Session H27: Surface Waves, Vortex Dynamics, and Turbulence

Enhanced settling and dispersion of inertial particles in surface waves

Finite-size particles demonstrate enhanced settling and altered transport under surface gravity waves. In this talk, we derive an expression for the enhanced settling velocity for particles with small to intermediate Reynolds numbers for linear wave theory under arbitrary depth. We discuss how this enhanced settling is a function of the wave steepness, wave depth, and particle parameters. In our analysis, we also show that a mechanism for dispersion exists in the system and that particles settling under waves will spread horizontally. Finally, we compare our results to experimental data which shows similar trends.

    

Direct Numerical Simulation of Surface Waves and Turbulent Boundary Layer Interaction

Wind-wave interaction happens when the wind blows across the surface water waves. The waves grow under the wind forcing, and at the same time, alter the turbulent boundary layer above them. The dynamics of this common but complex phenomenon is a long-standing problem that attracts both theoretical and practical interests. To seek a better physical understanding of this two-way coupling between wind and waves, we conduct direct numerical simulations of the two-phase Navier-Stokes equations with adaptive mesh refinement (AMR). A turbulent boundary layer flow interacts with a traveling wave train in a fully coupled manner, without any prescribed interfacial conditions. We explore a range of controlling parameters including wave age (ratio of wave speed and friction velocity) and wave slope. We analyze the dynamics of the turbulent air and water flow, as well as the wave growth. We also report the momentum and energy budgets, focusing on the pressure and shear stress partition. Such high fidelity simulations of the fully coupled wind-wave problem aim to improve the parameterization of the wind energy input term for wave growth, as well as provide references for the development of LES models of the marine atmospheric boundary layer that include surface wave effects.   

Numerical investigation of turbulence for surface gravity waves

In this work, we numerically study the wave turbulence of surface gravity waves. The purpose is to understand the variation of the scaling of the wave spectra with wavenumber k and energy flux P at different nonlinearity levels for different forcing/free-decay conditions. For three representative conditions (free-decay, narrow- and broadband forcing), we find that the spectral forms approach wave turbulence theory (WTT) solution S~k^-5/2 and S~P^1/3 at high nonlinearity levels. With the decrease of nonlinearity level, the spectra for all cases become steeper, with the narrow-band forcing case exhibiting the most rapid deviation from WTT. Two hypothetical mechanisms on bound waves and finite-size effect to explain these spectral variations are investigated. Through a tri-coherence analysis, we find that the finite-size effect is responsible for the steepening of the spectra and reduced capacity of energy flux at lower nonlinearity levels in all cases. Bound waves are found to be the main reason leading to the fastest deviation from WTT with the decrease of nonlinearity in the narrow-band forcing case.   

Nonlinear regimes of tsunami waves generated by a granular collapse

Tsunami waves generated by subaerial landslides are a threat to human activities along coastal areas, as illustrated by recent events such as the partial flank collapse of Anak Krakatau (2018). To improve our prediction of such events, we consider the collapse of a granular column into water in a quasi-two-dimensional setup. Our experiments reveal three nonlinear wave regimes, depending on the Froude number Frf based on the ratio of the velocity of the advancing granular front at the interface and the velocity of linear gravity waves in shallow water. For large Frf, transient bores are generated, while for intermediate values of Frf quasi-symmetrical solitary-like waves are produced. Finally, nonlinear transition waves are observed at small Frf. The relative wave amplitude increases with the local Froude number in the three regimes with different nonlinear scalings, while the relative wavelength is an increasing or decreasing function of the local Froude number depending on the wave regime. We rationalize these wave regimes using shallow water equations by considering that the advancing granular front acts as a vertical piston pushing the water, and report that nonlinear transition waves are found to be a transition from shallow to deep-water conditions.  The present modeling contributes to a better understanding of the rich hydrodynamics of the impulse waves generated by grains entering into water.   

Analysis of an ensemble of plunging breaking events

The dynamics of three plunging breaking waves is studied through measurements of the evolution of their free surface profiles during 10 repeated breaking events for each wave. The waves are created from dispersively focused wave packets which are generated by a highly accurate programmable wave maker. The wave maker motions that create the three breakers are identical except for the overall amplitude. Breaker profiles are measured with a cinematic laser induced fluorescence technique covering a streamwise region of approximately one wavelength. The 10 repeated sets of breaker profiles are spatially aligned at the time of jet impact. The aligned data is used to create spatio-temporal maps of the ensemble average surface height and the standard deviation of both the local normal distance from the instantaneous mean profile and the local arc length relative to the local mean arc length of the instantaneous mean profile. It is found that the mean and standard deviation maps contain strongly correlated localized features that indicate that the transition from laminar to turbulent flow is a highly repeatable process. Regions of high standard deviation include the splash created by the plunging jet impact as well as the site where the air pocket entrained under the plunging jet comes to the surface and pops on the back face of the wave.   

On the Distributions and Scaling of Energy Flux in Wave Turbulence

While energy cascades in nonlinear dispersive wave systems are widely studied, the properties of these cascades are often in disagreement with the predictions of wave turbulence theory (WTT). We present numerical experiments of a model equation in a two-dimensional periodic domain with fully-resolved steady distributions of forward energy flux P(t) for a range of nonlinear strengths. We compute the contributions to P(t) from four-wave interactions with frequency mismatch |Δω|, yielding a direct measurement of P_q(|Δω|,t), the distribution of P(t) in |Δω|. In regimes of high nonlinearity, our analysis shows that quasi-resonant interactions dominate the mean flux P and drive the large fluctuations present in P(t). We also identify a relationship between P_q(|Δω|,t) and the number of interactions with the same frequency mismatch |Δω|. By using the WTT closure model, we measure P as predicted by the wave kinetic equation (WKE), P_KE. We show that the kinetic scaling of inertial range wave-action N ~ P^1/3 is approximately satisfied even when quasi-resonances are dominant at high nonlinearity levels, however P_KE differs from the true flux P by a factor difference.   

Saturation of the inverse cascade in surface gravity-wave turbulence

Wave turbulence models the statistical properties of stochastic nonlinear wave fields. For ocean surface waves, the formation of an inverse cascade towards large scales has been predicted theoretically in the 1980s and confirmed numerically fifteen years ago. By replacing the usual absorbing beach of a wave basin by a reflective wall, we are able to evidence this inverse cascade for the first time in a large-scale basin. We also report a saturation of the evolution of the inverse cascade due to the emergence of nonlinear dissipative structures. In such a statistically stationary and isotropic wave field, we then study the statistics of rogue waves generated by nonlinear wave interactions (and not directly by a wavemaker), a situation thus close to realistic sea states that still remains poorly known.

E. Falcon, G. Michel, G. Prabhudesai, A. Cazaubiel, M. Berhanu, N. Mordant, S. Aumaître, and F. Bonnefoy, Saturation of the inverse cascade in surface gravity-wave turbulence, Phys. Rev. Lett. 125, 134501 (2020).

G. Michel, F. Bonnefoy, G. Ducrozet, and E. Falcon, Statistics of rogue waves in isotropic wave fields, submitted to Phys. Rev. Lett. (2021).   

Effects of elevated inflow turbulence intensity on vortex-induced vibration of smooth circular cylinders

Experiments were conducted to investigate the effects of elevated turbulence intensity (Ti) on vortex-induced vibration (VIV) of smooth circular cylinders. A Makita-type active grid turbulence generator was used to create Ti levels of ~13% and ~19% over a Reynolds number range of 5×10³ – 3.56×10⁴. The dynamic response of the cylinder undergoing VIV is plotted as a function of reduced velocity. The results are compared to the baseline (quasi-laminar) without the active grid where Ti ~ 2.2%. The elevated Ti cases were found to result in an identifiable suppression of VIV amplitudes and the crossflow force compared to the quasi-laminar case. Elevated levels of free-stream turbulence are distributed over a large range of frequencies and are not concentrated near the natural frequency of the system; as a result, the vibration amplitudes are suppressed during lock-in. We discuss our findings by comparing plots of amplitude spectral density and phase maps of instantaneous crossflow velocities/displacements.   

Coupling of a Vortex with Turbulence - Limitation of Core Dynamics and Bursting

Variation in the vortex core diameter inherently drives vortex line coiling/uncoiling, called core dynamics, associated with meridional flow – radial and axial velocities. Data for large core variations show coiled vortex lines with azimuthal vorticity (ω_θ) forming packets, which collide and result in a vortex ring dipole; the eruption of this dipole is called vortex bursting. The dipole is unstable, thus the question of how turbulence couples with core dynamics and bursting arises – studied here using DNS at a Reynolds number (vortex circulation/viscosity) of 10,000 – the limit of current computation. Core dynamics couple with the turbulence via the meridional flow. Meridional flow tilting of vorticity is the most dominant mechanism within the core, as the mean strain tilting is negligible. Notably, generation of radial vorticity (ω_r) alters vortex line coiling, which causes the packet to be diffused. This is most impactful when the packets collide to form the dipole. Tilting of the turbulent ω_r locally generates positive and negative ω_θ – hence, the packet transforms into a clustering of fine scale ω_θ regions. The disruption of the packet interrupts the dipole formation and prevents bursting – an obstacle to using bursting for control of aircraft trailing vortices.