Coupling Wave and Surge Models on Steep Slopes

Source: ICHE Conference Archive - https://mdi-de.baw.de/icheArchiv

The effects of natural structure on estimated tropical cyclone surge extremes

Abstract The past 12 years have seen significant steps forward in the science and practice of coastal flood analysis. This paper aims to recount and critically assess these advances, while helping identify next steps for the field. This paper then focuses on a key problem, connecting the probabilistic characterization of flood hazards to their physical mechanisms. Our investigation into the effects of natural structure on the probabilities of storm surges shows that several different types of spatial-, temporal-, and process-related organizations affect key assumptions made in many of the methods used to estimate these probabilities. Following a brief introduction to general historical methods, we analyze the two joint probability methods used in most tropical cyclone hazard and risk studies today: the surface response function and Bayesian quadrature. A major difference between these two methods is that the response function creates continuous surfaces, which can be interpolated or extrapolated on a fine scale if necessary, and the Bayesian quadrature optimizes a set of probability masses, which cannot be directly interpolated or extrapolated. Several examples are given here showing significant impacts related to natural structure that should not be neglected in hazard and risk assessment for tropical cyclones including: (1) differences between omnidirectional sampling and directional-dependent sampling of storms in near coastal areas; (2) the impact of surge probability discontinuities on the treatment of epistemic uncertainty; (3) the ability to reduce aleatory uncertainty when sampling over larger spatial domains; and (4) the need to quantify trade-offs between aleatory and epistemic uncertainties in long-term stochastic sampling

Soliton Turbulence in Shallow Water Ocean Surface Waves

We analyze shallow water wind waves in Currituck Sound, North Carolina and experimentally confirm, for the first time, the presence of $soliton$ $turbulence$ in ocean waves. Soliton turbulence is an exotic form of nonlinear wave motion where low frequency energy may also be viewed as a $dense$ $soliton$ $gas$, described theoretically by the soliton limit of the Korteweg-deVries (KdV) equation, a $completely$ $integrable$ $soliton$ $system$: Hence the phrase "soliton turbulence" is synonymous with "integrable soliton turbulence." For periodic/quasiperiodic boundary conditions the $ergodic$ $solutions$ of KdV are exactly solvable by $finite$ $gap$ $theory$ (FGT), the basis of our data analysis. We find that large amplitude measured wave trains near the energetic peak of a storm have low frequency power spectra that behave as $\sim\omega^{-1}$. We use the linear Fourier transform to estimate this power law from the power spectrum and to filter $densely$ $packed$ $soliton$ $wave$ $trains$ from the data. We apply FGT to determine the $soliton$ $spectrum$ and find that the low frequency $\sim\omega^{-1}$ region is $soliton$ $dominated$. The solitons have $random$ $FGT$ $phases$, a $soliton$ $random$ $phase$ $approximation$, which supports our interpretation of the data as soliton turbulence. From the $probability$ $density$ $of$ $the$ $solitons$ we are able to demonstrate that the solitons are $dense$ $in$ $time$ and $highly$ $non$ $Gaussian$.Comment: 4 pages, 7 figure

Extreme Runup Statistics on Natural Beaches

Source: https://erdc-library.erdc.dren.mil/jspui/Wave runup data collected on a natural beach a t the Coastal Engineering Research Center's Field Research Facility (FRF) are analyzed. The FRF data are supplemented by addition l runup data collected on two beaches within San Francisco Bay, California. Analyses focused on developing a method to predict the upper limit of wave runup on natural beaches. It was found that beach runup at the FRF was strongly dependent on a surf similarity parameter based on beach face slope and incident wave conditions. However, correlation between the runup and surf parameter was quite sensitive to the location where wave conditions were measured. Runup predictions using wave information from a gage in 8 m of water were better than similar predictions using information from gages in depths of 17 and 2 m. It was also found that scaling using the local wave length was superior t o scaling by the deep-water wave length. A statistical framework is developed for estimating the extreme wave runup during a storm. This framework is specifically applicable to the FRF, but analysis indicates that it is general enough to be used for the San Francisco Bay beaches and possibly for most natural sand beaches. For idealized, constant conditions, a simple procedure is presented for estimating the expected maximum runup elevation during a storm

Full Boltzmann Discrete Spectral Wave Model, Implementation and Nondimensional Tests

Source: https://erdc-library.erdc.dren.mil/jspui/A full Boltzmann integration scheme is implemented within a functioning discrete spectral wave model. Preliminary testing (academic) is presented and compared to alternate solution methods. It is found that third-generation models depend on a detailed balance among source terms, and it is important that these source terms be specified accurately. In the present state of the art, information on all of the source terms does not appear to be sufficient to permit definitive estimates of all source terms in the detailed balance evaluations. Older means of estimating the nonlinear wave-wave interaction (Snl) are much less accurate than the full Boltzmann method. Even the Discrete Interaction Approximation (WAMDIG 1988) representation for Snl used in the only documented third-generation wave model (WAM) is shown incapable of providing an accurate estimate of Snl. The full Boltzmann model should provide an improved method to investigate several important wave generation and decay situations. The WAM source terms are inconsistent with observed wave-growth laws and equilibrium-range behavior from the Joint North Sea Wave Project (Hasseimann et al. 1973). New source terms postulated in this report provide a very good match to the JONSWAP wave growth rates and equilibrium-range behavior. The present version of the full Boltzmann model should be regarded as a research tool. It is a very new model and, as such, will need to undergo considerable additional testing over several years before it could be considered as a viable option for an operational model

Inconsistent spectral evolution in operational wave models due to inaccurate specification of nonlinear interactions

The introduction of third-generation (3G) models was based on the premise that wave spectra could evolve without prior shape restrictions only if the representation for nonlinear interactions contained as many degrees of freedom as the discretized spectrum being modeled. It is shown here that a different criterion is needed to accurately represent nonlinear spectral evolution within models, a more rigorous criterion such that the number of degrees of freedom in the nonlinear source term must be equal to the intrinsic number of degrees of freedom in the theoretical form of this source term, which is larger than the degrees of freedom in the spectrum. Evolution of spectral shapes produced by the current approximation for nonlinear interactions in 3G models, the discrete interaction approximation (DIA), is compared to the full integral solution for three different time scales: 1) relaxation of the equilibrium range following a perturbation, 2) spectral evolution of the equilibrium range during an interval of constant winds, and 3) the evolution of spectral shape during transition to swell during propagation over long distances. It is shown that the operational nonlinear source term produces significant deviations in the evolution of the wave spectra at all of these scales because of its parametric reduction of the number of degrees of freedom and incorrect energy flux scaling. It is concluded that the DIA does not meet the critical criterion for allowing a spectrum to evolve to spectral shapes consistent with those observed in nature

A new approach for modeling dissipation due to breaking in wind wave spectra

A robust spectral dissipation term for wind waves has long been a goal of detailed-balance spectral modeling and is represented by many different approximations in spectral models of random wave fields. A Monte Carlo approach is employed here to create a random-phase sea surface that is used to simulate the distribution of horizontal surface velocities at the sea surface and to relate these velocities to deep-water wind wave breaking. Results are consistent with many recent studies that show a kinematic-based breaking criterion can provide a consistent depiction of the onset of wave breaking. This criterion is combined with the calculated nonlinear flux rates to estimate a transition point within a spectrum at which a spectrum changes from an f24 equilibrium-range form to an f25 region dominated by dissipation, potentially an important factor within several air–sea interaction mechanisms, turbulence at the sea surface, and remote sensing applications. It also has the potential to improve operational modeling capabilities

On the tuning-free statistical model of ocean surface waves

Absence of mathematically justified criteria during development of the wind energy input and wave breaking energy dissipation source terms in Hasselmann equation (HE), used as the framework of modern operational wave forecasting models, lead to creation of plethora of parameterizations, having enormous scatter, disconnected from the physical background and obeying dozens of tuning parameters to adjust the HE model to the specific situation. We show that it\u27s possible, based on analytical analysis and experimental observation data, to create the new set of source terms, reproducing experimental observations with minimal number of tuning parameters. We also numerically analyze six historically developed and new wind input source terms for their ability to hold specific invariants, related to HE selfsimilar nature. The degree of preservation of those invariants could be used as their selection tool. We hope that this research is the step toward the creation of physically justified tuning-free operational models