Self-similarity: Dimensional analysis, and intermediate asymptotics

1980 ◽  
Vol 44 (2) ◽  
pp. 267-272 ◽  
Author(s):  
G.I. Barenblatt
Keyword(s):  
Dimensional Analysis ◽  
Self Similarity ◽  
Intermediate Asymptotics

scholarly journals Dimensional analysis and stage-discharge relationship for weirs: a review

2017 ◽  
Vol 48 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Mohammad Bijankhan ◽  
Vito Ferro
Keyword(s):  
Dimensional Analysis ◽  
Review Paper ◽  
Hydraulic Structure ◽  
Drainage Network ◽  
Self Similarity ◽  
Weir Flow ◽  
Flow Motion ◽  
Approach Channel ◽  
Rating Curves ◽  
Flow Stage

Deducing the weir flow stage-discharge relationship is a classical hydraulic problem. In this regard Buckingham’s theorem of dimensional analysis can be used to find simple and accurate formulas to obtain the rating curves of different weir types. At first, in this review paper the rectangular weir that is a very common hydraulic structure is studied. It is indicated that the crest shape, approach channel width, obliquity (angle between the weir crest and the direction normal to the flow motion) and vertical inclination (pivot weir) are the key-parameters affecting the flow over the rectangular weirs. The flow over the triangular, labyrinth, parabolic, circular, elliptical, and W-weirs are also studied using dimensional analysis and incomplete self-similarity concept. For all mentioned weirs the stage-discharge relationships are presented and the application limits are discussed. The results of this paper can be used and implemented by the irrigation and drainage network designers to simplify the procedure of weir design.

scholarly journals Assessing, measuring and modelling erosion in calanchi areas: a review

2016 ◽  
Vol 47 (4) ◽  
pp. 181 ◽  
Author(s):  
Nathalie Almaru Caraballo-Arias ◽  
Vito Ferro
Keyword(s):  
Dimensional Analysis ◽  
Recent Literature ◽  
Similarity Theory ◽  
Rapid Development ◽  
The Self ◽  
Geometric Features ◽  
Self Similarity ◽  
Full Size ◽  
Space And Time ◽  
Geomorphic Processes

Calanchi are erosion landforms characterised by a heavily dissected terrain with steep, unvegetated slopes and channels with a dendritic pattern, which rapidly incise and extend headwards. Recent literature focusing on badland systems highlights their similarity with other larger fluvial landforms, stating that these behave as a full size laboratory, due to their rapid development in space and time and to the diversity of geomorphic processes involved. In this paper, a brief review of the most important results on badland research is firstly presented. Then, the morphometric similarity between calanchi and other erosion landforms is discussed. Finally, models quantitatively relating the volume of sediments eroded from calanchi landforms and a set of geometric features of their tributary areas, by exploiting the dimensional analysis and the self-similarity theory, are presented.

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