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.