Model help:Sedflux

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

Input Files and Directories

Ports

Run Parameters

Processes

Output Grids

About

Parameter	Description	Unit
Input directory	path to input files	-
Site prefix	site prefix for Input/Output files	-
Case prefix	case prefix for Input/Output files	-

Parameter	Description	Unit
Water discharge port	use the water discharge provides port	-
Erosion port	Use the erosion provides port	-

Parameter	Description	Unit
Run duration	simulation run time	years
Grid resolution in x-direction		m
Grid resolution in y-direction		m
Grid resolution in z-direction		m

Parameter	Description	Unit
Avulsion standard deviation		degrees
Minimum river angle		degrees
Maximum river angle		degrees
Row position of river hinge point		-
Column position of river hinge point		-
Velocity of coastal current		m / s
Suspended load concentration	pre-grain suspended sediment concentration	-
Distance to dump bedload		-
Bed load flux	bed load flux at river mouth	kg / s

Parameter	Description	Unit
Output directory	path to output grid files	-
Interval between output files		-
SeaFloorDepth file	output file prefix for variable	-
SeaFloorSlope file	output file prefix for variable	-
SeaFloorElevation file	output file prefix for variable	-
SeaFloor Thickness file	output file prefix for variable	-
SeaFloorGrain file	output file prefix for variable	-
SeaFloorAge file	output file prefix for variable	-
SeaFloorSand file	output file prefix for variable	-
SeaFloorSilt file	output file prefix for variable	-
SeaFloorClay file	output file prefix for variable	-
SeaFloorMud file	output file prefix for variable	-
SeaFloorFacies file	output file prefix for variable	-
SeaFloorDensity file	output file prefix for variable	-
SeaFloorPorosity file	output file prefix for variable	-
SeaFloorPermeability file	output file prefix for variable	-
SeaFloorBasement file	output file prefix for variable	-
SeaFloorRiver_mouth file	output file prefix for variable	-

Parameter	Description	Unit
Model name	name of the model	-
Author name	name of the model author	m

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}}\right ) + {\frac{\partial}{\partial x}} \left (K {\frac{\partial I}{\partial 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 ) }[/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 h_c)

[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 h_c)

[math]\displaystyle{ q_{s} = k_{c} \underline{x}^ \left ( 1 - m \right ) {\frac{dh}{dx}} }[/math]

(49)

Nomenclature

C_si

Notes

Any notes, comments, you want to share with the user

Numerical scheme

Examples

An example run with input parameters, BLD files, as well as a figure / movie of the output

Follow the next steps to include images / movies of simulations:

• Upload file: http://csdms.colorado.edu/wiki/Special:Upload
• Create link to the file on your page: [[Image:<file name>]].

See also: Help:Images or Help:Movies

Developer(s)

Name of the module developer(s)

References

Key papers

Links

Any link, eg. to the model questionnaire, etc.

Symbol	Description	Unit
Q0	water discharge from the river	m3 / s
u0	mean river mouth flow velocity	m / s
b0	channel width	m
h0	channel depth	m
Qs0	mean suspended load entering the ocean basin	kg / s
concentration of the ith grain size intervals	kg / m3
Qb	bedload at the river mouth	kg / s
Qc	critical discharge below which no bedload transport occurs	kg / s
ρs	grain density	kg / m3
ρ	fluid density	kg / m3
g	acceleration due to gravity	m / s2
β	bedload rating term	-
s	slope of the riverbed	-
eb	bedload efficiency	-
f	limiting angle of repose of sediment grains lying on a river bed	-
X	river distributary	-
Θ	anglar position of X distributary	-
D (in bedload dumping)	sedimentation rate of bedload	m / s
x	longitudinal or axial direction	-
y	lateral direction	-
u	longitudinal velocity	m / s
v	lateral velocity	m / s
I	sediment inventory of the plume	-
λ	first-order removal rate constant for each grain size (take marine flocculation into account)	-
K	sediment diffusivity driven by turbulence (assumed equal to the turbulent diffusivity and the eddy viscosity)	-
Fr	Froude number	-
v0	ambient coastal current velocity	m / s
C1	empirically derived and found to be 0.109	-
C0		-
uc		-
qs	amount of bottom sediments that can be reworked by resuspension and diffusion (resuspended sediment)	kg / s
k	diffusion coefficient	-
t	time	s
z	water depth	m
D (in diffusion of seafloor sediments)	grain size	mm
βi (in diffusion of seafloor sediments)	user-defined index (between 0 and 1), reflect the ability of resuspension to move the ith grain size	-
b	width of a slice of near-shore sediment	m
c	cohension of near-shore sediment	-
W	linear weight of the sediment	-
u (in sediment failure)	excess pore pressure	-
φ	sediment friction angle	-
α	the slope of the failure surface	-
Ftotal	factor of safety for the entire failure	-
γ'	submerged specific weight of the sediment, equals to (γ - γf)g	-
z	depth of the failure plane with respect to the seafloor	-
a		-
T		-
m	sediment rate	-
Cv	consolidation coefficient for the sediment	-
g0	reduced gravity	-
u (in River mouth turbidity currents)	downslope velocity	-
α (in River mouth turbidity currents)	slope	-
E (in River mouth turbidity currents)	entrainment coefficient that controls the rate seawater dilutes the gravity flow	-
CD (in River mouth turbidity currents)	drag coefficient	-
h (in River mouth turbidity currents)	flow thickness	-
ρ (in River mouth turbidity currents)	ambient fluid density	-
ρf (in River mouth turbidity currents)	density of the flow	-
ρs (in River mouth turbidity currents)	grain density	-
C (in River mouth turbidity currents)	bulk volume concentration of sediment in the flow	-
Ci (in River mouth turbidity currents)	volume concentration of the ith grain size in the flow	-
n (in River mouth turbidity currents)	number of discrete grain sizes carried by the flow	-
W (in River mouth turbidity currents)	width of the canyon or basin floor	-
Q (in River mouth turbidity currents)	volume discharge	-
Ji (in River mouth turbidity currents)		-
ERi (in River mouth turbidity currents)	the rate of erosion of the ith grain size of the seafloor by the current	-
day (in River mouth turbidity currents)	86400 s	-
δa (in River mouth turbidity currents)	gradient in the shear strength of the seafloor sediment	-
δb (in River mouth turbidity currents)	shear strength of the sediment at the seafloor	-
DRi (in River mouth turbidity currents)	rate of deposition of the ith grain size in the flow	-
ucr (in River mouth turbidity currents)	critical velocity for deposition	-
hf (in River mouth turbidity currents)	flow thickness	-
Ew (in River mouth turbidity currents)	water entrainment coefficient	-
S (in River mouth turbidity currents)	bottom slope gradient	-
Cd (in River mouth turbidity currents)	drag coefficient, equals to 0.004	-
(in River mouth turbidity currents)	drag coefficient, equals to 0.004	-