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 Turbulence in the Ocean Surface Layer

AbstractObservations of winds, waves, and turbulence at the ocean surface are compared with several analytic formulations and a numerical model for the input of turbulent kinetic energy by wave breaking and the subsequent dissipation. The observations are generally consistent with all of the formulations, although some differences are notable at winds greater than 15 m s−1. The depth dependence of the turbulent dissipation rate beneath the waves is fit to a decay scale, which is sensitive to the choice of vertical reference frame. In the surface-following reference frame, the strongest turbulence is isolated within a shallow region of depths much less than one significant wave height. In a fixed reference frame, the strong turbulence penetrates to depths that are at least half of the significant wave height. This occurs because the turbulence of individual breakers persists longer than the dominant period of the waves and thus the strong surface turbulence is carried from crest to trough with the wave orbital motion.</jats:p

Wave-Breaking Turbulence in the Ocean Surface Layer

Observations of winds, waves, and turbulence at the ocean surface are compared with several analytic formulations and a numerical model for the input of turbulent kinetic energy by wave breaking and the subsequent dissipation. The observations are generally consistent with all of the formulations, although some differences are notable at winds greater than 15 m s⁻¹. The depth dependence of the turbulent dissipation rate beneath the waves is fit to a decay scale, which is sensitive to the choice of vertical reference frame. In the surface-following reference frame, the strongest turbulence is isolated within a shallow region of depths much less than one significant wave height. In a fixed reference frame, the strong turbulence penetrates to depths that are at least half of the significant wave height. This occurs because the turbulence of individual breakers persists longer than the dominant period of the waves and thus the strong surface turbulence is carried from crest to trough with the wave orbital motion.This is the publisher’s final pdf. The published article is copyrighted by the American Meteorological Society and can be found at: https://www.ametsoc.org/ams/index.cfm/publications/journals/journal-of-physical-oceanography/The SWIFT wave, wind, and turbulence data are available online (at www.apl.uw.edu/swift) by serial number. The waverider spectra are available as station 166 from the Coastal Data Information Program (CDIP) at the Scripps Institution of Oceanography or the National Data Buoy Center (NDBC) as station 46246.KEYWORDS: Wave breaking, Waves, oceanic, Atmosphere-ocean interaction, Turbulence, Wind waves, Circulation/ Dynamics, Atm/Ocean Structure/ Phenomena, Sea stat

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

Introduction to special section on Recent Advances in the Study of Optical Variability in the Near-Surface and Upper Ocean

Optical variability occurs in the near-surface and upper ocean on very short time and space scales (e.g., milliseconds and millimeters and less) as well as greater scales. This variability is caused by solar, meteorological, and other physical forcing as well as biological and chemical processes that affect optical properties and their distributions, which in turn control the propagation of light across the air-sea interface and within the upper ocean. Recent developments in several technologies and modeling capabilities have enabled the investigation of a variety of fundamental and applied problems related to upper ocean physics, chemistry, and light propagation and utilization in the dynamic near-surface ocean. The purpose here is to provide background for and an introduction to a collection of papers devoted to new technologies and observational results as well as model simulations, which are facilitating new insights into optical variability and light propagation in the ocean as they are affected by changing atmospheric and oceanic conditions

Introduction to special section on Recent Advances in the Study of Optical Variability in the Near-Surface and Upper Ocean

Optical variability occurs in the near-surface and upper ocean on very short time and space scales (e.g., milliseconds and millimeters and less) as well as greater scales. This variability is caused by solar, meteorological, and other physical forcing as well as biological and chemical processes that affect optical properties and their distributions, which in turn control the propagation of light across the air-sea interface and within the upper ocean. Recent developments in several technologies and modeling capabilities have enabled the investigation of a variety of fundamental and applied problems related to upper ocean physics, chemistry, and light propagation and utilization in the dynamic near-surface ocean. The purpose here is to provide background for and an introduction to a collection of papers devoted to new technologies and observational results as well as model simulations, which are facilitating new insights into optical variability and light propagation in the ocean as they are affected by changing atmospheric and oceanic conditions