The Littoral Sedimentation and Optics Model (LSOM) Timothy Keen Naval Research Laboratory Code 7322...
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Transcript of The Littoral Sedimentation and Optics Model (LSOM) Timothy Keen Naval Research Laboratory Code 7322...
The Littoral Sedimentation and Optics
Model (LSOM)
Timothy KeenNaval Research Laboratory
Code 7322Stennis Space Center, Mississippi
10 May 2002
Motivation
The Navy needs a capability to predict nearshore bottom properties and water column optical characteristics at forecast intervals up to 72 hours.
OUTLINE
• Overview of LSOM• Resuspension• Active Layer• Transport Algorithms• Mass (bed) Conservation• Bed Definitions
LSOM: OVERVIEW
• 2D finite-difference computation grid• 1D BBLM computes profiles• Mass-conservation equations for spectrum
of silt/sand sizes• Mud algorithms• Bed load, advection, and diffusion terms• Spectral and total erosion and deposition• Algorithms for optical scattering and diver
visibility
LSOM: FLOWINPUT: 2D current, wave, and sediment parameter fields
BBLMu*, C0, hA, etc.
OUTPUT: 2D beds; sediment profiles; scattering coefficients; diver visibility;
Sediment profiles
2D GRID LOOP
SIZE LOOP
Resuspension depth HR
Reduce reference concentration.
Recompute profiles
Bed, suspended, and diffusion fluxes
Solve mass conservation
equation
HR > hA
Bed parameters
YES
Integrated bed parameters
BBLM: FLOWINPUT: CURRENT, WAVE, AND SEDIMENT PARAMETERS
Find mean and maximum shear stresses u*c and u*cw, apparent
bottom roughness kbc, and wave boundary layer height
Guess reference current UA and physical roughness kb
Find skin friction
Calculate kb and reference concentrations
Find total shear stress using kb and UA
Calculated and specified reference currents match?
Find current profile
NO
OUTPUT: SHEAR STRESSES; CURRENT PROFILE; SEDIMENT REFERENCE CONC., C0; RIPPLE PARAMETERS
YES
SILT/SAND REFERENCE CONCENTRATION
• Instantaneous reference concentration cn(z0)
• Average over wave period to find mean concentration cmn(z0)
'0
'0
0 1)(
n
nbmnmn S
Sczc
normalized excess skin friction
instantaneous resuspension coefficient
size class
bed concentration
COHESIVE SEDIMENT DYNAMICS: ENTRAINMENT
mcndt
a
• Resuspended concentration*:
(kg/m2)
• Need to examine the empirical coefficients a, n, and m using mineralogical and chemical data.
• Replace power-law formulation with physical models for clay
diagenesis and entrainment.
Time since deposition
Empirical Coefficients
SUSPENDED SEDIMENT PROFILES
Mean concentration within wave boundary layer:
cw
fnu
w
mnmn z
zzczc
*
00)()(
Diffusivity parameter
Dimensionless fall velocity
Mean concentration above wave boundary layer:
c
fnu
w
wwmnmn
zczc
*
)()(
Wave boundary layer height
• The BBLM computes a resuspension depth for each size class.
• depth is limited by:
– near-bed transport:
– ripple height:
ACTIVE LAYER CALCULATION
2
7.0)2/1(42'
c
mcTm dsh
Relative density
diameter
Critical Shields parameter
Max Shields parameter
16.0`
22.0
c
mbA
5.1`
8.0*48.0
c
mbAS
Break-off range
Sediment parameter
Equilibrium range
Wave orbital diameter
COUPLING BBLM TO TRANSPORT MODEL
• The BBLM is applied independently at each grid point on a 2D horizontal grid.
• The corrected suspended sediment profiles are coupled to 2D transport equations for all size classes.
• The active layer is found from near-bed transport and ripple height.
MASS-CONSERVATION EQUATIONS
• The suspended sediment ADVECTION flux in x direction for size n:
1
)()(z
z
mnyn
o
dzzczuS
BED LOAD
• Modified Bagnold formulation:
ncwncwk
z
bnbn uuci b
b
***tan
log
Bed concentration
Thrust height on grain
Dynamic friction coefficient
Critical shear velocity
Critical shear stress
SEDIMENT DIFFUSION EQUATIONS
• The suspended sediment DIFFUSION flux in x direction for size n:
1
)(z
z
mnHyn
o
dzzcAD
Horizontal diffusivity
•AH is Smagorinsky formulation
MASS-CONSERVATION EQUATIONS
• Total derivative in x direction for size n:
01
)1(
x
D
x
Si
xGz
tnn
bnynys
Sediment density
Bed porosity
Y dimension
Elevation change
Bedload transport rate
Suspended sediment advection flux
Suspended sediment diffusion flux
BED DEFINITIONS
• Storm Bed: thickness of reworked sediment
• Resuspension Bed: equivalent thickness of resuspended sediment
• Transported Bed: sediment deposited after transport by steady currents from another location
INSTANTANEOUS TOTAL BEDSResuspensionDepositionErosionInitial
Apparent Erosion Depth ZS
Reference Elevation ZR
Bed Elevation ZB
Resuspended Bed
Storm Bed
Transported Bed
BR
BCBT
These definitions apply to a single time step in the model.
CUMULATIVE TOTAL BEDS
ZS
ZR
ZB
Resuspended Bed BR
Total bed BCTransport
Bed BT
BC = ZB - ZS BR = ZR - ZSBT = ZB - ZR
These beds are present after last model integration.
CONCLUSIONS
• LSOM is a modular, scalable, multipurpose model for Navy needs.
• It is being enhanced with cohesive sediment algorithms.
• A PC-based windows version is currently under development.