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...</sub> defined as 4 times the total energy density, spectral peak period ''T''_''p'', and spectral peak frequency ''f''_''p''), and |'''''T'''''_'''''p'' ''''''(sec)'''^'''a'''

== ''Case 1'' (<math>H</math>=1.65 m, <math>T</math>=11 s) == heights for Case 1 (<math>H</math> = 1.65 m, <math>T</math>= 11 s). For display purposes, wave

* Mase, H., K. Oki, T. S. Hedges, and H. J. Li. 2005. Extended energy-balance-equation wave model

...dled by modifying the equilibrium concentration as <math>C_{t*}^' = min(C_{t*}, C_t)</math> in both the sedment transport and bed change equations. The ...is implemented in CMS. The equations are obtained by substituting <math>C_{t*k}^{n+1} = p_{1k}^{n+1}C_{tk}^{*n+1}</math> into the bed change and sortin

...x'' is zero at the boundary, then the ''y'' differential with respect to ''t'' is also zero, meaning ''y'' does not change over time. <math> y^{t+1}_n = y^t_N + y_{RC} </math>

Table 4. Offshore significant wave height H_mo, peak wave period T_p,, incident wave period Θ_o, water level η<sub>0</su |align = "center"|T_p, s

|| PRTOUT || Output to PRFILE || yes (t), no (f) || || PRWARN || Print warnings || yes (t), no (f) ||

...ange (<math>\Delta z</math>) at each time step of simulation (<math>\Delta t</math>) is calculated as follows: <center><math>\Delta z = \frac{f_{morph} \Delta t}{\rho_s (1-\rho)} (\alpha_t \omega_s (C_t-C_t^* )+S_b)</math></center>

...b|right|600px| Figure 3. Computed bed elevations and current velocities at t=10 hrs.]]

...nts include a single groin (Figure 2), a detached breakwater (Figure 3), a T-head groin (Figure 4), a seawall with a groin to force shoreline erosion to Image:Figure32.jpg|Figure 4. GenCade straight shoreline with T-head groin domain.

...artial (r_{sk} C_{tk})}{\partial x_j} \biggr] + \alpha _t \omega _{sk} (C_{t*k} - C_{tk}) ...lated to the total-load adaptation length (L_t ) and time (T_t) by

\frac{\partial (h C)}{\partial t} + \frac{\partial (u_j h C)}{\partial x_j} = \frac{\partial }{\partial x_j} ...al q_{b*j}}{\partial x_j} + \frac{\partial }{\partial x_j} \biggl[ D_s |q_{t*}| \frac{\partial \zeta}{\partial x_j} \biggr] + E_b - D_b

Mase, H., K. Oki, T. S. Hedges, and H. J. Li. 2005. Extended energy-balance-equation wave model

...>''w''</sub> = ''T''_''wc'' + ''T''_''wt'', in which ''T''_''w'' is the wave period), and _''pl'',''b'' a coe ...T}_{wc}}}\int_{0}^{{{T}_{wc}}}{\frac{1/2{{f}_{cw}}{{\left[ {{u}_{w}}\left( t \right)+{{U}_{c}}\text{cos}\varphi \right]}^{2}}}{\left( s-1 \right)g{{d}_

| <math>q_{t*}</math>

q_{t} = A_w \biggl[ \frac{(\tau_{b,max} - \tau_{cr}) U }{\rho g } \biggr] ...</math> and <math> A_w </math> is semi-orbital excursion <math> A_w = U_w T / (2 \pi) </math>.

...mb|left|600px| Figure 2. Computed bed elevations and current velocities at t=10 hrs.]]

|align = "center"|'''L/T* Ratio''' <nowiki>*</nowiki>L/T Ratio is the ratio between the laminar and turbulent resistance terms

\bar{\eta}_E (t) = \sum f_i A_i \cos (\omega_i t + V_{i}^0 + \hat{u}_i - \kappa_i) :''t'' = elapsed time from midnight of the starting year [hrs]

{{Equation|<math>\bar{\eta}_E (t) = \Sigma f_i A_i cos (\omega_i t + V_i ^0 + \hat{u}_i - \kappa_i)</math>|2-18}} :t = elapsed time from midnight of the starting year [hrs]