Diffusion_eqn_derivation_plus_fault_scarp_applications

Diffusion_eqn_derivation_plus_fault_scarp_applications -...

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Unformatted text preview: Mathematical Description of Processes Conservation of Mass [Sketch] α cos z h = α cos x s ∆ = ∆ Volume of sediment (V); Volume flux of soil (q v ) [x-component]; Depth of soil (h); Elevation soil surface (z); ∆ s; ∆ x; ∆ t Note for creep processes volume flux of soil includes the pore space (not volume flux of sediment), for sheetwash can define transport rate of soil or transport rate of sediment; the latter requires a porosity correction in mass balance equation. Volume of sediment in box (unit width) x z x z s h V ∆ = ∆ = ∆ = α α cos cos Change in volume of sediment in box: t q t q x z s h V out in v v ∆- ∆ = ∆ ∆ = ∆ ∆ = ∆ s q q t h in out v v ∆-- = ∆ ∆ ; x q q t z in out v v ∆-- = ∆ ∆ ; x q t z v ∂ ∂ ∂ ∂- = E. Soil Mantled Slopes: Steady State Forms Generic Transport Relationship Kirkby (1971): n m n m v S x k S kq q ′ = = ' Kirkby gives empirical evidence for m,n values for different hillslope processes. We will (later) examine evidence and derive values from theory, develop understanding of geologic, climatic and biotic control of various parameters....
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Diffusion_eqn_derivation_plus_fault_scarp_applications -...

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