# Labs WMT ROMSLIte SettlingRates

## Introduction to Regional Ocean Modeling - Settling Rates and Critical Shear Stress

This lab has been designed and developed by Courtney Harris, Julia Moriarty, and Danielle Tarpley, Virginia Institute of Marine Sciences, Gloucester Point, VA

with assistance of Irina Overeem, CSDMS, University of Colorado, CO

**Classroom organization**

This is the second lab in a mini series to introduce a Web-Based version of the Regional Ocean Modeling System (ROMS) for inexperienced users. ROMS is a three-dimensional hydrodynamic ocean model (see Haidvogel et al. 2008; myroms.org). ROMS solves the conservation of mass and three-dimensional momentum equations and includes transport equations for temperature and salinity. The version implemented here also accounts for suspended sediment transport and deposition, following Warner et al. (2008). Here we present a basic configuration of ROMS in the framework of the Web Modeling Tool (WMT). This series of labs is designed for inexperienced modelers to gain some experience with running a numerical model, changing model inputs, and analyzing model output. The example provided looks at the influence of a river plume on the hydrodynamics and sediment transport within an idealized continental shelf.

This lab focuses on sediment settling rates and critical shear stress for motion. Basic theory on settling rates and suspended sediment is presented in these slides File:ROMS Lite Introduction.pptx.

This lab will likely take ~ 3hours to complete in the classroom.

If you have never used the Web Modeling Tool, learn how to use it here. The WMT allows you to set up simulations, but once you are ready to run them, you will need an account on the CSDMS supercomputer to successfully submit and run your job.
More information on getting an account can be found here HPCC Access. Note that getting permission for access takes a few days after your request.

**Learning objectives**

- familiarize with a basic configuration of the Regional Ocean Modeling System
- learn how to manipulate parameters in ROMS-Lite and set up different experiments

- physics of settling rates
- bed shear stress and threshold to incipient motion
- Rouse number
- influence of settling velocity and critical shear stress on fluvial deposition

**Lab Notes**

>> Open a new browser window and open the Web Modeling Tool here and select the ROMS project

>> This WMT project is unique in that there is only a single driver, ROMS-Lite. It is a pre-compiled instance of the larger ROMS system specially configured to the river plume case for teaching use. For this lab, you will need to visualize in Matlab, you can download a library here File:Riverplume mfiles.tar.gz.

The numerical experiment has been designed to use idealized inputs and a configuration considered representative for a medium-sized river draining into the coastal ocean. This ROMS model implementation represents sediment using three separate sources: two classes are used to represent sediment discharged by the river, and the third class represents sediment from the seabed. Each sediment class has fixed attributes of grain diameter, density, settling velocity, critical shear stress for erosion, and the erodibility constant. The user can modify the settling velocity, critical shear stress for erosion, and erodibility constant from the WMT GUI interface.

Sediment suspended in the water column is transported, like other conservative tracers (e.g., salinity) by solving the advection–diffusion equation with a source/sink term for vertical settling and erosion. The ROMS model represents sediment using separate cohesive and non-cohesive categories, in this ROMS-Lite model there are 3 non-cohesive sediment classes. Each class has fixed attributes of grain diameter, density. For the duration of the model run the settling velocity, critical shear stress for erosion, and erodibility are constant. These properties are used to help determine the bulk properties of each bed layer.

**Settling Velocity**

The settling velocity, fall velocity, or terminal velocity of a sediment particle is defined as the rate the sediment particle settles in still fluid. The settling velocity equals the velocity at the point when the weight of the sediment particle is balanced by frictional drag with the fluid. It is diagnostic of grain size, but is also sensitive to the shape (roundness and sphericity) and density of the grain as well as to the viscosity and density of the fluid. It integrates all of these into a key transport parameter. In general, larger, more dense particles have higher settling velocities. Specification of settling velocity for fine-grained particles (muds, clays, fine silts) is especially difficult because these tend to flocculate and form large, less dense, groups of particles. The settling velocities of these will be larger than individual disaggregated grains in the water column; and the settling velocities of these aggregates vary over several orders of magnitude (e.g. Hill and McCave, 2001).

The base case assigned settling velocities to the two sediment types delivered by the river as 0.05 mm/s and 0.1 mm/s (these are size classes 0 and 1 in the WMT ROMS-LITE).

Look at the difference in sediment distribution for the two sediment types delivered by the river. Which of the two sediment types do you expect to travel further from the river mouth before settling to near the bed? Test your ideas by plotting the near-bed suspended sediment concentrations for each of these two size classes.

How do you expect the near-bed concentrations to change if you increase the settling velocities by a factor of 10? Change the settling velocities in the WMT for size classes 0 and 1, and resubmit the job. Then download the new results and plot the near bed concentrations.

**Resuspension and Rouse Number**

Sediment suspension depends on turbulent diffusion overpowering settling. The shear velocity of a flow provides a scale for the turbulent diffusion, and the shear velocity, u* , is defined as

u* = √(τb/ρ);

where τb is the bed shear stress, and ρ is the fluid density. For sediment to be suspended, the ratio of settling velocity over shear velocity must be low (less than about 1). This is often expressed as the Rouse Number, defined as

P = ws/( κ u* )

where κ is von Karman’s constant (κ= 0.408). Sediment can be suspended when P < 2.5.

Calculate the Rouse Numbers for the sediment classes in the base case. To do this you will first need to find the bed shear stress from the model output file. ROMS stores the bed shear stress as a vector having components in both the x- and the y-directions, with the variable names for this implementation being τb,x = “bustrcwmax” and τb,y = “bvstrcwmax”. Pull the bed stress variables out of the netcdf output file, these will be two-dimensional in space, and time dependent. Calculate the magnitude of the stress vector at the last time step τb = √(τb,x2 + τb,y2). Where on the continental shelf is bed stress high?

Now: calculate the Rouse number for the two sediment size classes that are delivered by the river. Given the way that the Rouse numbers change with water depth, where on the continental shelf do you expect sediment to be most easily suspended?

**Critical Shear Stress**

Another important hydrodynamic property of sediment is its “critical shear stress”, τcr. This defines the threshold where the drag exerted by the fluid on the seabed moves sediment. Like settling velocity, the critical shear stress depends on grain size, density, shape of the particle, among other factors. In general, larger more dense sediment particles have higher critical shear stresses. Researchers generally use curves that are based on empirical data to estimate the critical shear stress of sediment; the curve below, based on Miller et al. (1977) relates the diameter of quartz –density sediment grains to the critical shear velocity (u* in the figure), and critical shear stress (τo in the figure).

.

Based on the shear velocities calculated previously, and the Miller et al. (1977) plot, what sediment grain diameter could be mobilized for the base case at a water depth of 20 m?

The critical shear stresses assumed in the base case for the sediment delivered by the river was 0.04 Pa and 0.14 Pa. Compared to the bed shear stresses calculated above, at what water depths would the flows in the base case be sufficient to mobilize these sediments?

How do you expect sediment deposition to depend on critical shear stress for erosion? Decrease the critical shear stresses used in the base case for sediment types 0 and 1, and re-run the model. Plot the results for sediment deposition of each size class for the base case, and the reduced – critical shear stress models to test your ideas.

**References**

- Warner, Sherwood, Signell, Harris, and Arango, 2008 "Development of a three-dimensional, regional, coupled wave, current, and sediment-transport model", Computers & Geosciences.
- Threshold of sediment motion under unidirectional currents, M. C. Miller, I. N. McCave, P. D. Komar, Sedimentology (1977) 24, 507-527.
- Hill, P.S., McCave, I.N., 2001. Suspended particle transport in benthic boundary layers. In: Boudreau, B.P., Jorgensen, B.B.(Eds.), The Benthic Boundary Layer. Oxford University Press, pp. 78–103.