UW Wind Wave Predictor

Empirical Methods: SMB, USACE-SPM, and Young-Verhagen (Y-V)

SMB Method

Hs: 0.00 m
Ts (Significant): 0.00 s
State: Calculating...

USACE-SPM

Hm0: 0.00 m
Tp (Peak): 0.00 s
State: Calculating...

Young-Verhagen

Hs: 0.00 m
Tp (Peak): 0.00 s
State: Calculating...

Engineering Reference & Model Equations

1. SMB Method (Deep Water)

  • Wind Scale: Evaluated using raw $U_{10}$ directly.
  • Limitations: Assumes deep water (no depth friction constraints).
$$\frac{g H_s}{U_{10}^2} = 0.283 \tanh \left[ 0.0125 \hat{F}^{0.42} \right]$$
$$\frac{g T_s}{2\pi U_{10}} = 1.2 \tanh \left[ 0.077 \hat{F}^{0.25} \right]$$
  • Duration-Limited Constraint:
$$\begin{aligned} \frac{gt_{\min}}{U_{10}} &= 6.5882 \exp \Big\{ \Big[0.016(\ln \hat{F})^2 \\ &- 0.3692\ln \hat{F} + 2.2024\Big]^{0.5} + 0.8798\ln \hat{F}\Big\} \end{aligned}$$ where $\hat{F} = \frac{gF}{U_{10}^2}$
  • Duration limits are implicitly evaluated via a numerical solver on the above relation.

2. USACE-SPM (Transitional)

  • Wind Scale: Scales with stress factor $U_A = 0.71 \cdot U_{10}^{1.23}$.
  • Asymptote: Restricted by finite structural depth caps.
$$\frac{g H_{m0}}{U_A^2} = 0.283 \tanh(A) \tanh \left[ \frac{0.00565 \hat{F}^{0.5}}{\tanh(A)} \right]$$ where $A = 0.530 \hat{d}^{0.75}$
  • Duration Constraint: Capped via: $$\frac{g t_{\min}}{U_A} = 68.8 \hat{F}^{2/3}$$

3. Young-Verhagen (Finite Depth)

  • Wind Scale: Standard 10-meter metric ($U_{10}$).
  • Asymptote: Explicit dissipative criteria for shallow, narrow lagoons.
$$\frac{g H_s}{U_{10}^2} = 0.241 \left[ \tanh(A_H) \tanh \left( \frac{0.00313 \hat{F}^{0.57}}{\tanh(A_H)} \right) \right]^{0.87}$$ where $A_H = 0.493 \hat{d}^{0.75}$
  • Duration checks track peak period thresholds: $\hat{t}_{\text{req}} = 537 \hat{T}_{p}^{7/3}$.