Session L15: Free-Surface Flows: Waves & Turbulence

A comparison of optical techniques for free-surface measurements along wave- and turbulence-driven flows

The free surface at an air-water interface has been shown to relay information about inner-flow characteristics, including the manifestation of turbulence through rising coherent structures. We explore existing optical techniques that enable free-surface reconstruction in a cost-effective and efficient manner. These techniques measure the apparent distortions of a reflected or refracted reference pattern that vary linearly with the gradient of the surface elevation. We compare the performance of three imaging techniques (Free-Surface Synthetic Schlieren, Total Internal Reflection-Deflectometry, Moon-Glade Background Oriented Schlieren) to characterize the perturbations along a dynamic free-surface. Surface reconstruction is performed using an optical flow algorithm that provides an improvement over cross-correlation techniques. This is in part due to the higher spatial resolution of the resulting displacement field coupled with a superior performance in computing larger displacements with higher straining/dilatation of the background reference pattern. Surface motions are induced in two ways: 1) turbulent free-shear flow emanating from a submerged jet that impinges the underside of the free-surface and 2) gravity-capillary waves that arise from flow across an overspill weir. These two flow conditions simulate surface dynamics in an open-channel flow where the bottom roughness triggers coherent structures that impact the free surface. The physics of each technique is assessed, and the surface reconstruction results are compared to one another. We will discuss the advantages and drawbacks of each technique in terms of accuracy and practicality. Finally, we use the surface elevation results to untangle the gravity-capillary wave mechanics in terms of their dispersive properties as well as to investigate the manifestation of turbulence within the energetic and random surface roughness that is generated from the submerged jet.

    

Surface wave spectrum in boxed free-surface turbulence

In the present study free surface turbulence (FST) is explored in a canonical FST facility based on a non-intrusive optical diagnostic for reconstruction of liquid-gas interfaces in the 3D space and time with one single laser plane and camera. 

The 3D interfacial topography is acquired based on a robust ray tracing algorithm by imaging from the gas phase a 2D, vertical grid written directly in the liquid phase. The nature of the grid and its orientation allow to adapt the technique in various spatio-temporal scales, perform the profilometry simultaneously with velocimetry, simplify the experimental set up and extend the applicability of the refraction-based profilometers to both small and steep waves. The images can be processed both as individual and time resolved events; the latter case provides up to 30% more points in steep FS regions.

The FST facility design principles are similar to the ones in traditional “boxed turbulence” configurations; symmetrically placed agitators disrupt the flow in an open cylindrical chamber. FS-wall interactions are minimized with a passive wave breaker. Data from this facility, wave spectra and more details about the algorithm will be presented at the conference.   

Turbulent diffusive transport of floating discs

Understanding floating particle transport is crucial for the global response to plastic pollution. One key issue is the rate at which floating particles of different shapes and sizes spread over the surface of turbulent waters. Here we study experimentally the diffusive transport of floating discs in free-surface grid turbulence using particle tracking velocimetry. We consider discs larger than the dissipative flow scales and investigate their inertial filtering, i.e., the ability to filter out small-scale fluctuations. This behaviour, long identified in studies concerning particles in three-dimensional turbulence, may result in longer time-correlated motion as compared to fluid elements, and thus increased diffusivity. However, the applicability of classic turbulence theory to free-surface turbulence is debated. To substantiate this notion, we consider the Lagrangian motion of the discs and compare them to that of floating tracers of the free-surface flow. Specifically, we determine the discs' diffusion coefficient by integrating the velocity auto-correlation function following the classical framework of Taylor diffusion. We verify their spreading rate by calculating the mean-square displacement due to turbulent fluctuations along the particle trajectories.   

Reconstruction of three-dimensional turbulent flow structures using surface measurements for free-surface flows based on convolutional neural network

We present a machine learning model to reconstruct three-dimensional turbulent flow structures using surface measurements for free-surface flows. The proposed model, which is based on the convolutional neural network (CNN) and is trained using the data obtained from direct numerical simulations of turbulent open-channel flows, can predict the velocity fluctuation field near the free surface and large-scale flow structures away from the surface with high accuracy. The CNN model outperforms a traditional linear stochastic estimation (LSE) model considerably. Further analyses of the CNN model and LSE model provide insights into how the two models are related to the flow physics of the subsurface turbulence. 

    

Wave-resolved direct numerical simulation and statistical analysis of Langmuir turbulence

Langmuir turbulence generated by the interaction between progressive surface waves and wind shear-induced turbulence is simulated using a wave-resolved direct numerical simulation (DNS) approach. The incipient generation and time evolution of the Langmuir turbulence caused by wave-turbulence interaction are analyzed statistically. The DNS results are also compared with the numerical modeling results obtained using the classical wave-averaged Craik–Leibovich (CL) model. A detailed analysis of the turbulent kinetic energy (TKE) budget shows that although the characteristics of the Langmuir turbulence obtained by the two models are similar, the detailed mechanisms for TKE production through wave-turbulence interaction are different in the flow fields obtained from the wave-resolved DNS and the wave-averaged CL model.   

Validation of CFD Predictions of Wave Propagation and Forces on a Cylinder in a Long Flume

During hurricanes, coastal residential structures are subjected to high winds in combination with storm surge and subsequent waves. Elevating a building above the Base Flood Elevation will reduce flood damage, but the effects of wind-wave interaction in the areas surrounding and beneath the structure on the pressure distributions seen during extreme weather events are not well understood. Our long-term goal is to enable computational fluid dynamics (CFD) predictions of combined wind-wave loading. 

The objective of this initial study is to validate CFD predictions of the pressure distributions on a cylinder resulting from wave-only loading conditions. Numerical results from multiphase 2D and 3D RANS simulations using the OpenFOAM toolbox will be validated against experimental data of regular surface waves propagating down the OSU Large Wave Flume in still air and interacting with a steel cylinder. The full 87.64m flume is included in the CFD domain. Surface elevations, velocity profiles, wave run-up on pile, and pressure distributions will be compared. The sensitivity of the numerical wave and wind profiles to various model parameters is investigated. 

Preliminary results show good agreement between numerical and experimental results. The findings of this study will be used to inform next steps toward validated simulation of coupled wind-wave loading on coastal structures.   

Effects of turbulence in high-speed winds on wind-wave coupled simulations

The impacts of climate-driven hazards in coastal regions escalate due to sea level rise and anthropogenic warming, causing severe direct losses and fatalities. To enhance the resilience of communities to extreme events, the NICHE team aims to design a full-scale testing infrastructure to model the impacts of wind and coastal hazards. The design will rely on physical experiments in existing wind-wave facilities, as well as numerical simulations.

This talk will present progress towards establishing validated high-fidelity large-eddy simulations (LES) of coupled wind-wave problems to inform the design of NICHE. We investigate the consequence of using different interface capturing schemes on the turbulence characteristics of both the wind and water velocity field. Moreover, we compare the results of LES with different subgrid models, and Reynolds-averaged Navier-Stokes simulations with different turbulence models. Finally, the effects of turbulence in high-speed winds on the wave propagation, wave morphology and wave breakup event are quantified.   

Statistics of extreme ship motions in broad-band wave field

We consider the evaluation of extreme ship motion probability in a broad-band irregular wave field. For this problem, the previous techniques developed for the parameterization of the narrow-band wave field, i.e., methods based on the wave group structures, cannot be directly applied. The group-based statistics that are widely used in existing works also become ambiguous. In this work, we develop a new framework to directly resolve the temporal exceeding probability, defined as the fraction of time that ship motions exceed a given threshold. The parameterization of the wave field will be based on structures with elevations exceeding some threshold that are well suited to broad-band waves.  The effectiveness of the proposed approach will be demonstrated in multiple broad-band wave fields with ship motion simulated by nonlinear roll equations.

    

On the linearity of wave energy temporal growth in the initial stage of Phillips theory

In 1957, Phillips proposed a prominent theory to elucidate the role of the resonance mechanism in the initial growth of surface waves from a flat air-water interface. The resonance between turbulent airflow and water deformation occurs when the convection velocity of air pressure fluctuations at the water surface matches the phase velocity of water waves. Near the resonance curve in the wavenumber space, the wave energy spectrum component grows quadratically with time. The overall temporal evolution of surface elevation variance exhibits a linear feature. Here, we present numerical evidence on the resonance mechanism in the initial stage of the Phillips theory based on direct numerical simulation data. We also provide a rigorous proof of the linear growth of surface elevation variance in the initial stage. We show that for gravity waves the leading order term of surface elevation variance is bounded by a linear function of time from an asymptotic analysis.   

Modeling and predicting oscillating surge wave energy converter behavior using dynamic mode decomposition

Modeling wave energy converters (WECs) to accurately predict their hydrodynamic behavior has been a notoriously difficult challenge for the wave energy field, particularly in polychromatic sea states. A key challenge is that accurate, physics-based WEC modeling is too computationally expensive to be used for future-state prediction and optimal control, two areas of active research in the wave energy field. We propose the use of dynamic mode decomposition (DMD) to provide a purely data-driven technique to overcome these issues. In this study, we use DMD to develop a linear model of a grid-scale Oscillating Surge WEC (OSWEC) operating in polychromatic seas. Our goal is to model and predict the behavior of the OSWEC for use in optimal control schemes, such as model predictive control (MPC), without requiring an infeasible computational cost or sacrificing accuracy. We show that by using DMD, we can accurately model and predict OSWEC behavior in response to polychromatic sea states with appropriate model rank and training time. These findings provide insight on the use of DMD on systems with limited time-resolved data and present a framework for applying similar analysis to lab-scale experiments, high-fidelity simulations, or data from OSWECs operating in the field.