Rough boundary

The sample area however is difficult to measure due to the air inclusions (holes) and the rough boundaries of the sample. Therefore we scanned the samples with a HP deskscan (ScanJet 3c) at highest resolution (600 dpi) to a pcx-file. Every pixel corresponds to a square of 42.3 pm X 42.3 pm. A determination of the surface area is possible by a summation of the number of black pixels (i.e. the pixels that are covered by the sample area). The error is due to the fact, that the CCD-elements of the scanner counts a pixel as black if more than 50 % (but not necessarily all) of the pixel area is covered by the sample. This happens only at the border of the sample. Therefore the error is as low as 0.5 %. 

Integral relations are common for the boundary layer approach and express the fundamental conservation laws for momentum, heat, and mass. Similar laws hold in easily penetrable roughness boundary layers. 

Cheng, H. and Castro, I. (2002) Near wall flow over urban-like roughness, Boundary-Layer Met. 104, 229-259. 

Bed roughness boundary layer and bed load deposition in vegetated area of a stream... 

Bed roughness boundary layer thickness in vegetated area... 

The bed roughness boundary layer thickness is subjected to the characteristics of vegetation and dimensional analysis propose the relation between OJh and XDh. By considering 0 may decrease with the vegetation density and tends to the flow depth with sufficiently disperse density, the following relation is proposed as a favorable formula to estimate the bed roughness boundary layer thickness (see Fig. 3). 

Velocity distribution in bed roughness boundary layer is investigated, and logarithmic law is expected to be applied. 

As for the calculated results, those employed the conventional resistance law and the presently proposed one for the vegetated area are compared with the measured data. The present model can describe the deposition profile with steeper downstream slope with faster migration because of the higher value of the shear stress and it shows better conformity with the experimental result. Thus it is concluded that introduction of the present proposal of the resistance law based on the concept of bed roughness boundary layer in vegetated area. 

The modification of the resistance law by introducing the bed roughness boundary layer brings less changes in flow calculation represented by depth and depth-averaged velocity but significant correction of shear velocity and subsequently sediment transport. The proposed modification will affect other aspects in fluvial processes, which will be clarified successively. 

In the vegetated area, the turbulence diffusivity exists only in the bed roughness boundary layer, and the kinematic eddy viscosity will be formulated as follows ... 

And, the layer-averaged concentrations, for roughness boundary layer and for the... 

In this paper, fundamental differences between vegetated and non-vegetated zones are discussed and in particular the characteristics of flow and sediment suspension are investigated based on the introduction of the concept of bed roughness boundary layer in the vegetated area. 

Jeon, H.S., M. Obana T. Tsujimoto. 2014. Bed roughness boundary layer and bed load transport in vegetated area. Proc. Conf. on Hydarulic Eng., Hong Kong. 

J. Nevard and J. B. KeUer, Homogenization of rough boundaries and interfaces. SIAM J. Appl. Math., 57,1660-1686, (1997). 

W. Jager and A. Mikelic, Couette flows over a rough boundary and drag reduction, Commun. Math. Phys., 232,429-455 [2003). 

Microstructure of porcelain enamel (a) cross-section of enamel-metal interface showing rough boundary (500x) (b) top view of bubble structure at metal-enamel interface provides... 

Figure 1.17 Experimental phase diagram of the Genamin TO2O/H2O/CUSO4 system La, lamellar Li, micellar L2, crystalline. The dashed lines are rough boundaries. Reprinted with permission from Longww/r 1999, 75, 3738-47 1999 American Chemical Society.

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