l2 mass mom cons 沉积地质学.pdfVIP

Coordinate System All descriptions of fluid and sediment transport will be referenced to the following orthogonal coordinate system. In this system, x refers to the streamwise or down-slope direction, y refers to the cross-stream or cross-slope direction, and z refers to the vertical direction. The fluid velocity component in the x direction will be referred to as u, the fluid velocity component in the y direction will be referred to as v, and the component in the z direction is w. A subscript s will be added to each velocity component to distinguish the velocity of the sediment grains from the velocity of the fluid. Vector Notation X = X = x + y + z ~ i U = U = u + v + w ~ i Reference Frame h = depth of flow Figure by MIT OCW. The Erosion Equation is derived by integrating the expression for mass conservation through the entire depth of the flow and applying the following boundary conditions….. ε on the top side of the water surface = 0 s u on the under side of the sediment bed = 0 s ∂η 1 ⎛ ∂ ⎞ 1 ⎛⎜⎛⎜∂qs ∂qsy ∂qs ⎞⎟ ∂V ⎞⎟ − ⎜∇⋅ + Vs ⎟ − x + + z + s ∂t ε ⎜⎝ qs ∂t ⎠⎟ ε ⎜⎜⎜⎜ ∂x ∂y ∂z ⎟⎟ ∂t ⎟⎟ ~