Modelling the Impact of Squall on Wind Waves with the Generalized Kinetic Equation

Abstract

This is a first study of short-lived transient sea states, arising from fast variations of wind fields. This study considers the response of a wind-wave field to a sharp increase of wind over a short time interval (a squall). Conventional wind-wave models based on the Hasselmann equation assume quasi stationarity of a random wave field and are a priori inapplicable for such transient states. To describe fast spectral changes, the authors use the generalized kinetic equation (GKE) derived without the quasi-stationarity assumption. A novel efficient highly parallelized algorithm for the numerical simulation of the GKE is presented. Simulations with the GKE and the Hasselmann equation are examined and compared. While under steady wind, the spectral evolution in both cases is shown to be practically identical, but after the squall the qualitative difference emerges: the GKE predicts formation of a transient sea state with a considerably narrower peak.

Kinetic equations in a third-generation spectral wave model

“…Under this steady wind forcing, traditional wave parameters and are practically insensitive to the frequency of phase mixing (), as already demonstrated in GS13 and Annenkov & Shrira (2016). In line with Annenkov & Shrira (2015), even for wave spectra subject to turning winds (i.e. a sudden change in wind direction), the GKE/JKE produces comparable results to the HKE.…”

“…In line with Annenkov & Shrira (2015), even for wave spectra subject to turning winds (i.e. a sudden change in wind direction), the GKE/JKE produces comparable results to the HKE.…”

“…The JKE and GKE (blue and red markers) are not dissimilar to the HKE. Although unexpected, this is, however, in line with findings from Annenkov & Shrira (2015) who found the HKE and GKE produce nearly identical results during a squall event (sharp increase in wind speed). The significant differences between distinct kinetic equations as observed by GB16 for comparable situations are primarily attributed to the two numerical flaws (discretization and source term integration) in their computations.…”

“…For 1-D spectra, the advantage of modern kinetic equations (JKE, GKE) over the HKE is beyond controversy (Janssen 2003, GS13). For directional wave spectra, however, findings from previous studies, particularly GB16 and Annenkov & Shrira (2015, 2016, 2018), are not fully consistent.…”

“…Considering (i) that wind blows steadily in this duration-limited case and, hence, the wave field evolves slowly and (ii) that wave spectra are sufficiently broad and, thus, non-resonant interactions contribute little to the development of wind waves, we expect that the three kinetic equations (HKE, JKE and GKE) should yield essentially the same evolution of wave spectrum (Annenkov & Shrira 2015, 2016). Using the HKE-based results as the baseline reference, we quantify the accuracy of the JKE and GKE simulations with the following metrics: where and represent integral wave parameters from the GKE/JKE and HKE runs, respectively.…”