Showing papers on "Swell published in 1987"

Radar scattering and equilibrium ranges in wind‐generated waves with application to scatterometry

Abstract: To provide theoretical basis for the connection between observed radar scattering and wind-generated waves, a model for the response of surface waves in the gravity-capillary equilibrium region of the spectrum is proposed on the basis of a local (in wavenumber) balance between wind input and dissipation. The wind input function was constructed on the basis of laboratory observations of short-wave growth, while the dissipation function was developed from ideas of viscous dissipation and wave breaking in response to local accelerations and modified by kinematic effects of phase and group velocity differences. The model was exercised at L, C, X, and Ka bands to demonstrate the differences in wind speed and water temperature sensitivity.

Shallow‐Water Waves. I: Theory

Abstract: Based on a generalized treatment of geometric scaling laws inherent in the Boltzmann integral for nonlinear wave-wave interactions, a theoretical framework for the characteristic form of equilibrium spectra in water of arbitrary depth is developed. A theoretical consequence of this spectral equilibrium range formulation is that a strong, constant flux of wave energy exists through the equilibrium range of the spectrum, analogous to the Komolgorov range in a turbulence spectrum. One possibly important conclusion from the theoretical material presented here is that the equilibrium range of a wind wave spectrum should be a depth-independent constant in terms of a representation of the spectral action density, rather than the spectral energy density. Another point of particular interest to wave generation in shallow water is the apparent existence of a natural limit to the evolution of the frequency of the spectral peak into lower frequencies. This removes the necessity of requiring that only bottom friction can limit wave growth in shallow water.

Modified Free Swell Index for Clays

Abstract: Free swell tests are commonly used for identifying expansive clays and to predict the swelling potential. The method as proposed by Holtz and Gibbs suffers from inaccuracies in volume measurement of dry powder in air. In this paper, a nondimensional modified free swell index is proposed, which removes the uncertainties present in the Holtz and Gibbs method. The modified free swell index is shown to bear unique correlations with liquid limit (volume basis) and percent swell of oedometer specimens compacted to proctor optimum conditions.

Computations of the response of a wave spectrum to a sudden change in wind direction

Abstract: The response of a wind-sea spectrum to a step function change in wind direction is investigated theoretically for a sequence of direction changes ranging from 30° to 180°, in increments of 30°. Two spectral energy balance models are used: the model EXACT-NL, in which the nonlinear transfer is represented exactly, and the model 3G-WAM, in which the nonlinear transfer is approximated by the discrete interaction parameterization. In both modes the input and dissipation source functions are taken from the energy balance proposed by Komen et al. The operational model 3G-WAM reproduces fairly closely the EXACT-NL results. For wind direction changes less than 60°, the wind-sea direction adjusts smoothly. The high-frequency components relax more rapidly to the new wind direction than the low-frequency components. The computed relaxation rates are generally consistent with the analysis of measured directional spectra by D.E. Hasselman et al. and Allender et al. However, the relaxation rate is found to be ...

Lithospheric heating by mantle plumes

Abstract: Summary. A broad topographic swell is associated with the Hawaiian hotspot. A kinematic model is developed assuming that downstream of the hotspot this swell is produced by lithospheric heating by a mantle plume. Material from the model plume flows radially in the asthenosphere and eventually heats the lower lithosphere. Upstream from the hotspot, the model swell owes its existence mainly to hot material at asthenospheric depths. The model predicts extensive lithospheric heating downstream from the hotspot. Interpreted data to tell if the lower lithosphere behaves in this way are lacking.

Attenuation of wind waves by monomolecular sea slicks and the Marangoni Effect

Abstract: Previous observations of wind wave damping by monomolecular surface films (“slicks”) have shown a pronounced energy detraction (“dip”) in the short gravity wave range of the wind wave spectra. In this work, wind wave tunnel experiments with mechanically generated water waves have supplied experimental evidence which clearly shows that this dip is predominantly caused by the film-induced “Marangoni effect.”

A pseudo-time integral method for non-isothermal viscoelastic flows and its application to extrusion simulation

Abstract: A pseudo-time integral scheme based on a finite streamline element method is developed to combine variable temperature with viscoelasticity. A specific KBKZ integral model for isothermal flow is transformed to its non-isothermal version by introducing a pseudo-time and applying the Morland-Lee hypothesis. The coupling between momentum and energy equations is through the time-temperature shifting factor by which the pseudo-time is defined. The observer time and the pseudo-time are simultaneously calculated when tracing the strain history for the stress calculation in a non-homogeneous temperature field. Using this scheme, a full non-isothermal numerical simulation of some IUPAC extrusion experiments is carried out. Results show that while the temperature distribution near the die exit plane is an important factor controlling extrudate swell, either self-heating inside the die tube or external cooling on the free surface dominantly determines the temperature distribution near the die exit when the wall temperature is kept constant, depending on whether the Peclet number is large or small. The hot layer effect predicted by the inelastic swell mechanism is confirmed and well illustrated by the computation. Calculations with reasonable thermal boundary conditions further convince us that the isothermal assumption in our earlier numerical simulation is a good approximation in this particular case.

Reynolds stresses under wind waves

Abstract: This paper describes a series of wave measurements, taken from an oceanographic tower, concerning water particle kinematics. Attention is focused on the phase relationship between surface elevation and the velocity components. Large phase shifts with respect to the expected values are found under active wave conditions, while swell behavior closely follows the linear theory. The reliability of the measurements is analyzed in detail. Possible physical reasons for the findings are indicated in the final discussion.

Delayed die swell

Abstract: The experiments reported here establish that there is a general critical condition associated with die swell which we call delayed die swell. This condition is defined by a critical speed which is the area-averaged velocity, the extrusion velocity, at the exit of the pipe when the swell is first delayed. The delayed swell ratio and delay distance first increase for larger, post-critical values of the extrusion velocity; then the increases are terminated either by instabilities or by smoothing. The maximum post-critical velocity at the pipe exit was always greater than the shear wave speed measured on the shear-wave-speed meter. The post critical area averaged velocity at the position of maximum swell before termination was always less than the shear wave speed. There were always points in the region of swelling where the ratio of the local velocity to the shear wave speed, the viscoelastic Mach number, was unity. The swelling of the jet is a nonlinear phenomenon which we suggest is finally terminated either by instability or when the variations of the velocity, vorticity and stress field are reduced to zero by the inward propagation of shear waves from the free surface of the jet. This propagation is generated by discontinuous “initial” data along χ in which the prescribed values of velocity at the boundary change from no-slip in the pipe to no-shear in the jet. The measurements raise the possibility that the delay may be associated with a change of type from supercritical to subcritical flow.

Reflection of water waves in a channel with corrugated bed

Abstract: Intended as a contribution towards understanding the multiple processes entailed in the development of coastal sand bars due to wave action, this theoretical and experimental study deals with the Bragg reflection of long-crested surface waves in a water channel whose bed is corrugated sinusoidally. The present findings complement and in a few respects improve upon those in previous investigations, particularly Davies & Heathershaw (1984).In §2 a linearized theory is presented, being directed to the elucidation of experimental situations where monochromatic waves propagate into a channel with a limited stretch of corrugations on its bed and an imperfectly absorbing beach at its far end. Allowance is made fully for dispersive effects (§2.2) and approximately for small frictional effects (§2.3). Points of interpretation (§2.4) include accounts of degenerate but non-trivial solutions that apply at frequencies terminating the stopping band, wherein the spatial wavefield has an exponential envelope. The experimental results presented in §4 derive from measurements of the wavefield over a stretch of 24 corrugations, at various frequencies both inside and outside the stopping band. Quantitative comparisons (§4.2 and 4.3) demonstrate close agreements with the theory.

High-frequency ice floe collisions in the Greenland Sea During the 1984 Marginal Ice Zone Experiment

Abstract: During the 1984 Marginal Ice Zone Greenland Sea Experiment, we carried out a field study on the relation between ice floe collisions and ocean swell. The experiment consisted of the deployment on separate ice floes of three buoys, each of which contained a compass and a set of triaxial accelerometers. The floes had characteristic diameters of 100 m and thicknesses of 1–5 m. From two major deployments of these buoys, we gathered 16 days of data. From the vertical accelerometer data, we calculated the variation in the long-period ocean swell with time; from the horizontal accelerometers, we determined the individual and mean collision properties. Examination of the individual collisions showed that two types of collisions occurred: a short-period spike that recurred with the period of the ocean swell, and a longer period acceleration event that was uncorrelated with the swell. We observed several hundred of the first type of collision in our data set but only eight of the second type. The number of periodic collisions in a 9-min sample and the energy of these collisions were generally correlated with the ocean swell energy. The ocean swell measured at the floes had root-mean-square (rms) amplitudes of 1–30 mm and periods between 10 and 18 s. After removal of the ocean swell signal, the collisions had characteristic horizontal displacements of 5–35 mm, with rms velocities of the order of 1 mm s−1.

Numerical Simulation of Coextrusion from a Circular Die

Abstract: A numerical simulation of coextrusion flow in a capillary die has been undertaken for polymer melts used in a previously reported experimental study of coextrusion. Viscosity data are used for PS, HDPE, and LDPE melts. A Newton–Raphson scheme is employed to solve the equations for a fully developed pressure-driven flow of two concentric layers in a capillary. A finite element method is used to simulate the full flow field behavior, including determination of the interface and free surface of the exiting stream. Double nodes have been used at the interface to ensure continuity of velocities and stresses and to capture the pressure discontinuities. Pressure gradients, extrudate swell, interface swell, and other relevent flow characteristics are presented and compared with the experimental findings. The finite element analysis revealed that satisfactory convergence of the interface location is found for the cases when the less viscous material wets the capillary walls, which is also the preferential configuration in coextrusion. For the opposite configuration, convergence proved either difficult or impossible depending upon the viscosity ratio. Discrepancies were found to exist between the theoretically predicted and experimentally measured pressure gradients.

Composite‐roughness theory applied to scattering from fetch‐limited seas

Abstract: The prediction of surface scattering strength using composite‐roughness theory requires a detailed knowledge of the ocean wave spectrum. While extensive research in the past has produced a good empirical representation of the wavenumber spectrum of a fully developed sea, only recently have the spectra of fetch‐limited seas been examined. A fetch‐limited sea spectrum is similar in most respects to a spectrum at reduced windspeed except that a small region of ‘‘overshoot’’ occurs on the high‐frequency side of the swell peak. Scattering strength computations show that the fetch‐limited condition has an effect only on the near‐specular returns where values can be 2–10 dB higher than those for a fully developed sea. Computations with composite‐roughness theory including the Fresnel phase approximation and source beam patterns are also made. Comparisons are shown with surface scattering data in both monostatic backscattering and bistatic forward scattering geometries.

Intrinsic frequency spectra of short gravity-capillary waves obtained from temporal measurements of wave height on a lake

Abstract: Intrinsic frequency spectra of water waves in the range of 6-17 Hz were obtained as a function of both wind speed and wind stress from point measurements of wave height. In a lake with a limited fetch, there are two types of surface motions causing Doppler shift in the frequencies of short waves: orbital velocity of long waves and surface wind drift. The former was estimated from long-wave amplitude by using a linear wave theory. The error in this estimate is of the order of the long-wave slope, and for this work it is typically 10 percent. The latter was approximated by the friction velocity. The friction velocity could be either taken as 3 percent of the mean wind speed measured at a height of 10 m or obtained from direct measurements of the wind stress. The surface drift velocities obtained by these two approaches were found to be in close agreement. Doppler frequency shift can be corrected in either the frequency or the equivalent spatial domain. The two techniques were found to produce comparable results. Experimental results showed that the spectral energy of short waves rapidly increased in response to increasing winds and jumped up by an order of magnitude when wave breaking occurred.

Effect of die temperature on the flow of polymer melts. Part II: Extrudate swell

Abstract: The effect of die wall temperature on the extrudate swell of polymer melts flowing through dies with single and dual circular channels was studied. Extrudate swell was measured at constant flow rates using an Instron capillary rheometer with a modified die section. It was found that under isothermal conditions, extrudate swell plotted against the average wall shear stress gave rise to a temperature independent correlation for polystyrene. Under non-isothermal conditions, such a correlation did not exist, which might be due to the change of wall shear stress in the axial direction. The extrudate swell in the non-isothermal cases can be better correlated with the wall shear stress at die exit. For the two-hole die, changes of die wall temperature varied both the flow rate ratio and the extru date swell ratio. The latter is, however, much less sensitive to the die wall temperature than the former.

Extrudate swell of Newtonian fluids from converging and diverging annular dies

Abstract: Finite element results are presented for the extrudate swell of Newtonian fluids from converging and diverging annular dies. Numerical calculations for a variety of diameter ratios and taper angles show the dependance of diameter and thickness swell on the angle. For diverging dies a thickness contraction occurs for angles greater than 30 degrees, while the diameter swell increases rapidly. For converging dies the design is limited to angles that do not allow contact of the inner free surfaces. The present results show that the diameter swell is highest for the diverging, followed by the straight and then the converging dies.

Prey localization by surface wave ray-tracing: fish track bugs like oceanographers track storms.

Abstract: Surface-feeding fish accurately determine direction and distance to the center of a concentric wave stimulus, even if only a single, short lasting wave train is presented1,2. It has been suggested that one cue used by these fish to localize the wave center is the distance dependent frequency modulation of the initial part of a wave stimulus3,4. Here we show how the distance information contained in the fractional frequency change of a capillary wave group can be decoded. We suggest that wave source localization in surface-feeding fish in part is based on a principal similar to that used by oceanographers to track storms by the frequency change of forerunners of swell.

Edge waves on the Sydney coast

Abstract: Pressure and current oscillations at periods of 40 s to 17 min observed during storm conditions at two locations separated by 560 m in the alongshore direction in the coastal ocean near Sydney, Australia, indicate the existence of infragravity waves having amplitudes of ∼20 cm and velocities of ∼10 cm s−1. The observed infragravity waves appear to be locally forced by the wind wave envelope through radiation stress, yet the observed alongshore phase differences of the infragravity waves are consistent with those predicted from free edge wave theory for low-mode edge waves travelling northward and the relationship of pressure to velocity at each location is also consistent with free edge wave theory. As a function of time, the infragravity wave spectral energy grows and decays in step with the longer-period wind waves, suggesting a continuous transfer of energy. The infragravity waves appear to contain energy in both directly forced and freely propagating (edge wave) oscillations. The edge waves may be generated either by radiation stress as outlined above, by a resonant triad mechanism, or by a combination of the two.

Transformation of Significant Wave Heights

Abstract: A formula for transforming significant wave heights of wind seas between locations of differing depths is developed from the concept of the equilibrium range in the spectrum. The transformation is assumed valid for single‐peaked equilibrium wind seas which do not contain swell components. The method does not account for the effects of refraction, diffraction, or situations which may be fetch‐ or duration‐limited, therefore the method should not be applied when these effects may be dominant. The transformation is tested using 198 data pairs which seemed to fit the necessary criteria. The significant wave height at the shallower gage (8 m depth) was predicted using the measured significant wave height at the deeper gage (18 m depth). Comparisons between predicted and measured significant wave heights indicate that the wind sea transformation generally performs better than unrefracted shoaling of significant wave height using linear theory, but that underprediction occurs at longer wave periods.

Continental shelf wave scattering by a semi-infinite coastline

Abstract: In seeking to determine how the energy in a continental shelf wave that has travelled across the Great Australian Bight can reach the east Australian coast, the reflection/ transmission process at the southern tip of Tasmania is modelled by using a doublesided continental shelf of exponential/constant depth profile on which the coastline is semi-infinite. The Wiener-Hopf technique provides a suitable method for solution but the factorization is non-trivial because |k | enters to ensure exponential decay in the ocean and the newly required “ridge” modes are determined by a more complicated transcendental equation than that for the shelf wave modes. The number of modes is usually the same on the shelf or ridge but in the latter case, the longest mode has such a large wavelength that it essentially represents a “swell”, with dissipation into the ocean. Practically all the reflected and transmitted energy is contained in the modes having the longer wavelength with preference towards those correspondi...

Remote sensing of wave patterns with oceanographic implications

Abstract: First, a general review is presented of wave-current interaction processes ( for horizontal shears) and their effect on radar backscatter and radar imagery ( SAR/ RAR ) Then numerical results on the refraction of wave energy trajectories by complex bottom topography (finite depth) and a linear shear current are presented. For deep water, the wave-energy trajectories are given for mesoscale currents ( e.g. eddies and double-vortex configurations). The focusing of wave energy by variable currents found here should have important influence on the spatial scale of wind stress over the ocean, and on optical and acoustic properties of the upper layer of the ocean.

The age and source of ocean swell observed in Hurricane Josephine

Abstract: A simple kinematic model is applied to SIR-B observations in the far field of Hurricane Josephine in order to estimate the swell origin in space and time. The SIR data was obtained on October 12, 1984, and the geometry of the hurricane swell kinematic model is described. Estimates of the wavenumber and wave age and generation regions of the system are graphically presented and examined. The data reveal that the waves of Hurricane Josephine were generated 0-9 hours before the SIR-B overpass.

Beach Erosion along the West Coast of Aruba Netherlands Antilles

Abstract: Beach erosion along the west coast of Aruba was studied in order to design adequate protection measures for the resort beaches Along the west coast of Aruba two different wave -induced longshore current systems can be distinguished The first pattern refers to the normal east trade wind waves, refracted around the north and south capes and meeting at the utmost west point of the island The second group of wave patterns is related to two different types of refracted swell waves, generated by hurricanes or storms tracking outside and inside the Caribbean Island Arch As a result of these patterns there is a longshore sand transport in the breaker zone towards the west during the wind wave conditions and towards the east during the occasional swell wave events In the long run there is a net sand movement towards the west However, in the short run considerable eastward sand movement and severe beach erosion occur during the swell events After such events the beach recovery by the wind wave system normally takes more time Thus there is a delicate balance between both opposing phenomena Based on the sand transport patterns and budgets several possible engineering measures to protect the beaches are briefly discussed