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Distribution of resistive body‐force in curved free‐surface flow
Author(s) -
Sivakumaran N. S.,
Dressler R. F.,
Brosowski B.
Publication year - 1986
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670080132
Subject(s) - mechanics , body force , resistive touchscreen , boundary layer , mathematics , external flow , boundary value problem , wedge (geometry) , geometry , flow (mathematics) , potential flow , open channel flow , classical mechanics , mathematical analysis , physics , electrical engineering , engineering
The customary procedure for including resistive effects in turbulent hydraulic and stratified atmospheric flows is to integrate the empirically‐known boundary shears over the entire wetted boundary of a thin fluid slab. A resistive body‐force is then assumed to exist everywhere in each slab to replace the boundary shearing force. For the classical Saint‐Venant model, this body‐force can be shown to have a constant distribution in the vertical direction, and therefore can be evaluated for use in the momentum differential equation. In the newer Dressler theory, however, for unsteady flow over curved beds, it is proved here that a constant body‐force distribution is not possible. We determine its variable distribution and its magnitude for use in the curved‐flow equations. This vasriable distribution acts to produce an equal resultant in every thin layer of fluid parallel to the bed in an angular wedge over the curved channel bed. The new curved‐flow equations are therefore extended to include resistive effects.