1. The Littoral Sedimentation and Optics Model (LSOM)
Timothy Keen
Naval Research Laboratory
Code 7322
Stennis Space Center, Mississippi
10 May 2002

2. Motivation
The Navy needs a capability to predict nearshore bottom properties and water column optical characteristics at forecast intervals up to 72 hours.

3. OUTLINE Overview of LSOM Resuspension Active Layer
Transport Algorithms
Mass (bed) Conservation
Bed Definitions

4. 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

5. LSOM: FLOW INPUT: 2D current, wave, and sediment parameter fields
2D GRID LOOP
BBLM
u*, C0, hA, etc.
SIZE LOOP
Sediment profiles
Resuspension depth HR
Recompute profiles
YES
Reduce reference concentration.
HR > hA
Bed, suspended, and diffusion fluxes
OUTPUT: 2D beds; sediment profiles; scattering coefficients; diver visibility;
Solve mass conservation equation
Bed parameters
Integrated bed parameters

6. BBLM: FLOW INPUT: CURRENT, WAVE, AND SEDIMENT PARAMETERS
Guess reference current UA and physical roughness kb
Find skin friction
Calculate kb and reference concentrations
Find total shear stress using kb and UA
OUTPUT: SHEAR STRESSES; CURRENT PROFILE; SEDIMENT REFERENCE CONC., C0; RIPPLE PARAMETERS
Find mean and maximum shear stresses u*c and u*cw, apparent bottom roughness kbc, and wave boundary layer height
Find current profile
Calculated and specified
reference currents match? NO
YES

7. SILT/SAND REFERENCE CONCENTRATION
Instantaneous reference concentration cn(z0)
Average over wave period to find mean concentration cmn(z0)
normalized excess skin friction
bed concentration
size class
instantaneous resuspension coefficient

8. COHESIVE SEDIMENT DYNAMICS: ENTRAINMENT
Resuspended concentration*:
Empirical Coefficients
(kg/m2)
Time since deposition
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.
Lick’s theory and model for entrainment is soundly based on measurements
simple power law
need to examine the empirical coefficients
future collaboration with 7400 researchers on early diagenesis of clay minerals

9. SUSPENDED SEDIMENT PROFILES
Dimensionless fall velocity
Mean concentration within wave boundary layer:
Mean concentration above wave boundary layer:
Diffusivity parameter
Wave boundary layer height

10. ACTIVE LAYER CALCULATION
The BBLM computes a resuspension depth for each size class.
depth is limited by:
near-bed transport:
ripple height:
Relative density
Critical Shields parameter
Max Shields parameter
diameter
Break-off range
Equilibrium range
Sediment parameter
Wave orbital diameter

11. 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.

12. MASS-CONSERVATION EQUATIONS
The suspended sediment ADVECTION flux in x direction for size n:

13. BED LOAD Modified Bagnold formulation: Thrust height on grain
Critical shear velocity
Critical shear stress
Bed concentration
Dynamic friction coefficient

14. SEDIMENT DIFFUSION EQUATIONS
The suspended sediment DIFFUSION flux in x direction for size n:
Horizontal diffusivity
AH is Smagorinsky formulation

15. MASS-CONSERVATION EQUATIONS
Total derivative in x direction for size n:
Suspended sediment diffusion flux
Suspended sediment advection flux
Bed porosity
Elevation change
Sediment density
Bedload transport rate
Y dimension

16. 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

17. INSTANTANEOUS TOTAL BEDS
Initial
Erosion
Deposition
Resuspension
Reference Elevation ZR
Bed Elevation ZB
Apparent Erosion Depth ZS
Resuspended Bed
Storm Bed
Transported Bed
These definitions apply to a single time step in the model. BT BC BR

18. CUMULATIVE TOTAL BEDS Transport Bed BT Resuspended Bed BR Total bed BCZB ZR ZS
BT = ZB - ZR
BC = ZB - ZS
BR = ZR - ZS
These beds are present after last model integration.

19. 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.