# On ST6 Source Terms Model Assessment and Alternative

^{1}

^{2}

^{3}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Numerical Models

#### 2.2. Theoretical Background: Self-Similar Solutions

#### 2.3. Theoretical Background: Nonlinear Interactions

#### 2.4. ST6 Model Numerical Simulation

^{2}is in a good agreement with the target dependence KC1992 for the 5–40 km fetch span as well as the numerical results of [15]. The situation is different, however, for other curves corresponding to lower shore total wave energy levels $2.2\xb7{10}^{-5}$ m

^{2}and $1.2\xb7{10}^{-7}$ m

^{2}, which exhibit noticeable deviation from the KC1992 target dependence. Additionally, in the simplified model Equation (2), we were not able to reach the “steady sea state” observed in the numerical experiments by [15] for the 200–600 km fetch range. One more difference (idealization) with WW3 and other wave models is disactivating the linear input term, which is important at the initial stage of wave development. The effect of this is seen as a difference between PGZ-2 and other models for short dimensionless fetches. We plan to perform more detailed tuning of parts of our model to minimize the effect of numerical problems [37].

## 3. Results

#### 3.1. Alternative PGZ-2 Model: Wind Energy Input and Wave Dissipation Source Functions

#### 3.2. Alternative PGZ-2 Model: Tuning and Numerical Results

- Fourier space domain ${f}_{low}<f<{f}_{high}$, resolved by 72 logarithmically positioned discrete frequencies with ${f}_{low}=0.1$ Hz and ${f}_{high}=2.0$ Hz;
- Angular domain $-\pi <\theta \le \pi $ with 36 discrete angular directions, given the wind angle ${\theta}_{wind}=0$;
- Wind velocity ${U}_{10}=10$ m/s at a 10 m height above the ocean surface

## 4. Discussion

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Limited fetch problem geometry. Constant wind of 10 m/s is blowing orthogonally to the fetch.

**Figure 6.**Spectral wave energy density $\epsilon $ as the function of the frequency $\omega $ and angle $\theta $ for ST6 case.

**Figure 7.**Decimal logarithm of the angle averaged wave energy spectral density $\frac{1}{2\pi}{\int}_{0}^{2\pi}\epsilon (\omega ,\theta )d\theta $ as the function of the decimal logarithm of frequency f for ST6 case. Dashed line—the KZ spectral fit $\phantom{\rule{-0.166667em}{0ex}}\sim \phantom{\rule{-0.166667em}{0ex}}{\omega}^{-4}$; dashed/dotted line—the Phillips spectral fit $\phantom{\rule{-0.166667em}{0ex}}\sim \phantom{\rule{-0.166667em}{0ex}}{\omega}^{-5}$.

**Figure 8.**Spectral wave energy density $\epsilon $ as the function of the frequency $\omega $ and angle $\theta $ for PGZ-2 case.

**Figure 9.**Decimal logarithm of the angle-averaged wave energy spectral density $\frac{1}{2\pi}{\int}_{0}^{2\pi}\epsilon (\omega ,\theta )d\theta $ as the function of the decimal logarithm of frequency f for PGZ-2 case. Dashed line—the KZ spectral fit $\sim \phantom{\rule{-0.166667em}{0ex}}{\omega}^{-4}$; dashed/dotted line—the Phillips spectral fit $\sim \phantom{\rule{-0.166667em}{0ex}}{\omega}^{-5}$.

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**MDPI and ACS Style**

Pushkarev, A.; Geogjaev, V.; Zakharov, V.
On ST6 Source Terms Model Assessment and Alternative. *Water* **2023**, *15*, 1521.
https://doi.org/10.3390/w15081521

**AMA Style**

Pushkarev A, Geogjaev V, Zakharov V.
On ST6 Source Terms Model Assessment and Alternative. *Water*. 2023; 15(8):1521.
https://doi.org/10.3390/w15081521

**Chicago/Turabian Style**

Pushkarev, Andrei, Vladimir Geogjaev, and Vladimir Zakharov.
2023. "On ST6 Source Terms Model Assessment and Alternative" *Water* 15, no. 8: 1521.
https://doi.org/10.3390/w15081521