Janet M. Becker

Energetics of M2 Barotropic-to-Baroclinic Tidal Conversion at the Hawaiian Islands

Abstract A high-resolution primitive equation model simulation is used to form an energy budget for the principal semidiurnal tide (M2) over a region of the Hawaiian Ridge from Niihau to Maui. This region includes the Kaena Ridge, one of the three main internal tide generation sites along the Hawaiian Ridge and the main study site of the Hawaii Ocean Mixing Experiment. The 0.01°–horizontal resolution simulation has a high level of skill when compared to satellite and in situ sea level observations, moored ADCP currents, and notably reasonable agreement with microstructure data. Barotropic and baroclinic energy equations are derived from the model’s sigma coordinate governing equations and are evaluated from the model simulation to form an energy budget. The M2 barotropic tide loses 2.7 GW of energy over the study region. Of this, 163 MW (6%) is dissipated by bottom friction and 2.3 GW (85%) is converted into internal tides. Internal tide generation primarily occurs along the flanks of the Kaena Ridge and ...

The dissipation of wind wave energy across a fringing reef at Ipan, Guam

Field observations over a fringing reef at Ipan, Guam, during trade wind and tropical storm conditions are used to assess the transformation of sea and swell energy from the fore reef to the shoreline. Parameterizations of wave breaking and bottom friction developed for sandy beaches are found to represent the observed decay in wave energy with an increased friction coefficient. These parameterizations are incorporated into the one-dimensional energy flux balance, which is integrated across the reef to assess the effects of varying tidal range, incident wave height and reef bathymetry on the sea and swell band wave height and wave setup near the shoreline. Wave energy on the reef is strongly depth-limited and controlled by the reef submergence level. Shoreline wave energy increases with incident wave height largely due to the increase in water level from breaking wave setup. Increased tidal levels result in increased shoreline energy, since wave setup is only weakly reduced. The wave height at the shore is shown to be inversely proportional to the width of the reef flat due to dissipation.

Model Estimates of M2 Internal Tide Generation over Mid-Atlantic Ridge Topography

Abstract The conversion of barotropic to baroclinic M2 tidal energy is examined for a section of the Mid-Atlantic Ridge in the Brazil Basin using a primitive equation model. Model runs are made with different horizontal smoothing (1.5, 6, and 15 km) applied to a 192 km × 183 km section of multibeam bathymetry to characterize the influence of topographic resolution on the model conversion rates. In all model simulations, barotropic to baroclinic conversion is highest over near- and supercritical slopes on the flanks of abyssal hills and discordant zones. From these generation sites, internal tides propagate upward and downward as tidal beams. The most energetic internal tide mode generated is mode 2, consistent with the dominant length scales of the topographic slope spectrum (50 km). The topographic smoothing significantly affects the model conversion amplitudes, with the domain-averaged conversion rate from the 1.5-km run (15.1 mW m−2) 4% and 19% higher than for the 6-km (14.5 mW m−2) and 15-km runs (12....

Water level effects on breaking wave setup for Pacific Island fringing reefs

The effects of water level variations on breaking wave setup over fringing reefs are assessed using field measurements obtained at three study sites in the Republic of the Marshall Islands and the Mariana Islands in the western tropical Pacific Ocean. At each site, reef flat setup varies over the tidal range with weaker setup at high tide and stronger setup at low tide for a given incident wave height. The observed water level dependence is interpreted in the context of radiation stress gradients specified by an idealized point break model generalized for nonnormally incident waves. The tidally varying setup is due in part to depth-limited wave heights on the reef flat, as anticipated from previous reef studies, but also to tidally dependent breaking on the reef face. The tidal dependence of the breaking is interpreted in the context of the point break model in terms of a tidally varying wave height to water depth ratio at breaking. Implications for predictions of wave-driven setup at reef-fringed island shorelines are discussed.

Parametric excitation of an internally resonant double pendulum II

SummaryThe small, finite amplitude response of a damped, internally resonant double pendulum subject to parametric excitation at four times the frequency of the dominant pendulum is shown to exhibit chaotic behavoir for certain values of frequency offset and dissipation. This is in contrast to Miles [1], where the driving frequency approximated twice that of the dominant pendulum, and regular motion was found to exist for all values of frequency offset and dissipation.ZusammenfassungEs wird gezeigt, daß das Verhalten kleiner, endlicher Amplitude eines gedämpften, intern resonanten Doppelpendels unter parametrischer Erregung mit der vierfachen Eigenfrequenz des Hauptpendels chaotisch ist für bestimmte Frequenz- und Dissipationswerte. Dies steht im Gegensatz zu Miles [1], wo die erregende Frequenz ungefähr das zweifache der Eigenfrequenz betrug und sich normale Bewegung für alle Frequenzen und Dissipationen ergab.

Energy transfer between wind waves and low‐frequency oscillations on a fringing reef, Ipan, Guam

Field observations from a Guam fringing reef are used to examine the cross-reef energy exchange between high-frequency sea and swell (SS) and low-frequency infragravity (IG) and far infragravity (fIG) waves. Energetic SS waves (significant wave heights 2–4 m) break at the outer reef, leading to weak (<1 m) conditions on the shallow reef flat. As SS waves shoal on the reef face before breaking, IG and fIG energy fluxes both increase through nonlinear energy transfer from the SS waves. In contrast, through the surf zone, the IG energy flux decreases whereas fIG flux increases. The decrease in IG energy flux through the surf zone is attributed to breaking SS waves working against the incident bound IG wave energy, which dominates breakpoint forced IG waves, yielding a net flux decrease. In contrast, fIG energy flux increases through the surf zone, consistent with breakpoint forcing and the absence of an energetic bound fIG component on the reef face. IG and fIG energy fluxes decay on the shallow reef flat due primarily to frictional dissipation, with tidal modulations attributed to nonlinear conversion and friction. Forcing at fIG frequencies may lead to a normal mode response on the reef with comparable incoming and outgoing fIG energy fluxes at the outer reef flat, depending on water level over the reef flat and the degree of frictional dissipation.

Observations and estimates of wave‐driven water level extremes at the Marshall Islands

Wave-driven extreme water levels are examined for coastlines protected by fringing reefs using field observations obtained in the Republic of the Marshall Islands. The 2% exceedence water level near the shoreline due to waves is estimated empirically for the study sites from breaking wave height at the outer reef and by combining separate contributions from setup, sea and swell, and infragravity waves, which are estimated based on breaking wave height and water level over the reef flat. Although each component exhibits a tidal dependence, they sum to yield a 2% exceedence level that does not. A hindcast based on the breaking wave height parameterization is used to assess factors leading to flooding at Roi-Namur caused by an energetic swell event during December 2008. Extreme water levels similar to December 2008 are projected to increase significantly with rising sea level as more wave and tide events combine to exceed inundation threshold levels.

Reef Flat Wave Processes and Excavation Pits: Observations and Implications for Majuro Atoll, Marshall Islands

ABSTRACT Ford, M.R.; Becker, J.M., and Merrifield, M.A., 2013. Reef Flat wave processes and excavation pits: observations and implications for Majuro Atoll, Marshall Islands. An experimental deployment of pressure sensors was undertaken to assess the impact of reef flat excavation pits on wave processes at Majuro Atoll, Marshall Islands. Experiments were undertaken on two sections of an 80-m-wide fringing reef flat, one modified by the excavation of a 17-m wide, 4- to 5-m deep pit and the other an unmodified reef flat of comparable width, topography, and incident wave energy. A wave-driven inundation event during the experiment led to minor amounts of debris overwashing the road surface. The event was associated with southerly swell that was normally incident to the study site at high tide, resulting in enhanced shoreline energy in both the sea and swell and the infragravity frequency bands. The shoreline with the excavation pit received slightly smaller wave heights (∼8%) for all wave conditions, including the overwash event, compared to the unmodified shoreline. The statistically significant difference is largely a result of a decrease in infragravity wave energy over and shoreward of the pit that compensates for a weak increase in sea and swell energy. The influence on infragravity energy levels is likely to depend on the pit geometry and position, as well as the wave forcing; hence, not all pits are likely to lead to net wave energy dissipation. Implications of the findings are discussed with respect to the impacts of reef flat excavation on a highly developed, urbanised atoll.

STANDING RADIAL CROSS-WAVES

Standing radial cross-waves in an annular wave tank are investigated using Whithams average-Lagrangian method. For the simplest case, in which a single radial cross-wave is excited, energy is transferred from the wavemaker to the cross- wave through the spatial mean motion of the free surface, as described by Garrett (1970) for a purely transverse cross-wave in a rectangular tank. In addition, energy is transferred through spatial coupling since, in contrast to the purely transverse cross-wave in the rectangular tank, the (non-axisymmetric) radial cross-wave is three-dimensional. It is shown in an Appendix that this spatial coupling does occur for a three-dimensional cross-wave in a rectangular tank. The equations that govern this single-mode resonance are isomorphic to those that govern the Faraday resonance of surface waves in a basin of fluid subjected to vertical excitation (Miles 1984 a). It is found that the second-order Stokes-wave expansion for deep-water, standing gravity waves, which is regular for rectangular containers, may become singular for circular containers (Mack (1962) noted these resonances for finite-depth, standing gravity waves in circular containers). The evolution equations that govern two distinct types of resonant behaviour are derived : (i) 2 : 1 resonance between a radial cross-wave and a resonantly forces axisymmetric wave, corresponding to ap- proximate equality among the driving frequency, a natural frequency of the directly forced wave, and twice the natural frequency of a cross-wave; (ii) 2: 1 internal resonance between a radial cross-wave and a non-axisymmetric second harmonic, corresponding to approximate equality among the driving frequency, the natural frequency of a non-axisymmetric wave of even azimuthal wavenumber, and twice the natural frc.quency of the cross-wave. The axisymmetric, directly forced wave in (i) is resonantly excited and exchanges energy with the subharmonic cross-wave through spatial coupling, whereas the cross-wave in (ii) is parametrically excited and exchanges energy with the non-axisymmetric second harmonic through spatial coupling. The equations governing case (i) are shown to exhibit chaotic motions; those governing (ii) are shown to be isomorphic to the equations governing 2: 1 internal resonance in the Faraday problem (Miles 1984a,

Pattern formation on the interface of a two-layer fluid : bi-viscous lower layer

6), which have been shown to exhibit chaotic motions (Gu & Sethna 1987). Preliminary experiments on standing radial cross-waves are reported in an Appendix, and theoretical predictions of mode stability are in qualitative agreement with these experiments. For the single-mode theory, the interaction coefficient that is a measure of the energy exchange between the wavemaker and the cross-wave is evaluated numerically for a particular wavemaker. The maximum interaction