue a career in sedimentary transport, because it was too complicated. -- John Seabrook, from the July 22, 2013 The New Yorker (page 45).

Some Open Questions

A) Particle/turbulence interaction

A.I) How is a steady, uniform turbulent shear flow modified by particles in suspensions over a range of different particle/fluid density ratios and particle volume fractions?

A.II) What are effective settling velocities of particles in steady, uniform, turbulent shear flows over a range of different density ratios and volume fractions?

A.III) What is the appropriate expression for the unsteady drag force on a particle in a ballistic trajectory through steady, uniform, turbulent shear flow?

A.IV) What are the appropriate forms for the stresses in the fluid and particle phases and the interactions between the particles and the fluid when the turbulent shear flow is unsteady and/or non-uniform?

A.V) How do known results for mono-disperse suspensions of spherical particles need to be modified to be applicable to poly-disperse suspensions of irregularly shaped particles?

A.VI) How do the dynamics of suspensions change as we move from the Boussinesq regime of small density differences in turbidity currents and sediment transport to the strongly non-Boussinesq regime in powder snow avalanches, Aeolian transport, and pyroclastic flows?

B) Particle/bed interaction

B.I) What are the detailed mechanisms by which particles and fluid interact at small scales during erosion and deposition, across a range of particle/fluid density ratios and particle volume fractions?

B.II) How can these mechanisms be scaled up to describe geophysical phenomena via effective boundary conditions in continuum formulations of turbulent mixtures?

B.III) What is the appropriate continuum description of a dense particle-laden fluid near a particle bed?

C) Morphodynamics

C.I) Are there common morphodynamic organizing principles active across the entire range of particle/fluid density ratios and particle volume fractions, and between gas- and liquid-mediated flows? If so, what are these principles?

C.II) How is a turbulent shear flow modified by the presence of bed forms in gases and in liquids?

C.III) Which mechanisms dominate the wavelength selection of bed forms in different parameter regimes?

C.IV) What can linear and nonlinear stability theory based on continuum theory teach us about wavelength selection?

C.V) What are the mechanisms that govern relaxation times and saturation lengths?

C.VI) What types of additional field measurements should be conducted in order to allow for the formulation and testing of simplified models?