arXiv subjects

Ashleigh Simonis

Publications and source records attributed to Ashleigh Simonis.

4 recordsLinked to original sources

arXiv2026

Dissipation-driven champion solitons in one-dimensional shallow-water waves

In this paper, we identify a new mechanism for rogue wave formation in a shallow-water setting. We study a bidirectional shallow-water wave field in the context of the Kaup-Boussinesq equation, and introduce a weak high-wavenumber dissipative perturbation that breaks the underlying integrability of the system. In this setting, dominant solitons grow through successive interactions with weaker, co-propagating solitons, leading to the formation of a "champion soliton" in each direction of propagation. This behaviour is in contrast to the general intuition that dissipation damps coherent structures, and instead shows that weak dissipation can induce their intensification. Moreover, we find that weak dissipation alone is not sufficient for champion soliton formation; the presence of random waves plays a crucial role in the intensification process, catalysing the transfer of energy into dominant coherent structures. While champion solitons have previously been studied in non-integrable systems, these works primarily consider perturbations introduced through modifications of the nonlinear terms (e.g., higher-order Korteweg-de Vries and Schr\"odinger-type models). In the present work, high-wavenumber dissipation provides a more physically natural perturbation, since such small-scale damping is a common feature in many systems.

nlin.PS↗

arXiv2026

Bidirectional shallow-water wave turbulence

We study bidirectional one-dimensional (1-D) shallow-water waves within a class of Boussinesq equations, including the integrable Kaup-Boussinesq (KB) equation and a truncated-dispersion variant, which serves as a representative non-integrable model. For these two systems, the normal-form transformation yields an interaction coefficient of the same general structure, differing only through the dispersion relation. We derive this coefficient and numerically confirm that it vanishes on the resonant manifold for the KB equation, as expected in the literature. In contrast, the non-integrable model admits a non-vanishing interaction coefficient, producing a non-trivial wave kinetic equation (WKE), which is the first known in a 1-D shallow-water setting. The resulting WKE is non-homogeneous in nature due to the non-homogeneity of the corresponding dispersion relation; however, approximate Kolomogrov-Zakharov (KZ) solutions can be derived in a novel way under certain approximations. Numerical experiments in two settings validate the kinetic predictions and elucidate the underlying dynamics: (i) in free-evolution cases of the KB equation, despite complete integrability and the invariance of the discrete nonlinear spectrum guaranteed by isospectrality, an initial arbitrary wavenumber spectrum undergoes substantial evolution driven by quasi-resonant triad interactions; (ii) in forced-dissipated cases of the non-integrable equation, we find stationary power-law spectra that agree with the theoretical predictions.

nlin.CD↗

arXiv2024

Transition from weak turbulence to collapse turbulence regimes in MMT model

It is well known that wave collapses can emerge from the focusing one-dimensional (1-D) Majda-McLaughlin-Tabak (MMT) model as a result of modulational instability. However, how these wave collapses affect the spectral properties and statistics of the wave field has not been adequately studied. We undertake this task by simulating the forced-dissipated 1-D MMT model over a range of forcing amplitudes. Our results show that when the forcing is weak, the spectrum agrees well with the prediction by wave turbulence theory with few collapses in the field. As the forcing strength increases, we see an increase in the occurrence of collapses, together with a transition from a power-law spectrum to an exponentially decaying spectrum. Through a spectral decomposition, we find that the exponential spectrum is dominated by the wave collapse component in the non-integrable MMT model, which is in analogy to a soliton gas in integrable turbulence.

nlin.PS↗

arXiv2023

On the time scales of spectral evolution of nonlinear waves

As presented in Annenkov & Shrira (2009), when a surface gravity wave field is subjected to an abrupt perturbation of external forcing, its spectrum evolves on a ``fast'' dynamic time scale of $O(\varepsilon^{-2})$, with $\varepsilon$ a measure of wave steepness. This observation poses a challenge to wave turbulence theory that predicts an evolution with a kinetic time scale of $O(\varepsilon^{-4})$. We revisit this unresolved problem by studying the same situation in the context of a one-dimensional Majda-McLaughlin-Tabak (MMT) equation with gravity wave dispersion relation. Our results show that the kinetic and dynamic time scales can both be realised, with the former and latter occurring for weaker and stronger forcing perturbations, respectively. The transition between the two regimes corresponds to a critical forcing perturbation, with which the spectral evolution time scale drops to the same order as the linear wave period (of some representative mode). Such fast spectral evolution is mainly induced by a far-from-stationary state after a sufficiently strong forcing perturbation is applied. We further develop a set-based interaction analysis to show that the inertial-range modal evolution in the studied cases is dominated by their (mostly non-local) interactions with the low-wavenumber ``condensate'' induced by the forcing perturbation. The results obtained in this work should be considered to provide significant insight into the original gravity wave problem.

physics.flu-dyn↗