Information Technology The Breaking Wave Pdf Free Download ^HOT^

Now, MIT engineers have found a new way to model how waves break. The team used machine learning along with data from wave-tank experiments to tweak equations that have traditionally been used to predict wave behavior. Engineers typically rely on such equations to help them design resilient offshore platforms and structures. But until now, the equations have not been able to capture the complexity of breaking waves.

Their results, published today in the journal Nature Communications, will help scientists understand how a breaking wave affects the water around it. Knowing precisely how these waves interact can help hone the design of offshore structures. It can also improve predictions for how the ocean interacts with the atmosphere. Having better estimates of how waves break can help scientists predict, for instance, how much carbon dioxide and other atmospheric gases the ocean can absorb.

Information Technology The Breaking Wave Pdf Free Download

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To predict the dynamics of a breaking wave, scientists typically take one of two approaches: They either attempt to precisely simulate the wave at the scale of individual molecules of water and air, or they run experiments to try and characterize waves with actual measurements. The first approach is computationally expensive and difficult to simulate even over a small area; the second requires a huge amount of time to run enough experiments to yield statistically significant results.

Project Goals: This research opportunity focuses on the development and application of techniques to automatically identify actively breaking waves (location, breaking type) in remotely-sensed coastal imagery data in order to improve fundamental knowledge and modeling of surf-zone hydrodynamic processes. It is expected that successful candidates will evaluate state-of-the-art approaches, building on them to develop a rigorous approach to identify breaking wave location and type, that can be automated and run in near-realtime (and on historical datasets). The applicant should then propose to use these expansive observations of wave breaking within the analysis framework of the CMTB to improve the representation of wave breaking or any related hydrodynamic process in phase-resolved and/or phase-averaged numerical wave and circulation models.

Wave breaking is the main mechanism that dissipates energy input into ocean waves by wind and transferred across the spectrum by nonlinearity. It determines the properties of a sea state and plays a crucial role in ocean-atmosphere interaction, ocean pollution, and rogue waves. Owing to its turbulent nature, wave breaking remains too computationally demanding to solve using direct numerical simulations except in simple, short-duration circumstances. To overcome this challenge, we present a blended machine learning framework in which a physics-based nonlinear evolution model for deep-water, non-breaking waves and a recurrent neural network are combined to predict the evolution of breaking waves. We use wave tank measurements rather than simulations to provide training data and use a long short-term memory neural network to apply a finite-domain correction to the evolution model. Our blended machine learning framework gives excellent predictions of breaking and its effects on wave evolution, including for external data.

The importance of wave breaking, the main mechanism that dissipates energy input into ocean waves, is twofold. First, wave breaking provides an upper limit to how tall or steep waves can become, thereby limiting the steepening effects of winds1, currents2, crossing seas3, refraction by bathymetry4, abrupt depth transitions5,6, and nonlinear focusing7,8,9. Second, wave breaking itself plays a crucial role in important physical processes, such as the transport and dispersion of surface pollution including plastic debris and oil10, the energy, momentum, and mass fluxes in ocean-atmosphere interactions11,12 with climate applications such as atmosphere-ocean CO2 exchange13,14, and the formation of rogue waves15.

Despite its ubiquity and importance, no satisfying models for wave breaking exist. In potential-flow models, such as (variants of) the nonlinear Schrdinger (NLS) equation7,16 and higher-order spectral methods (HOSM)17, the effects of breaking and the vorticity the breaking induces are ignored as a direct consequence of the potential-flow assumption; they must be re-introduced through reduced-form breaking terms added to the model in ad-hoc fashion18,19,20,21. Such reduced-form breaking terms have been validated for highly simplified cases, but not for realistic broad-banded spectra, and require parameter tuning, yielding them unfit for prediction. On a larger scale, spectral wave models, such as WaveWatch III, include wave breaking through empirically determined dissipation modules22,23,24, but do not resolve individual waves.

In this paper, we develop a blended machine learning framework to model wave breaking and its effects on the nonlinear evolution of ocean waves. We show that the framework can be used for wave-resolving forecasting of breaking waves. In doing so, we overcome the challenge of having to explicitly model the turbulent nature of wave breaking. In the framework we develop, we use the viscous modified NLS (MNLS) equation7,16,36,37 as the physics-based model for non-breaking waves and wave tank measurements to serve as the ground truth.

Several mechanisms influence the evolution of waves, both in a tank and in the ocean. These include wind forcing, dispersion, nonlinear interactions, and dissipation as a result of kinematic viscosity, tank side-walls, and wave breaking. The MNLS is a canonical wave model that can predict the nonlinear and dispersive evolution of the (complex) envelope a of the free surface of unidirectional water waves accurately38 and at a very low computational cost, provided the waves are in deep water, do not break, there is no energy input from wind, and dissipative effects other than the kinematic viscosity are excluded. In non-dimensional form, the MNLS we use reads:

For the blended framework, high-fidelity turbulence-resolving direct numerical simulations remain too computationally expensive as a method to generate training data. We instead use measurements of breaking waves in a wave tank as the ground truth (see Methods). We obtain a training data set consisting of three wave types. Modulated plane waves (Wave Category I) are the simplest idealized example of breaking waves, reaching their maximum amplitude due to MI. Dispersively focused irregular waves (Wave Category II) provide a more realistic representation of the ocean47, and can reach a breaking amplitude due to focusing on the phases of the different-frequency wave components. Modulated plane waves and focused irregular waves (Wave Categories I-II) are chosen deliberately as they are the only two wave types for which breaking can be clearly and non-controversially detected in the spectrum. Finally, irregular waves with random phases (Wave Category III) are closest to a (unidirectional) sea state, where the number of breaking waves is sporadic, depending on the significant wave height, and breaking is harder to detect. The data set is split into training, validation, and test sets, of which only the first two are used in the training and training optimization process of the model. In addition, the model is only trained on segments of the total propagation length of the experiments.

We note that existing breaking models, such as the steepness threshold model by19 and the nonlinear dissipation term in18 correctly predict a spectral downshift for a modulated plane wave, although they have not been compared to experimental data therein (see Supplementary Information for a comparison with our results). The kinetic energy equation-based model20,21 also gives good qualitative agreement for the downshift with modulated plane wave experiments but requires parameter tuning.

Our framework employs experimental data as the ground truth instead of a high-fidelity numerical model. Using measurements allows previously inaccessible physics to be included in the model, as opposed to just achieving a speed-up of the simulation of known physics by a more complex model31,32,57,58,59. This direct access does come at a price when considered in the context of the growing body of work60,61,62,63 in which machine learning algorithms discover partial differential equations (PDEs), parts thereof, or their solutions. First, the ground truth is not always known in full at the model solver step, as required in an infinitesimal-domain blended model31,32, because of the finite resolution of measurements and the difficulty interpolating all aspects of the ground truth information to the required time step (such as the phase in this paper) or because it is notoriously difficult to measure them (such as the phase in optics49). Second, a convergence of the ML algorithm to a global minimum is not guaranteed if the error between measurements and the full solution (a PDE or PDE term to be discovered) is due to missing physics instead of simply Gaussian noise added to synthetic data60,61. Third, when measurement data is only available in limited quantities, purely data-driven approaches are not successful, and a physics-based model is essential to compensate for the lack of data61,64. For instance, for optical fibers, the evolutionary dynamics can be described by a Neural Network instead of the NLS equation65, when trained on large volumes of data. However, in the water-wave setting, obtaining such large quantities of wave tank experiments is prohibitively expensive.

While the finite-domain ML framework we have developed addresses some of these challenges, it has limitations. The evolution of the envelope over a finite domain strongly depends on the wave input, as the nonlinear interactions quickly mix the effects of all terms in the PDE. Therefore, over a finite domain, the difference in evolution with and without breaking has entangled in it the effects of both the wave type and its inherent nonlinear behavior and the breaking behavior. Consequently, the parameters that minimize the loss function of the network have different values for different wave types, and the FDML model cannot yet extrapolate from one wave type to another. If phase information at the solver step becomes available through either measurements or simulations, we envisage that the infinitesimal-domain method could remedy this limitation in future work as the effect of breaking on the spectrum and the nonlinear (non-breaking) spectral evolution itself then can become decoupled. e24fc04721