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A reduced complexity model for dynamic similarity in obstructed shear flows
Author(s) -
Papke A.,
Battiato I.
Publication year - 2013
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1002/grl.50759
Subject(s) - dynamic similarity , scaling , statistical physics , mechanics , reynolds number , permeability (electromagnetism) , scaling law , shear (geology) , geology , mathematics , physics , turbulence , geometry , petrology , membrane , biology , genetics
Coupled flows through and over permeable media, also known as obstructed shear flows, are ubiquitous to many environmental systems at different scales, including aquatic flows over sediment beds, and atmospheric flows over crops and cities. Despite their differences, such flows exhibit strong dynamic similarities among systems and scales, as evidenced by the recent finding of empirical universal scaling laws correlating relevant length and velocity scales. We propose a reduced complexity model for obstructed shear channel flows, which couples Brinkman with Reynolds equations to describe the flow within and above the obstruction. We derive scaling laws by intermediate asymptotic analysis of a Darcy‐Brinkman type solution in the low permeability limit. The approach highlights the importance of the effective permeability of the obstruction as a critical parameter governing the system dynamical response. The model results are in good agreement with the scaling laws empirically calculated in other studies.