Dynamical and statistical explanations of observed occurrence rates of rogue waves

Extreme surface waves occur in the tail of the probability distribution. Their occurrence rate can be displayed effectively by plotting ln(–ln <i>P</i>), where <i>P</i> is the probability of the wave or crest height exceeding a particular value, against the logarithm of that value. A Weibull distribution of the exceedance probability, as proposed in a standard model, then becomes a straight line. Earlier North Sea data from an oil platform suggest a curved plot, with a higher occurrence rate of extreme wave and crest heights than predicted by the standard model. The curvature is not accounted for by second order corrections, non-stationarity, or Benjamin-Feir instability, though all of these do lead to an increase in the exceedance probability. Simulations for deep water waves suggest that, if the waves are steep, the curvature may be explained by including up to fourth order Stokes corrections. Finally, the use of extreme value theory in fitting exceedance probabilities is shown to be inappropriate, as its application requires that not just <i>N</i>, but also ln<i>N</i>, be large, where <i>N</i> is the number of waves in a data block. This is unlikely to be adequately satisfied

A Note on the Phillips Spectral Framework for Ocean Whitecaps

There has been a recent upsurge in interest in quantifying kinematic, dynamic, and energetic properties of wave breaking in the open ocean, especially in severe sea states. The underpinning observational and modeling framework is provided by the seminal paper of O. M. Phillips. In this note, a fundamental issue contributing to the scatter in results between investigators is highlighted. This issue relates to the choice of the independent variable used in the expression for the spectral density of the mean breaking crest length per unit area. This note investigates the consequences of the different choices of independent variable presently used by various investigators for validating Phillips model predictions for the spectral density of the breaking crest length per unit area and the associated spectral breaking strength coefficient. These spectral measures have a central role in inferring the associated turbulent kinetic energy dissipation rate and the momentum flux to the upper ocean from breaking wave observations

Convergence analysis of a multigrid algorithm for the acoustic single layer equation

We present and analyze a multigrid algorithm for the acoustic single layer equation in two dimensions. The boundary element formulation of the equation is based on piecewise constant test functions and we make use of a weak inner product in the multigrid scheme as proposed in \cite{BLP94}. A full error analysis of the algorithm is presented. We also conduct a numerical study of the effect of the weak inner product on the oscillatory behavior of the eigenfunctions for the Laplace single layer operator

Wave breaking in developing and mature seas

In response to the growing need for robust validation data for Phillips (1985) breaking wave spectral framework, we contribute new field results observed from R/P FLIP for the breaking crest length distributions, Λ, during two different wind-wave conditions, and breaking strength during one wind-wave condition. The first experiment in Santa Barbara Channel had developing seas and the second experiment in the central Pacific Ocean south of Hawaii had mature seas. These are among the first experiments to use dissipation rate measurements probing up into the breaking crest together with simultaneous measurements of breaking crest length distributions. We directly measured the effective breaking strength parameter to be inline image in mature seas with wave age, inline image, of 40–47. We also found that the velocity scale of the breaking dissipation rate peak decreases with increasing wave age. Further, the breaking crest length spectrum falls off slower than the inline image behavior predicted by Phillips (1985). The integrated dissipation rate was consistently higher for mature seas compared to developing seas due to higher energy and momentum fluxes from the wind

An overview of sea state conditions and air-sea fluxes during RaDyO

Refining radiative-transfer modeling capabilities for light transmission through the sea surface requires a more detailed prescription of the sea surface roughness beyond the probability density function of the sea surface slope field. To meet this need, exciting new measurement methodologies now provide the opportunity to enhance present knowledge of sea surface roughness, especially at the microscale. In this context, two intensive field experiments using R/P Floating Instrument Platform were staged within the Office of Naval Research's Radiance in a Dynamic Ocean (RaDyO) field program in the Santa Barbara Channel and in the central Pacific Ocean south of Hawaii. As part of this program, our team gathered and analyzed a comprehensive suite of sea surface roughness measurements designed to provide optimal coverage of fundamental optical distortion processes associated with the air-sea interface. This contribution describes the ensemble of instrumentation deployed. It provides a detailed documentation of the ambient environmental conditions that prevailed during the RaDyO field experiments. It also highlights exciting new sea surface roughness measurement capabilities that underpin a number of the scientific advances resulting from the RaDyO program. For instance, a new polarimetric imaging camera highlights the complex interplay of wind and surface currents in shaping the roughness of the sea surface that suggests the traditional Cox-Munk framework is not sufficient. In addition, the breaking crest length spectral density derived from visible and infrared imagery is shown to be modulated by the development of the wavefield (wave age) and alignment of wind and surface currents at the intermediate (dominant) scale of wave breaking

Defining and quantifying microscale wave breaking with infrared imagery

Breaking without air entrainment of very short wind-forced waves, or microscale wave breaking, is undoubtedly widespread over the oceans and may prove to be a significant mechanism for enhancing the transfer of heat and gas across the air-sea interface. However, quantifying the effects of microscale wave breaking has been difficult because the phenomenon lacks the visible manifestation of whitecapping. In this brief report we present limited but promising laboratory measurements which show that microscale wave breaking associated with evolving wind waves disturbs the thermal boundary layer at the air-water interface, producing signatures that can be detected with infrared imagery. Simultaneous video and infrared observations show that the infrared signature itself may serve as a practical means of defining and characterizing the microscale breaking process. The infrared imagery is used to quantify microscale breaking waves in terms of the frequency of occurrence and the areal coverage, which is substantial under the moderate wind speed conditions investigated. The results imply that ”bursting“ phenomena observed beneath laboratory wind waves are likely produced by microscale breaking waves but that not all microscale breaking waves produce bursts. Oceanic measurements show the ability to quantify microscale wave breaking in the field. Our results demonstrate that infrared techniques can provide the information necessary to quantify the breaking process for inclusion in models of air-sea heat and gas fluxes, as well as unprecedented details on the origin and evolution of microscale wave breaking

Rain-induced turbulence and air-sea gas transfer

Author Posting. © American Geophysical Union, 2009. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research 114 (2009): C07009, doi:10.1029/2008JC005008.Results from a rain and gas exchange experiment (Bio2 RainX III) at the Biosphere 2 Center demonstrate that turbulence controls the enhancement of the air-sea gas transfer rate (or velocity) k during rainfall, even though profiles of the turbulent dissipation rate ɛ are strongly influenced by near-surface stratification. The gas transfer rate scales with ɛ inline equation for a range of rain rates with broad drop size distributions. The hydrodynamic measurements elucidate the mechanisms responsible for the rain-enhanced k results using SF6 tracer evasion and active controlled flux technique. High-resolution k and turbulence results highlight the causal relationship between rainfall, turbulence, stratification, and air-sea gas exchange. Profiles of ɛ beneath the air-sea interface during rainfall, measured for the first time during a gas exchange experiment, yielded discrete values as high as 10−2 W kg−1. Stratification modifies and traps the turbulence near the surface, affecting the enhancement of the transfer velocity and also diminishing the vertical mixing of mass transported to the air-water interface. Although the kinetic energy flux is an integral measure of the turbulent input to the system during rain events, ɛ is the most robust response to all the modifications and transformations to the turbulent state that follows. The Craig-Banner turbulence model, modified for rain instead of breaking wave turbulence, successfully predicts the near-surface dissipation profile at the onset of the rain event before stratification plays a dominant role. This result is important for predictive modeling of k as it allows inferring the surface value of ɛ fundamental to gas transfer.This work was funded by a generous grant from the David and Lucile Packard Foundation and the Lamont-Doherty Earth Observatory Climate Center. Additional funding was provided by the National Science Foundation (OCE-05-26677) and the Office of Naval Research Young Investigator Program (N00014-04-1-0621)

Tidal and atmospheric influences on near-surface turbulence in an estuary

Estuarine near-surface turbulence is important for transport, mixing, and air-water exchanges of many important constituents but has rarely been studied in detail. Here, we analyze a unique set of estuarine observations of in situ atmospheric and full water column measurements, estimated air-sea exchanges, and acoustic measurements of several terms in the turbulent kinetic energy (TKE) budget. Observations from a 5.1 m deep site in the Hudson River estuary include dissipation at 50 cm depth (ɛ50), as well as profiles of TKE, shear production of TKE (P), and net turbulent vertical TKE transport (TD). Regressions suggest that the principal controlling factor for ɛ50 was wind (through the surface shear velocity, U*) and that the surface heat flux and tidal currents played a secondary role. For ebb spring tides, the TKE budget at 50 cm depth was closed within noise levels. Ebbs had high ɛ50 due to local shear production, which nearly balanced ɛ50. Floods had TD approaching P in the upper water column but generally weak near-surface shear and turbulence. Examining buoyancy fluxes that impact near-surface stratification and can indirectly control turbulence, solar heat input and tidal straining caused similar buoyancy fluxes on a sunny, calm weather day, promoting ebb tide restratification. Wind-driven mixing was found to dominate during a fall season storm event, and strong overnight heat loss after the storm helped delay restratification afterward. These results demonstrate the utility of combining detailed air-sea interaction and physical oceanographic measurements in future estuary studies

On the shape and likelihood of oceanic rogue waves

We consider the observation and analysis of oceanic rogue waves collected within spatio-Temporal (ST) records of 3D wave fields. This class of records, allowing a sea surface region to be retrieved, is appropriate for the observation of rogue waves, which come up as a random phenomenon that can occur at any time and location of the sea surface. To verify this aspect, we used three stereo wave imaging systems to gather ST records of the sea surface elevation, which were collected in different sea conditions. The wave with the ST maximum elevation (happening to be larger than the rogue threshold 1.25H s) was then isolated within each record, along with its temporal profile. The rogue waves show similar profiles, in agreement with the theory of extreme wave groups. We analyze the rogue wave probability of occurrence, also in the context of ST extreme value distributions, and we conclude that rogue waves are more likely than previously reported; the key point is coming across them, in space as well as in time. The dependence of the rogue wave profile and likelihood on the sea state conditions is also investigated. Results may prove useful in predicting extreme wave occurrence probability and strength during oceanic storms

The pilot project of the mineral collections from the University of Barcelona: An opportunity to create updated teaching material to be shared with other universities

The Mineralogy teaching collection from the University of Barcelona has proved to be a successful tool for students. The urge of its renewal to meet the necessities of modernCindustry brought the idea to replicate this collection in order to offer high quality teaching material to other universities worldwide. This project has led to an international collaboration aiming to enhance international solidarity among universities and make evident the importance of Mineralogy in Geology studies