Numerical investigation of turbulence of surface gravity waves

In this paper, we numerically study the wave turbulence of surface gravity waves in the framework of Euler equations of the free surface. The purpose is to understand the variation of the scaling of the spectra with wavenumber $k$ and energy flux $P$ at different nonlinearity levels under different forcing/free-decay conditions. For all conditions (free decay and narrow-band and broad-band forcing) that we consider, we find that the spectral forms approach the wave turbulence theory (WTT) solution $S_\eta \sim k^{-5/2}$ and $S_\eta \sim P^{1/3}$ at high nonlinearity levels. With a decrease of nonlinearity level, the spectra for all cases become steeper, with the narrow-band forcing case exhibiting the most rapid deviation from WTT. We investigate bound waves and the finite-size effect as possible mechanisms causing the spectral variations. Through a tri-coherence analysis, we find that the finite-size effect is present in all cases, which is responsible for the overall steepening of the spectra and the reduced capacity of energy flux at lower nonlinearity levels. The fraction of bound waves in the domain generally decreases with the decrease of nonlinearity level, except for the narrow-band case, which exhibits a transition at a critical nonlinearity level below which a rapid increase is observed. This increase serves as the main reason for the fastest deviation from WTT with the decrease of nonlinearity in the narrow-band forcing case.

The formation of strip-like vortex motion by surface gravity waves

We studied experimentally the generation of vortex flow by non-collinear gravity waves with a frequency of 2.34 Hz. The vortices formed on the water surface have the form of stripes, the width L=π/(2k sin θ) of which is determined by the wave vector k and the angle between them, and the length is determined by the size of the system. We demonstrate that the measured dependence Ω(t) can be described within the recently developed model that considers the Eulerian contribution to the generated vortex flow and the effect of surface contamination.

Dynamics and Transformation of Sea Surface Gravity Waves at the Shelf of Decreasing Depth

This paper reviews the results of the processing of synchronized data on hydrosphere pressure variations and the Earth’s crust deformation in the microseismic range (5–15 s), obtained over the course of numerous experiments, using a coastal laser strainmeter and laser meters of hydrosphere pressure variations installed in various points of the Sea of Japan shelf. Interpreting the results, we have discovered new regularities in the dynamics of surface progressive gravity waves, and their transformation into primary microseisms, when waves move at the shelf of decreasing depth. For example, we found non-isochronous behavior of progressive waves, which manifests itself in a decrease in the periods of gravity waves due to the transformation of a part of their energy into the energy of primary microseisms. Furthermore, when processing the synchronous fragments of the records, made by laser strainmeters and laser meters of hydrosphere pressure variations, we identified approximate zones of the most effective transformation of the energy of gravity progressive waves into the energy of primary microseisms, which start from the depth of less than a half-wavelength and stretch to the surf zone.

Saturation of the internal tide over the inner continental shelf. Part II: Parameterization

Here, we develop a framework for understanding the observations presented in the accompanying paper (Part I) by Becherer et al. (2021). In this framework, the internal tide saturates as it shoals due to amplitude limitation with decreasing water depth (H). From this framework evolves estimates of averaged energetics of the internal tide; specifically, energy, 〈APE〉, energy flux, 〈FE〉, and energy flux divergence, ∂x 〈FE〉. Since we observe that 〈D〉 ≈ ∂x 〈FE〉, we also interpret our estimate of ∂x 〈FE〉 as 〈D〉. These estimates represent a parameterization of the energy in the internal tide as it saturates over the inner continental shelf. The parameterization depends solely on depth-mean stratification and bathymetry. A summary result is that the cross-shelf depth dependencies of 〈APE〉, 〈FE〉 and ∂x 〈FE〉 are analogous to those for shoaling surface gravity waves in the surf zone, suggesting that the inner shelf is the surf zone for the internal tide. A test of our simple parameterization against a range of data sets suggests that it is broadly applicable.