CMS-Flow:Boundary Conditions: Difference between revisions

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= Tidal Constituent=
= Tidal Constituent=
The water level predictions are based on a harmonic equation with several arguments
The water level predictions are based on a harmonic equation with several arguments
\begin{equation} \tag{1}
{{Equation|<math>
  \eta(t) =  \sum_{i=1}^N f_i A_i \cos (\omega_i t + V_{i}^0 + u_i - \kappa_i)
  \eta(t) =  \sum_{i=1}^N f_i A_i \cos (\omega_i t + V_{i}^0 + u_i - \kappa_i)
\end{equation}
</math>|1}}


where <math>A</math> is the constituent ''mean '' amplitude, <math>f</math> is a factor that reduces the mean amplitude and varies in time, <math>V_0+u</math> are the constituents ''equilibrium '' phase and <math>\kappa</math> is the constituent phase lag or epoch. Table 1 shows a list of the currently supported tidal constituents in CMS.  
where <math>A</math> is the constituent ''mean '' amplitude, <math>f</math> is a factor that reduces the mean amplitude and varies in time, <math>V_0+u</math> are the constituents ''equilibrium '' phase and <math>\kappa</math> is the constituent phase lag or epoch. Table 1 shows a list of the currently supported tidal constituents in CMS.  
Line 38: Line 38:
The water flux is specified as m^3/sec per cell along the cell string. This value is multiplied by the number of cells in the cell string to obtain the total flux.
The water flux is specified as m^3/sec per cell along the cell string. This value is multiplied by the number of cells in the cell string to obtain the total flux.
The total flux is then redistributed along the boundary according to
The total flux is then redistributed along the boundary according to
\begin{equation} \tag{2}
{{Equation|<math>
  q_i  = \frac{Q_{b}}{ \sum \Delta s_i h_i^{1+r}/n_i} \frac{ h_i^{1+r}} {n_i}
  q_i  = \frac{Q_{b}}{ \sum \Delta s_i h_i^{1+r}/n_i} \frac{ h_i^{1+r}} {n_i}
\end{equation}
</math>|2}}


= Cross-shore =
= Cross-shore =
Along a cross-shore boundary, it is assumed that a well-developed longshore current exists. Thus, the y (alongshore) momentum equation can be reduced as follows
Along a cross-shore boundary, it is assumed that a well-developed longshore current exists. Thus, the y (alongshore) momentum equation can be reduced as follows
\begin{equation} \tag{3}
{{Equation|<math>
  0 =  \frac{\partial}{\partial x} \biggl( \nu_t h \frac{\partial V}{\partial x} \biggr) + \tau_{sy} + \tau_{wy} - \tau_{by}  
  0 =  \frac{\partial}{\partial x} \biggl( \nu_t h \frac{\partial V}{\partial x} \biggr) + \tau_{sy} + \tau_{wy} - \tau_{by}
\end{equation}
</math>|3}}
    
    
The water level setup due to waves and winds at the cross-shore boundary can be determined by assuming a zero alongshore gradient of water level, or using the following equation reduced from the x (cross-shore) momentum equation
The water level setup due to waves and winds at the cross-shore boundary can be determined by assuming a zero alongshore gradient of water level, or using the following equation reduced from the x (cross-shore) momentum equation
\begin{equation} \tag{4}
{{Equation|<math>
  0 = \rho g \frac{\partial \eta}{\partial x} + \tau_{sx} + \tau_{wx}  
  0 = \rho g \frac{\partial \eta}{\partial x} + \tau_{sx} + \tau_{wx}  
\end{equation}
</math>|4}}
   
   
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Revision as of 15:01, 22 October 2012

Water Level

Water Level and Current Velocity

Tidal Constituent

The water level predictions are based on a harmonic equation with several arguments

  (1)

where is the constituent mean amplitude, is a factor that reduces the mean amplitude and varies in time, are the constituents equilibrium phase and is the constituent phase lag or epoch. Table 1 shows a list of the currently supported tidal constituents in CMS.

Constituent Speed Constituent Speed Constituent Speed Constituent Speed
SA 0.041067 SSA 0.082137 MM 0.54438 MSF 1.0159
MF 1.098 2Q1 12.8543 Q1 13.3987 RHO1 13.4715
O1 13.943 M1 14.4967 P1 14.9589 S1 15
K1 15.0411 J1 15.5854 OO1 16.1391 2N2 27.8954
MU2 27.9682 N2 28.4397 NU2 28.5126 M2 28.9841
LDA2 29.4556 L2 29.5285 T2 29.9589 S2 30
R2 30.0411 K2 30.0821 2SM2 31.0159 2MK3 42.9271
M3 43.4762 MK3 44.0252 MN4 57.4238 M4 57.9682
MS4 58.9841 S4 60 M6 86.9523 S6 90
M8 115.9364

Flux

The water flux is specified as m^3/sec per cell along the cell string. This value is multiplied by the number of cells in the cell string to obtain the total flux. The total flux is then redistributed along the boundary according to

  (2)

Cross-shore

Along a cross-shore boundary, it is assumed that a well-developed longshore current exists. Thus, the y (alongshore) momentum equation can be reduced as follows

  (3)

The water level setup due to waves and winds at the cross-shore boundary can be determined by assuming a zero alongshore gradient of water level, or using the following equation reduced from the x (cross-shore) momentum equation

  (4)
Symbol Description
Time
Constituent mean amplitude
Constituent nodal factor
Constituent equilibrium argument
Constituent equilibrium argument
Constituent phase or epoch

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