Model help:ROMS: Difference between revisions
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==Main equations== | ==Main equations== | ||
1) Equations of motion | 1) Equations of motion | ||
a) Momentum balance in the x-directions, respectively | a) Momentum balance in the x-directions, respectively | ||
::::{| | ::::{| | ||
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|width=50p=x align="right"|(21) | |width=50p=x align="right"|(21) | ||
|} | |} | ||
<div class="NavFrame collapsed" style="text-align:left"> | |||
<div class="NavHead">Nomenclature</div> | |||
<div class="NavContent"> | |||
{| {{Prettytable}} class="wikitable sortable" | |||
!Symbol!!Description!!Unit | |||
|- | |||
| D<sub>u</sub>,D<sub>v</sub>,D<sub>T</sub>,D<sub>S</sub> | |||
| diffusive terms | |||
| - | |||
|- | |||
| F<sub>u</sub>,F<sub>v</sub>,F<sub>T</sub>,F<sub>S</sub> | |||
| forcing terms | |||
| - | |||
|- | |||
| f | |||
| coriolis parameter | |||
| - | |||
|- | |||
| g | |||
| acceleration of gravity | |||
| m/s<sup>2</sup> | |||
|- | |||
| h | |||
| bottom depth | |||
| m | |||
|- | |||
| ν | |||
| horizontal viscosity | |||
| | |||
|- | |||
| κ | |||
| horizontal diffusivity | |||
| | |||
|- | |||
| K<sub>m</sub>,K<sub>T</sub>,K<sub>S</sub> | |||
| vertical viscosity and diffusivity | |||
| - | |||
|- | |||
| P | |||
| total pressure, approximately -ρ<sub>O</sub> gz | |||
| | |||
|- | |||
| Φ | |||
| dynamic pressure, Φ = (P/ρ<sub>O</sub>) | |||
| | |||
|- | |||
| ρ + ρ(x,y,z,t) | |||
| total in situ density | |||
| | |||
|- | |||
| S | |||
| salinity | |||
| | |||
|- | |||
| t | |||
| time | |||
| | |||
|- | |||
| T | |||
| potential temperature | |||
| | |||
|- | |||
| u,v,w | |||
| the (x,y,z) components of vector velocity | |||
| - | |||
|- | |||
| x,y | |||
| horizontal coordinate | |||
| | |||
|- | |||
| z | |||
| vertical coordinate | |||
| | |||
|- | |||
| ζ | |||
| surface elevation | |||
| | |||
|- | |||
| E | |||
| evaporation | |||
| - | |||
|- | |||
| P | |||
| precipitation | |||
| | |||
|- | |||
| γ<sub>1</sub> | |||
| linear bottom stress coefficient | |||
| - | |||
|- | |||
| γ<sub>2</sub> | |||
| quadratic bottom stress coefficient | |||
| - | |||
|- | |||
| Q<sub>T</sub> | |||
| surface heat flux | |||
| - | |||
|- | |||
| τ<sub>S</sub> <sup>x</sup>, τ<sub>S</sub> <sup>y</sup> | |||
| surface wind stress | |||
| | |||
|- | |||
| τ<sub>b</sub> <sup>x</sup>, τ<sub>b</sub> <sup>y</sup> | |||
| bottom stress | |||
| - | |||
|- | |||
| T<sub>ref</sub> | |||
| surface reference temperature | |||
| | |||
|- | |||
|} | |||
'''Output''' | |||
{| {{Prettytable}} class="wikitable sortable" | |||
!Symbol!!Description!!Unit | |||
|- | |||
| q<sub>bT</sub> | |||
| total volume gravel bedload transport rate per unit width summed over all sizes | |||
| L<sup>2</sup> / T | |||
|- | |||
| τ<sub>sg</sub> <sup>*</sup> | |||
| Shields number based on surface geometric mean size | |||
| - | |||
|- | |||
| D<sub>sg</sub> | |||
| geometric mean size of the surface material | |||
| L | |||
|- | |||
| σ<sub>sg</sub> | |||
| geometric standard deviations of the surface materials | |||
| - | |||
|- | |||
| D<sub>lg</sub> | |||
| geometric mean size of the bedload | |||
| L | |||
|- | |||
| σ<sub>lg</sub> | |||
| geometric standard deviation of the bedload | |||
| - | |||
|- | |||
| σ<sub>l</sub> | |||
| arithmetic standard deviations of bedload materials | |||
| - | |||
|- | |||
| σ | |||
| arithmetic standard deviations of the surface materials | |||
| - | |||
|- | |||
| D<sub>sx</sub> | |||
| grain size in the surface material, such that x percentage of the material is finer | |||
| L | |||
|- | |||
| D<sub>lx</sub> | |||
| grain size in the bedload material, such that x percentage of the material is finer | |||
| L | |||
|- | |||
| σ<sub>lx</sub> | |||
| arithmetic standard deviations of bedload materials | |||
| L | |||
|- | |||
|} | |||
</div> | |||
</div> | |||
==Notes== | ==Notes== |
Revision as of 15:56, 22 July 2011
ROMS
ROMS is a community model shared by a large user group around the world, with applications ranging from the study of entire ocean basins to coastal sub-regions.
Model introduction
ROMS incorporates advanced features and high-order numerics, allowing efficient and robust resolution of mesoscale dynamics in the oceanic and coastal domains. The model solves the free surface, hydrostatic, primitive equations of the fluid dynamics over variable topography using stretched; terrain-following coordinates in the vertical and orthogonal, curvilinear coordinates in the horizontal. This allows enhancement of the spatial resolution in the regions of interest.
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
1) Equations of motion
a) Momentum balance in the x-directions, respectively
[math]\displaystyle{ {frac{\partial u}{\partial t}} + \vec{v} \nabla u - fv = -{\frac{\partial \phi}{\partial x}} + F_{u} + D_{u} }[/math] (1)
b) Momentum balance in the y-directions, respectively
[math]\displaystyle{ {frac{\partial v}{\partial t}} + \vec{v} \nabla u - fv = -{\frac{\partial \phi}{\partial y}} + F_{v} + D_{v} }[/math] (2)
c) Advective-diffusive equations for temperature
[math]\displaystyle{ {\frac{\partial T}{\partial t}} + \vec{v} \nabla T = F_{T} + D_{T} }[/math] (3)
d) Advective-diffusive equations for salinity
[math]\displaystyle{ {\frac{\partial S}{\partial t}} + \vec{v} \nabla S = F_{S} + D_{S} }[/math] (4)
e) Equation of state
[math]\displaystyle{ \rho = \rho \left (T,S,P \right ) }[/math] (5)
f) Vertical momentum equation
[math]\displaystyle{ {\frac{\partial \rho}{\partial z}} = {\frac{- \rho g}{\rho_{o}}} }[/math] (6)
g) continuity equation for an incompressible fluid
[math]\displaystyle{ {\frac{\partial u}{\partial x}} + {\frac{\partial v}{\partial y}} + {\frac{\partial w}{\partial z}} = 0 }[/math] (7)
2) Vertical boundary conditions a) top boundary condition ( z = ζ (x,y,t ))
[math]\displaystyle{ K_{m} {\frac{\partial u}{\partial z}} = \tau_{S}^x \left (x,y,t \right ) }[/math] (8)
[math]\displaystyle{ K_{m} {\frac{\partial v}{\partial z}} = \tau_{S}^y \left (x,y,t \right ) }[/math] (9)
[math]\displaystyle{ K_{T} {\frac{\partial T}{\partial z}} = {\frac{Q_{T}}{\rho_{O} c_{P}}} + {\frac{1}{\rho_{O} c_{P}}}{\frac{d Q_{T}}{dT}} \left ( T - T_{ref} \right ) }[/math] (10)
[math]\displaystyle{ K_{S} {\frac{\partial S}{\partial z}} = \left (E - P \right ) S }[/math] (11)
[math]\displaystyle{ w = {\frac{\partial \zeta}{\partial t}} }[/math] (12)
b) bottom boundary condition (z = -h(x,y))
[math]\displaystyle{ K_{m}{\frac{\partial u}{\partial z}} = \tau _{b}^x \left (x,y,t \right ) }[/math] (13)
[math]\displaystyle{ K_{m}{\frac{\partial v}{\partial z}} = \tau _{b}^y \left (x,y,t \right ) }[/math] (14)
[math]\displaystyle{ K_{T}{\frac{\partial T}{\partial z}} = 0 }[/math] (15)
[math]\displaystyle{ K_{S}{\frac{\partial S}{\partial z}} = 0 }[/math] (16)
[math]\displaystyle{ -w + \vec{v} \nabla h = 0 }[/math] (17)
[math]\displaystyle{ \tau_{b}^x = \left ( \gamma_{1} + \gamma_{2} \sqrt{u^2 + v^2} \right ) u }[/math] (18)
[math]\displaystyle{ \tau_{b}^y = \left ( \gamma_{1} + \gamma_{2} \sqrt{u^2 + v^2} \right ) v }[/math] (19)
c) Horizental boundary conditions (Eastern and western boundary)
[math]\displaystyle{ {\frac{\partial}{\partial x}} \left ( {\frac{h \nu}{mn}}{\frac{\partial^2 u}{\partial x^2}} \right ) = 0 }[/math] (20)
Horizental boundary conditions (Northern and southern boundary)
[math]\displaystyle{ {\frac{\partial}{\partial y}} \left ( {\frac{h \nu}{mn}}{\frac{\partial^2 u}{\partial y^2}} \right ) = 0 }[/math] (21)
Symbol | Description | Unit |
---|---|---|
Du,Dv,DT,DS | diffusive terms | - |
Fu,Fv,FT,FS | forcing terms | - |
f | coriolis parameter | - |
g | acceleration of gravity | m/s2 |
h | bottom depth | m |
ν | horizontal viscosity | |
κ | horizontal diffusivity | |
Km,KT,KS | vertical viscosity and diffusivity | - |
P | total pressure, approximately -ρO gz | |
Φ | dynamic pressure, Φ = (P/ρO) | |
ρ + ρ(x,y,z,t) | total in situ density | |
S | salinity | |
t | time | |
T | potential temperature | |
u,v,w | the (x,y,z) components of vector velocity | - |
x,y | horizontal coordinate | |
z | vertical coordinate | |
ζ | surface elevation | |
E | evaporation | - |
P | precipitation | |
γ1 | linear bottom stress coefficient | - |
γ2 | quadratic bottom stress coefficient | - |
QT | surface heat flux | - |
τS x, τS y | surface wind stress | |
τb x, τb y | bottom stress | - |
Tref | surface reference temperature |
Output
Symbol | Description | Unit |
---|---|---|
qbT | total volume gravel bedload transport rate per unit width summed over all sizes | L2 / T |
τsg * | Shields number based on surface geometric mean size | - |
Dsg | geometric mean size of the surface material | L |
σsg | geometric standard deviations of the surface materials | - |
Dlg | geometric mean size of the bedload | L |
σlg | geometric standard deviation of the bedload | - |
σl | arithmetic standard deviations of bedload materials | - |
σ | arithmetic standard deviations of the surface materials | - |
Dsx | grain size in the surface material, such that x percentage of the material is finer | L |
Dlx | grain size in the bedload material, such that x percentage of the material is finer | L |
σlx | arithmetic standard deviations of bedload materials | L |
Notes
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Numerical scheme
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- Upload file: http://csdms.colorado.edu/wiki/Special:Upload
- Create link to the file on your page: [[Image:<file name>]].
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