Anomalous sea surface structures as an object of statistical topography

Area of Science:

• Fluid dynamics
• Statistical physics
• Oceanography

Background:

• Sea surface dynamics are complex, influenced by stochastic processes.
• Understanding anomalous wave structures (highs and gaps) is crucial for maritime safety and coastal engineering.

Purpose of the Study:

• To analyze the stochastic boundary problem of anomalous sea surface structure emergence.
• To model the probability density of surface elevation and its gradient under stochastic conditions.

Main Methods:

• Exploiting statistical topography concepts.
• Applying the stochastic Liouville equation with diffusion approximation for hydrodynamic velocity fields.
• Deriving a joint probability density equation for surface elevation and gradient.
• Accounting for stochastic bottom irregularities and the infinitely deep ocean assumption.

Main Results:

• A model for the probability density of surface elevation and its gradient was derived.
• Clustering in the absolute surface elevation gradient field occurs with unit probability.
• This clustering leads to the frequent emergence of rare events like anomalous high structures and deep gaps.

Conclusions:

• Stochastic bottom irregularities and velocity fields significantly influence sea surface topography.
• The derived model accurately predicts the formation of extreme sea surface features.
• Findings have implications for predicting and mitigating risks associated with extreme sea states.