User Guide 006
figure 2-47
Wall Boundary The wall boundary condition is a closed boundary and is applied at any cell face between wet and dry cells. Any unassigned boundary cells at the edge of the model domain are assumed to be closed and are assigned a wall boundary. A zero normal flux to the boundary is applied at closed boundaries. Two boundary conditions are available for the tangential flow: 1. Free-slip: No tangential shear stress (wall friction) 2. Partial-slip: Tangential shear stress (wall friction) calculated based on the log-law Assuming a log-law for a rough wall, the partial-slip tangential shear stress is given by (2 10) where is the magnitude of the wall parallel current velocity and is the wall friction coefficient equal to (2 11
Here is the roughness length of the wall and is assumed to be equal to that of the bed (i.e. ). is the distance from the wall to the cell center. Notes: • When SMS generates a new grid, cellstrings are automatically gen-erated along all boundaries. The default boundary type is the wall boundary. It is recommended to delete all boundary cellstrings which are not open boundary conditions, since the wall boundary conditions are automatically assigned within the model. Deleting the cellstrings avoids confusion when assigning the boundary con-ditions. • Since the wall boundary is a closed boundary and all unassigned boundaries are treated as closed, the wall boundary cellstring in-formation does not need to written to the CMS-Flow Card File.
Flux Boundary The flux boundary condition is typically applied to the upstream end of a river or stream and is specified as either a constant or time-series of total water volume flux. In a 2DH model, the total volume flux needs to be dis-tributed across the boundary in order to estimate the depth-averaged ve-locities. This is done using a conveyance approach in which the current velocity is assumed to be related to the local flow depth and Manning’s as (i.e. ). Here is an empirical conveyance coefficient equal to approximately 2/3 for uniform flow. The smaller the value the more uniform the current velocities are across the flux boundary. The water volume flux, qi , at each boundary cell i is calculated as (2 12)
where i = subscript indicating a boundary cell
= volume discharge at boundary cell i per unit width [m2/s] = unit vector for inflow direction = inflow direction measured clockwise from North [deg] = boundary face unit vector (positive outward) = total volume flux across the boundary [m3/s]
n = Manning’s coefficient [s/m1/3] r =empirical constant equal to approximately 2/3
=cell width in the transverse direction to flow [m] = ramp function [-]
The total volume flux is positive into the computational domain. Since it is not always possible to orient all flux boundaries to be normal to the flux boundaries, the option is given to specify an inflow direction . The angle is specified in degrees clockwise from true North. If the angle is not specified, then the inflow angle is assumed to be normal to the boundary. The total volume flux is conserved independently of the inflow direction.
As mentioned above, the total water volume flux may be specified as a constant value or a single time-series curve. A description of the CMS-Flow cards used to specify the flux boundary condition information is provided in the table below.
table 2-42
example 1
Step-by-Step Flux Boundary Specification in SMS The flow rate boundary condition specifies a time series of water fluxes in units of m3/s per cell. To assign a flux BC in SMS: 1. If not already created by SMS, create the cellstring at the flux boundary (see section Creating and Deleting Cell Strings in SMS for details). 2. Select the cellstring (see section Selecting a Cellstring for details) 3. Open the CMS-Flow Boundary Conditions Window (see section Assigning a Boundary Condition for details). 4. Enter a time series of total flux values on and select OK button. 5. Save the SMS project File (*.sms) or CMS-Flow Simulation File (*.cmcards). Total flow rate specified is divided between the total number of cells in the cellstring with each assigned a portion of the total flux as function of the local water depth and bottom friction.
Notes: • The flux boundary type may ONLY be specified along cellstrings which are straight (i.e. the cellstring may not wrap around corners). • Cellstrings have to be at least three cells long. • Positive fluxes are directed inward and negative fluxes are directed outward. By default the inflow/outflow angles are assumed to be normal to the boundary. The angle may be changed using the ad-vanced block structure described in the following section. • If the flux data file name and path are not specified, then they are assumed to be the same as for cellstring.
Water Level Boundaries The water level at a boundary can be specified as: 1. Constant value 1. Single time-series curve 2. Cell-specific time-series curves (i.e. one time-series for each boundary cell) 3. Tidal constituents 4. Harmonic constituents 5. Extracted values from a parent grid simulation (nesting) 6. Tidal database The general formula for the boundary water surface elevation is given by (2 13) where
= boundary water surface elevation [m] = external boundary water surface elevation [m] = water surface elevation offset [m] = initial boundary water surface elevation [m] = correction to the boundary water surface elevation which is a function of the wind and wave forcing [m] = water surface elevation component derived from user speci-fied gradients [m] = ramp function [-]
The external water surface elevation may be spatially and temporally con-stant or variable. When a time series is specified, the values are interpolated using piecewise Lagrangian polynomials. By default, second order interpolation is used, but can be changed by the user. The water surface elevation offset is assumed spatially and temporally constant and may be used to correct the boundary water surface elevation for vertical datums, surge, and sea level rise. The correction is only applicable when is spatially constant as in the case of a single water surface elevation time-series. The component is intended to represent regional gradients in the water surface elevation, is assumed to be constant in time, and is only applicable when is spatially constant.
A small degree of relaxation is obtained by applying the water level forcing as a source term rather than assigning the water level at the boundaries. This technique is common practice in finite volume models and improves stability and convergence. When applying a water level boundary condition to the nearshore, local flow reversals and boundary problems may result if the wave-and wind-induced setup are not included. This problem is avoided by adjusting the local water level to account for the cross-shore wind and wave setup similar that described in Reed and Militello (2005).
Tidal Boundary Tidal or astronomic water level predictions are based on the official United States National Oceanographic and Atmospheric Administration (NOAA) Tides and Currents website: http://tidesandcurrents.noaa.gov and using the National Ocean Service (NOS) (http://co-ops.nos.noaa.gov) prediction formula (2 14) where
i = subscript indicating a tidal constituent = mean amplitude [m] = node (nodal) factor [-] = frequency [deg/hr] = elapsed time from midnight of the starting year [hrs] = equilibrium phase [deg] = phase lag or epoch [deg]
The nodal factor is a time-varying correction to the mean amplitude. The equilibrium phase has a uniform component and a relatively smaller periodic component. The zero-superscript of indicates that the constituent phase is at time zero. The table below provides a list of tidal constituents currently supported in CMS. More information on U.S. tidal constituent values can be obtained from NOAA and NOS.