The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

This review focuses on the applications of smoothed particle hydrodynamics (SPH) to incompressible or nearly incompressible flow. In the past 17 years, the range of applications has increased as researchers have realized the ability of SPH algorithms to handle complex physical problems. These include the disruption of free surfaces when a wave hits a rocky beach, multifluid problems that may involve the motion of rigid and elastic bodies, non-Newtonian fluids, virtual surgery, and chemical precipitation from fluids moving through fractured media. SPH provides a fascinating tool that has some of the properties of molecular dynamics while retaining the attributes of the macroscopic equations of continuum mechanics.

Smoothed Particle Hydrodynamics and Its Diverse Applications

Reciprocal interactions and adjustments between fluvial landforms and vegetation dynamics in river corridors: A review of complementary approaches

Field data are used to study the size distribution of bedload in paved gravel-bed streams. Similarity analysis yields the results that all grain size ranges are of approximately equal transportability when the critical condition for breaking the pavement is exceeded. This result is only approximately correct due to deviations from similarity. However, it is adequate to justify development of a method for calculating total bedload, which requires only the subpavement median grain size rather than the size distribution. A method for calculating bedload size distribution that accounts for deviation from similarity is also developed.

Closure of "Bedload and Size Distribution in Paved Gravel-Bed Streams"

http://www.vliz.be/imisdocs/publications/ocrd/267179.pdf

Erosion of mud/sand mixtures

A new 3D parallel SPH scheme for free surface flows

The non-stationary one-dimensional continuity equations of each granulometric class of sediments are written for the waterstream (suspended transport), the bottom layer (bedload transport) and the ...

A one-dimensional model for the transport of a sediment mixture in non-equilibrium conditions

Laboratory experiments are conducted to study the rheological behaviour of high-concentration granular-liquid mixtures. Steady uniform free-surface flows are obtained using a recirculating flume. Cases in which a loose deposit forms underneath the flow are contrasted with runs for which basal shear occurs along the flume bottom. The granular motions are observed through the channel sidewall, and analysed with recently developed Voronoi imaging methods. Depth profiles of mean velocity, solid concentration, and granular temperature are obtained, and complemented by stress estimates based on force balance considerations. These measurements are used to probe variations in rheological behaviour over depth, and to clarify the role of the granular temperature. The flows are found to evolve a stratified structure. Distinct sublayers are characterized by either frictional or collisional behaviour, and transitions between one and the other occur at values of the Stokes number which suggest that viscous effects intervene. The observed frictional behaviour is consistent with shear cell tests conducted at very low shear rates. On the other hand, the collisional data corroborate both the Bagnold description and the more recent kinetic theories of granular flows, provided that one accounts for the inertia of the interstitial liquid.

http://www2.ce.ntu.edu.tw/~mh/Publications/publications/ArmaniniCapartFraccarolloLarcher2005.pdf

Aronne Armanini

Papers

A new 3D parallel SPH scheme for free surface flows

A one-dimensional model for the transport of a sediment mixture in non-equilibrium conditions

Rheological stratification in experimental free-surface flows of granular-liquid mixtures

Two-dimensional simulation of debris flows in erodible channels

Flow resistance in open channel flows with sparsely distributed bushes