Model help:Sedflux: Difference between revisions
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6) Sediment flux within the near-shore zone (depth less than h<sub>c</sub>) | 6) Sediment flux within the near-shore zone (depth less than h<sub>c</sub>) | ||
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|width=500px|<math> q_{s} = k_{c} | |width=500px|<math> q_{s} = k_{c} \underline{x}^ \left ( 1 - m \right ) {\frac{dh}{dx}} </math> | ||
|width=50p=x align="right"|(49) | |width=50p=x align="right"|(49) | ||
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==Notes== | ==Notes== | ||
<span class="remove_this_tag">Any notes, comments, you want to share with the user</span> | <span class="remove_this_tag">Any notes, comments, you want to share with the user</span> |
Revision as of 16:34, 18 May 2011
Sedflux
SEDFLUX is a basin-fill model, written in ANSI-standard C, able to simulate the delivery of sediment and their accumulation over time scales of tens of thousands of years. It simulates the dynamics of strata formation of continental margins fuse information from the atmosphere, ocean and regional geology, and it can provide information for areas and times for which actual measurements are not available, or for when purely statistical estimates are not adequate by themselves.
Model introduction
Sedflux combines individual process-response models into one fully interactive model, delivering a multi-sized sediment load onto and across a continental margin. The model allows for the deposit to compact, to undergo tectonic processes and isostatic subsidence from the sediment load. The new version, Sedflux 2.0 introduces a series of new process models, and is able to operate in one of two models to track the evolution of stratigraphy in either 2D or 3D. Additions to the 2D mode include the addition of models that simulate (1) erosion and deposition of sediment along a riverbed, (2) cross-shore transport due to ocean waves, and (3) turbidity currents and hyperpycnal flows. New processes in the 3D mode include (1) river channel avulsion, (2) two-dimensional diffusion due to ocean storms, and (3) two-dimensional flexure due to sediment loading. The spatial resolution of the architecture is typically 1–25 cm in the vertical and 10–100 m in the horizontal when operating in 2D mode. In 3D mode, the horizontal resolution usually extends to kilometers. In addition to fixed time steps (from days to hundreds of years), Sedflux 2.0 offers event-based time stepping as a way to conduct long-term simulations while still modeling low-frequency but high-energy events.
Model parameters
Uses ports
This will be something that the CSDMS facility will add
Provides ports
This will be something that the CSDMS facility will add
Main equations
- River dynamics (using HydroTrend model)
1) Water discharge
[math]\displaystyle{ Q_{0}=u_{0}b_{0}h_{0} }[/math] (1)
2) Mean suspended load entering the ocean basin
[math]\displaystyle{ Q_{s0}= Q_{0} \sum\limits_{i=1}^N Cs_{i} }[/math] (2)
3) Bedload equation by Bagnold (1966)
[math]\displaystyle{ Q_{b}={\frac{\rho _{s}}{\rho _{s} - \rho}}{\frac{\rho g Q_{0}^ \beta s e_{b}}{g tan f}} }[/math] (3)
- Channel avulsion (using Avulsion model)
[math]\displaystyle{ \Theta _{n+1}=\Theta_{n} + X_{n} }[/math] (4)
- Bedload dumpling (not hyperpycnal flow)
[math]\displaystyle{ D={\frac{Q_{b}}{W_{d}L \rho}} }[/math] (5)
- River plumes
1) Advection-diffusion equation
[math]\displaystyle{ {\frac{\partial u I}{\partial x}} + {\frac{\partial v I}{\partial y}} + \lambda I = {\frac{\partial}{\partial y}} \left ( K {\frac{\partial I}{\partial y}} + {\frac{\partial}{\partial x}} \left (K {\frac{\partial I}{\parital x}}\right ) }[/math] (6)
2) Froude number
[math]\displaystyle{ Fr = {\frac{u_{0}}{\sqrt{g h_{0}}}} }[/math] (7)
3) Plume's centerline
[math]\displaystyle{ {\frac{x}{b_{0}}}=1.53 + 0.90 \left ({\frac{u_{0}}{v_{0}}}\right ) \left ({\frac{y}{b_{0}}}\right )^\left (0.37\right ) }[/math] (8)
4) Non-conservative concentration along and surrounding the centerline position
[math]\displaystyle{ C\left (x,y\right ) = C_{0}exp\left (-\lambda t \right ) \sqrt{{\frac{b_{0}}{\sqrt{\pi}C_{1} x}}} exp [-\left ({\frac{y}{\sqrt{2} C_{1} x}}\right )^2] }[/math] (9)
[math]\displaystyle{ t\left (x,y\right ) = {\frac{u_{0} + u_{c}\left (x\right ) + 7u\left (x,y\right )}{9}} }[/math] (10)
[math]\displaystyle{ u_{c}\left (x\right ) = u_{0} \sqrt{{\frac{b_{0}}{\sqrt{\pi} C_{1} x}}} }[/math] (11)
[math]\displaystyle{ u\left (x,y\right ) = u_{0} \sqrt{{\frac{b_{0}}{\sqrt{\pi} C_{1} x }}} exp [-\left ({\frac{y}{\sqrt{2} C_{1} x}}\right )^2] }[/math] (12)
- Diffusion of seafloor sediments
1) Amount of bottom sediments that can be reworked by resuspension and diffusion
[math]\displaystyle{ q_{s} = k\left (t,z,D\right ) \bigtriangledown z = k \left ( {\frac{\partial z}{\partial x}}\hat{i} + {\frac{\partial z}{\partial y}} \hat{j} \right ) }[/math] (13)
2) Amount and direction of transport of the ith grain size
[math]\displaystyle{ q_{si} = \beta _{i} q_{s} }[/math] (14)
- Sediment failure
1) Stability of a possible failure plane
[math]\displaystyle{ F_{total} = {\frac{ \sum\limits_{i=0}^N[b_{i}\left ( c_{i} + \left ( {\frac{W_{i}}{b_{i}}} - u_{i} \right ) tan \phi _{i} \right ) {\frac{sec \alpha _{i}}{1 + {\frac{tan \alpha _{i} tan \phi _{i}}{F_{total}}}}}]}{\sum\limits_{i=0}^N W_{i} sin \alpha _{i}}} }[/math] (15)
2) excess pore pressure using Gibson's graphical approximation (1958)
[math]\displaystyle{ u_{i} = {\frac{\gamma' z_{i}}{a_{i}}} }[/math] (16)
[math]\displaystyle{ a \equiv 6.4 \left ( 1 - {\frac{T}{16}} \right )^\left (17\right ) + 1 }[/math] (17)
[math]\displaystyle{ T \equiv {\frac{m^2 t}{c_{v}}} }[/math] (18)
- River mouth turbidity currents
[math]\displaystyle{ {\frac{\partial u}{\partial t}} = g_{0} sin \alpha C - {\frac{E + C_{d}}{h}}u^2 - g_{0} \left ({\frac{e^C - 1}{e - 1}}\right ) cos \alpha C tan \gamma }[/math] (19)
[math]\displaystyle{ C = \sum\limits_{i=1}^N C_{i} = {\frac{\rho _{f} - \rho}{\rho _{s} - \rho}} }[/math] (20)
Fluid continuity equation 1) one dimensional steady-state turbidity current model INFLO
[math]\displaystyle{ {\frac{\partial Q}{\partial x}} = E u W }[/math] (21)
Continuity equation for the ith grain size of the flow's suspeneded load
[math]\displaystyle{ {\frac{\partial J_{i}}{\partial x}} = E_{Ri} - D_{Ri} }[/math] (22)
The rate of erosion of the ith grain size of the seafloor by the current
[math]\displaystyle{ E_{R} = \left ({\frac{C_{D} \rho _{f} u^2 - \delta _{b}}{\delta _{a}}} \right ) {\frac{\varphi _{i} W}{day}} }[/math] (23)
Rate of deposition of the ith grain size in the flow
[math]\displaystyle{ D_{Ri} = \left\{\begin{matrix} 0 & if u \gt u_{cr} \\ {\frac{\lambda _{i} J_{i}}{u}} \left ( 1 - {\frac{u^2}{u_{cr}^2}}\right ) & if u \lt = u_{cr} \end{matrix}\right. }[/math] (24)
Critical velocity for deposition
[math]\displaystyle{ u_{cr} = {\frac{w_{s}}{\sqrt{C_{D}}}} }[/math] (25)
2) turbidity current model Sakura Governing equation
[math]\displaystyle{ {\frac{\partial h}{\partial t}} + {\frac{\partial}{\partial x}} \left (u h_{f} \right ) = E_{w} u }[/math] (26)
[math]\displaystyle{ {\frac{\partial}{\partial t}} \left (u h_{f} \right ) + {\frac{\partial}{\partial x}}\left (u^2 h_{f}\right ) = -{\frac{\left ( \rho _{s} - \rho _{w} \right ) g}{2 \rho_{w}}}{\frac{\partial}{\partial x}} \left (Ch_{f}^2 \right ) + {\frac{\left (\rho _{s} - \rho _{w} \right ) g h_{f} C S}{\rho_{w}}} - C_{d} \left ( 1 + \alpha \right ) u^2 }[/math] (27)
[math]\displaystyle{ {\frac{\partial}{\partial t}} \left ( Ch_{f} \right ) + {\frac{\partial}{\partial x}}\left ( u Ch_{f}\right ) = - F_{d} + F }[/math] (28)
[math]\displaystyle{ E_{w} = {\frac{0.00153}{0.0204 + Ri}} }[/math] (29)
[math]\displaystyle{ Ri = {\frac{\left (\rho_{s} - \rho_{w}\right ) g h_{f}C}{\rho_{w}u^2}} }[/math] (30)
[math]\displaystyle{ F_{d} = \left\{\begin{matrix} w_{s} C \left (2 - 1/p_{z} \right ) & p_{z} \lt 0.5 // 0 & p_{z} \gt = 0.5 \end{matrix}\right. }[/math] (31)
[math]\displaystyle{ F_{e} = \left ( \left (C_{d} \rho_{f} u^2 - b \right ) / \left ( a 86400 \right ) \right ) }[/math] (32)
[math]\displaystyle{ |log p_{z}|^\left (1/4 \right ) \cong 0.124 log_{2} Z_{0} + 1.2 }[/math] (33)
[math]\displaystyle{ Z_{0} \equiv w_{s}/ \left (\kappa u_{*} \right ) }[/math] (34)
- Debris flows
1) Depth-averaged debris flow equations (Continuity)
[math]\displaystyle{ {\frac{\partial D}{\partial t}} + {\frac{\partial}{\partial x}} [U_{p}D_{p} + {\frac{2}{3}}U_{p}D_{s}] = 0 }[/math] (35)
2) Depth-averaged debris flow equations (Momentum (shear layer))
[math]\displaystyle{ {\frac{2}{3}} {\frac{\partial}{\partial t}} \left (U_{p}U_{s} \right ) - U_{p} {\frac{\partial D_{s}}{\partial t}} + {\frac{8}{15}}{\frac{\partial}{\partial x}} \left ( U_{p}^2 D_{s} \right ) {\frac{2}{3}} U_{p} {\frac{\partial}{\partial x}} \left (U_{p} D_{s} \right ) = D_{s} g \left ( 1 - {\frac{\rho_{w}}{\rho_{\rho_{m}}}}\right ) S - D_{s} g {\frac{\partial D}{\partial x}} - 2 {\frac{\mu U_{p}}{\rho_{m} D_{s}}} }[/math] (36)
3) Depth-averaged debris flow equations (Momentum (plug flow layer))
[math]\displaystyle{ {\frac{\partial}{\partial t}} \left ( U_{p} D_{p}\right ) + {\frac{\partial}{\partial x}} \left (U_{p}^2 D_{p} \right ) + U_{p}{\frac{\partial D_{s}}{\partial t}} + {\frac{2}{3}}U_{p}{\frac{\partial}{\partial x}} \left (U_{p} D_{s} \right ) = D_{p} g \left ( 1 - {\frac{\rho_{w}}{\rho_{m}}} \right ) S - D_{p} g {\frac{\partial D}{\partial x}} - {\frac{\tau_{y}}{\rho_{m}}} }[/math] (37)
- Subsidence
1) Isostatic subsidence
[math]\displaystyle{ w \left (x\right ) = {\frac{p\left (x\right ) \alpha ^3}{8D}}exp \left( -{\frac{|x|}{\alpha}}\right ) + sin \left ({\frac{|x|}{\alpha}}\right ) \right ) }[/math] (38)
[math]\displaystyle{ \alpha \equiv ^4 \sqrt{{\frac{4D}{\rho_{m}g}}} }[/math] (39)
[math]\displaystyle{ W \left (x\right ) = \sum\limits_{i=-\propto}^\left (\propto\right ) w \left ( x - x_{i} \right ) }[/math] (40)
- Compaction
[math]\displaystyle{ {\frac{\partial \phi}{\partial \delta}} = - c \left ( \phi - \phi_{0}\right ) }[/math] (41)
- Subaerial erosion and deposition by river
[math]\displaystyle{ {\frac{\partial \eta}{\partial t}} = \nu {\frac{\partial ^2 \eta}{\partial x^2}} }[/math] (42)
Diffusion coefficient
[math]\displaystyle{ \nu \equiv {\frac{-8 \lt q\gt A \sqrt{c_{f}}}{C_{0}\left ( s - 1 \right )}} }[/math] (43)
- Cross-shore transport due to ocean storms
1) Closure depth
[math]\displaystyle{ h_{c} = 2.28 H_{ss} - 6.85 \left ({\frac{H_{ss}^2}{g T^2}}\right ) }[/math] (44)
2) Sediment flux for the outer shelf (depth greater than hc)
[math]\displaystyle{ q_{s} = {\frac{16}{3\pi}}{\frac{\rho}{\rho_{s} - \rho}}{\frac{C_{fs}\varepsilon _{ss}}{g}}I_{s}{\frac{U_{om}^3}{w_{s}}}\left ( v_{0} + {\frac{U_{om}^2}{5 w_{s}}}{\frac{\partial h}{\partial x}}\right ) }[/math] (45)
3) Equation for shoaling waves
[math]\displaystyle{ U_{om} \left (h\right ) = {\frac{\gamma b}{2}} \sqrt{g b_{b}} \left ({\frac{h}{h_{b}}}\right )^\left ({\frac{-3}{4}}\right ) }[/math] (46)
4) Komar's (1998) equation for the threshold of sediment motion
[math]\displaystyle{ {\frac{\rho u_{t}^2}{\left ( \rho_{s} - \rho \right ) g d}} = \left\{\begin{matrix} 0.21 \left ({\frac{d_{0}}{d}}\right )^ \left ({\frac{1}{2}}\right ) & for D \lt = 0.5 mm // 0.46 \pi \left ({\frac{d_{0}}{d}}\right )^\left ({\frac{1}{4}}\right ) & for D \gt 0.5 mm \end{matrix}\right. }[/math] (47)
5) Near-bottom threshold velocity
[math]\displaystyle{ u_{t} = {\frac{\pi d_{0}}{T}} = {\frac{\pi H}{T sinh \left (2 \pi h / L \right )}} }[/math] (48)
6) Sediment flux within the near-shore zone (depth less than hc)
[math]\displaystyle{ q_{s} = k_{c} \underline{x}^ \left ( 1 - m \right ) {\frac{dh}{dx}} }[/math] (49)
Notes
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