Water Wave Energy Research Articles

Energy of Water Waves Induced by Submarine Landslides

—Water waves generated by submarine landslides may constitute a serious hazard for coastal population and environment. These masses may be giant, as documented by several examples in recent history and by numerous geological traces of paleo-events. A theoretical investigation on wave generation and wave energy is performed here by using a model that is based on some simplifying assumptions. The landslide is treated as a rigid body moving underwater according to a prescribed velocity function. Water waves are governed by the shallow-water wave equations, where water velocity is constant through the water layer and vertical velocity is negligibly small. Geometrically simple basins are considered with either constant depth or constant slope, since attention is focused on the fundamental characteristics of the generation process. Analytical 1-D solutions as well as 1-D and 2-D numerical results obtained by means of a finite-element model are used to gain understanding of the energy transfer from a moving body to the water. From the 1-D examples, it is found that if slide duration is sufficiently long, water usually gains energy in the form of waves until a saturation point is reached, when body motion is no longer capable of producing a net transfer of energy from the rigid body to water. Finite-duration motions of a body moving at constant speed along a flat ocean floor can be used as canonical examples, since bottom slopes cannot significantly change the generated wave pattern. Typically, two trough-crest systems are developed that travel in opposite directions, with the leading crest in the direction of the slide and the leading trough toward the other direction. The amplitude of the former is generally higher, with amplitude controlled by the Froude number (ratio of body velocity to long waves phase celerity) and wavelength dictated by landslide length. Generation and propagation of 2-D cases show a more complicated pattern, since lateral radiation plays an important role. Some of the features present in the 1-D models are observed in 2-D wavefields, however substantial differences arise. The most significant difference is that no energy saturation takes place in 2-D, since the body transfers energy to the water as long as it moves.

Development of shore platforms on Kaikoura Peninsula, South Island, New Zealand: Part One: The role of waves

The role of waves in shore platform development has been investigated on Kaikoura Peninsula by direct measurement of waves in deep water and on platforms at high tide. This showed that the deepwater wave environment off the Kaikoura Peninsula is very energetic, but the amount of energy delivered to platforms is very low. In deep water, wave power ranged from 5900 to 106 700 N m s −1 per m of crest when calculated from mean significant wave height and when calculated from maximum wave height it ranged from 31 400 to 5 370 000 N m s −1 per m of crest. A comparison of deep water wave energy flux with wave energy flux at the high tide cliff of platforms showed that there was a reduction by as much as five orders of magnitude during storm conditions. An analysis of the role of breaking waves revealed that these are ineffective as an erosional agent because the depth of water offshore causes breaking before waves arrive on platform surfaces. Depth of water controlling wave breaking causes larger storm waves to break further from shore, preventing direct attack at the cliff base. Shear stresses and dynamic forces under waves were calculated from waves measured on shore platforms. This showed that these forces never exceeded the compressive strength of the platform rocks at Kaikoura. It is concluded that wave forces are not directly capable of causing erosion on shore platforms at Kaikoura.

Surf Zone Currents

A large fraction of the water-wave energy incident on beaches is dissipated as the waves break and travel towards the shore through the surf zone. However, the momentum associated with the incident waves is not destroyed and drives other motions within the surf zone. An analysis is given of the unsteady and irregular currents that may occur in the surf zone. The forcing due to a discrete group of waves, and the vorticity of the surf-zone currents are the major topics. In particular, the almost two-dimensional nature of the flow implies that significant eddies are likely to be generated. There is evidence that eddies arise from long-shore currents, and the combination of eddies of opposite sign gives rip currents. It is noted that generation of vorticity by non-uniformities in bores may be a useful way of considering the forcing of surf zone motion. Expressions for the rate of increase in the circulation about material circuits and the vorticity generated at bores are derived.

Energy properties and shoaling of higher-order stokes waves on a current

The energy density, the energy flux, the set-down, the radiation stress, and some wave energy velocities have been derived correct to fourth order in wave steepness for waves on a vorticity-free current. The energy flux and the set-down have been used for shoaling predictions for finite amplitude waves with and without a net volume flux. The results with a zero volume flux are compared with more accurate shoaling predictions showing rather good accordance, except for large steepnesses. This also applies to the deep water wave energy transport velocity. The results with a net volume flux show that the steepness of the waves reduces the influence of this flux on the wave evolution. Some problems in connection with the orders in Stokes waves are discussed, among others concerning the dispersion relation and the orders of integral properties. Bed shear and accompanying dissipation is neglected.

Miocene lacustrine algal reefs—southwestern Snake River Plain, Idaho

The Hot Spring limestone is a shallow-water algal carbonate within a late Tertiary transgressive lacustrine sequence exposed in the southwestern Snake River Plain. This 5 m thick lensoid sequence crops out over an 80 km 2 area that closely approximates original areal extent of nearshore carbonate accumulation. Reefal bodies consist of closely packed algal cylinders, several decimeters in height, each of which includes a dense laminated carbonate wall surrounding porous digitate carbonate that radiates outward and upward from one or more hollow tubes. These coalesce upsection into separate vertical columns several meters in diameter. Moderately well-sorted terrigenous and molluscan debris deposited between columns during growth indicates these structures were resistant to wave erosion and, therefore, were true reefs. Thick rings of littoral carbonate surrounding the upper walls of each column record the final stages of reef development. Structural attributes exhibited by these Miocene carbonate bodies are also common to a number of Tertiary and Quaternary algal buildups reported from other lacustrine settings. Although features within the Hot Spring limestone are complex in gross morphology and structural detail, both columnar reefs and algal cylinders display little variation in size, shape, or internal structure between areas of varying water depth and wave energy, thus reflecting the importance of biological processes as well as physical processes during reef development.

Halite depositional facies in a solar salt pond: A key to interpreting physical energy and water depth in ancient deposits?

Subaqueous deposits of aragonite, gypsum, and halite are accumulating in shallow solar salt ponds constructed in the Pekelmeer, a sea-level salina on Bonaire, Netherlands Antilles. Several halite facies are deposited in the crystallizer ponds in response to difference in water depth and wave energy. Cumulate halite, which originates as floating rafts, is present only along the protected, upwind margins of ponds where low-energy conditions foster their formation and preservation. Cornet crystals with peculiar mushroom- and mortarboard-shaped caps precipitate in centimetre-deep brine sheets within a couple of metres of the upwind or low-energy margins. Downwind from these margins, cornet and chevron halite precipitate on the pond floors in water depths ranging from a few centimetres to {approximately} 60 cm. Halite pisoids with radial-concentric structure are precipitated in the swash zone along downwind high-energy shorelines where they form pebbly beaches. This study suggests that primary halite facies are energy and/or depth dependent and that some primary features, if preserved in ancient halite deposits, can be used to infer physical energy conditions, subenvironments such as low- to high-energy shorelines, and extremely shallow water depths in ancient evaporite basins.

WAVE ENERGY ESTIMATES AND BLUFF RECESSION ALONG LAKE MICHIGAN'S SOUTHEAST SHORE∗

Recession rates for unconsolidated bluffs at 23 sites along Lake Michigan's southeast shore are compared with deep water wave energy probabilities to estimate the relative degradational importance of recurrent 5, 10, 20, 50, and 100-year storms. Recession rates are based on measured bluff crest retreat while wave energies are calculated using standard water wave theory and data interpolated from a meteorologically based hindcast model. Correlation and regression tests suggest the following: (1) although wave energy is certainly a destructive factor, it explains less than half of the variation in bluff crest recession, supporting the interpretation that shorezone erosion here results from the interaction of numerous factors; and (2) over long time periods the total effect of more frequent moderate intensity storms is greater than that from rare, especially high energy events.

Antrim Shale Depositional Environments, Diagenesis, and Source Rock Potential in Michigan Basin: ABSTRACT

The Antrim Shale in the Michigan basin is a significant reservoir of in-situ natural gas. Presently it is being drilled in only a few northern counties of Michigan, but may be producible basin-wide. Several authors have suggested that the reservoir resulted from fracturing. Two processes may have caused these fractures: (1) framework collapse due to volume reduction associated with the conversion of organic matter to gas, and (2) the loss of interstitial water resulting from the conversion of smectite to illite. It has been suggested that the sediments are thermally immature and that the natural gas is biogenic in origin. The Antrim Shale is a facies equivalent of other Mid-Continent Black Shales that are documented to have been deposited in an oxygen-stratified basin, with three zones, aerobic, dysaerobic, and anaerobic. Water depth and wave energy apparently controlled the amount of oxygen in the depositional environment and thus the preservation of organic matter in the sediments. If anaerobic conditions existed then bioturbation of the sediments was low and the preservability of organic matter was high. The organic content of the shales, and the potential production of natural gas, is related to environment of deposition. By understanding the facies relationships, the environmentmore » of deposition, and the vertical and areal distribution of these facies, nature of the fracture systems, and the maturation level of the hydrocarbons, a better exploration program can be developed for the exploitation of the Antrim Shale gas reservoirs.« less

Spatial and temporal transformation of shallow water wave energy

The surface wave spectra from the Atlantic Ocean Remote Sensing Land‐Ocean Experiment (ARSLOE), during the passage of a 26‐hour storm, were subjected to an empirical eigenfunction analysis. Results from the analysis are interpreted as the spatial and temporal variation of surface gravity waves propagating from deeper water into the shallow region where breaking finally occurs. The temporal variation is found to be approximately 7–17% of the total variance in the data and is considered as stochastic, with a fluctuation of about 2–3 cycles that appear correlated with the variation of the atmospheric forcing. The spatial variation (1–3%) is significantly less than the temporal variation but exhibits a deterministic part, indicating that the wave processes associated with the spatial variation can be considered deterministic. The principal eigenfunctions obtained from the analysis provide a good representation of the principal variations in the wave spectra as shown by the first eigenvalue of the covariance matrices. The radiative transfer equation is projected onto the eigenvector space, and the source function obtained from the suitable projection function is presented. By using the information extracted from the empirical eigenfunction analysis, various source functions for the wave field are inferred. The source functions evaluated in the present study are associated with the wave mechanisms of refraction and shoaling, atmospheric input, bottom friction, and wave‐wave nonlinear interaction. The functions provide a good picture of the spectral wave energy balance, although further development of the current work can provide more detailed information about the energy transfer and may enhance the present picture of wave energy balance in the shallow water.

Hydrons and Alongshore Migrating Undulating Beach Forms

A beach undulation (rhythmic topography) is an equilibrium beach form. The water wave energy flux depends upon the refraction of the hydrons (water wave packets), and the angle of the breaking waves is determined by the refraction of the wavelets within a hydron. The refraction of the hydrons and wavelets work together to provide a constant longshore drift of sediments.

Flow regime and bedforms in a ridge and runnel system, S.E. Spain

During landward migration, ridge and runnel systems are subjected to asymmetric oscillatory and/or unidirectional flow regimes, depending on the stage of development reached by these systems. In the early stages of evolution, when the ridge is situated in the upper shoreface, the whole system is subjected to asymmetric oscillatory flow. The runnel is under lower flow regime conditions and the ridge may be under upper or lower flow regime according to water depth and wave energy. Later, when the ridge has migrated to a position on the foreshore, the runnel is largely under a unidirectional lower flow regime while the ridge itself is under oscillatory upper flow regime. When the ridge welds to berm, it is largely emergent and exposed to high-tide swash action under upper flow regime conditions. The runnel is eventually filled with sand and transformed into a low-lying area. All these types grade laterally into each other. One or more ridge and runnel systems can occur at the same time. Wave energy, tide level and position of the ridge control the variations in the characteristics of the ridge and also the position of the zones of bedforms found at the upper shoreface.

Long-period water-wave measurements for the MILROW and CANNIKIN nuclear explosions

Three types of high-resolution, ocean-bottom instruments were installed to monitor predicted low-amplitude, long-period water-wave activity associated with the MILROW and CANNIKIN underground nuclear explosions at Amchitka Island, Alaska. These instruments provided data on: (a) permanent vertical oceanfloor displacements in the expected generation region up to 15 km from surface zero, (b) wave propagation in deep water at ranges beyond 15 km, and (c) shoaling and nearshore effects at Amchitka and several other islands in the Aleutian chain. For MILROW, permanent undersea displacements and propagating waves were unobservable above the natural long-period background level of ∼ 1 cm (rms). For CANNIKIN, areas of ocean-floor uplift were observed in both the Bering Sea and in the Pacific Ocean within 6 km of ground zero. Vertical displacements averaged several centimeters, with a more localized region showing 56 cm of uplift; these values seem to be consistent with results of land surveys on the island. Resonant oscillations having amplitudes up to 10 cm were induced in two bays on the Bering Sea coastline. The absence of observable tsunami-like waves at deep water instruments and at more distant islands suggests that much of the waterwave energy generated near CANNIKIN was constrained in edge-wave modes along the shallow offshore slope along the Bering Sea coastline of Amchitka, and was dissipated there.

Computer Simulation of Marine Sedimentation: ABSTRACT

Geology has lacked an effective experimental approach to many problems. Although some kinds of experiments can be carried out, such as sediment transport on a stream table, most geologic processes cannot be re-created in the laboratory. A mountain range can be observed in the field, but neither the mountain range nor the mountain-building processes can be duplicated in the laboratory. These are shortcomings of which geologists are fully aware. There is, however, another shortcoming in the geologist's kit of tools--namely, his difficulty in dealing with many interdependent variables or processes that mutually and simultaneously affect each other. However, computers can be used, in conjunction with appropriate mathematical geologic models, to perform kinds of experiments which otherwise could be performed only with difficulty, or not at all. Furthermore, these computer models are ideally suited for exploring the effects of interdependent geologic processes that are linked together to form dynamic systems. The processes of marine sedimentation are highly interdependent. All too commonly, geologists who study stratigraphic sequences attempt to interpret the depositional environments of the strata in terms of only one or two variables--such as water depth or wave energy. Clearly, methods of analyzing the effects of multiple interdependent geologic variables are needed. Computerized, dynamic mathematical models which represent geologic processes and products in two- or three-dimensional space provide one method of attack. These models are philosophically identical to dynamic oil-reservoir simulation models, and they also share many of their constructional details. Most dynamic geologic simulation models can be constructed from relatively few mathematical building blocks, which may be grouped into the following categories: (1) materials-balance accounting systems; (2) sources of random variables; (3) Markov chains; (4) flow and transport mechanisms using finite-difference methods of representing diffusion and fluid-flow processes; (5) feedback control; (6) optimization; and (7) graphic display. Virtually all models employ methods in which both space and time are compartmented into small increments. Experiments with relatively simple sedimentation models suggest that feed-back control exerts much influence on sedimentary sequences. A lag in the isostatic adjustment of the crust in response to the load imposed by deposition of sediment may be responsible for some of the large-scale rhythms in cyclic sedimentation. Simulation models can be used effectively to explore the results of different assumed lag factors in sedimentation/isostatic-adjustment feedback loops. End_of_Article - Last_Page 555------------

Sedimentary Processes Operative Along the Western Louisiana Shoreline

ABSTRACT Investigation of modern facies relationships along the southwestern Louisiana shoreline demonstrates the complex interaction of and of coastal (Bernard, 1965). Shallow water wave energy and proximity to suspended mud supply are qualitatively shown to be dominant variables. Facies tracts show variation through a broad spectrum of geometries and sediment types. Mudflats, both intertidal and subaqueous, show highest rates of progradation, as compared to normal sand-rich beaches with low rates of progradation. An type of strandline, represented by a thin sand beach resting on eroded mudflat and marsh sediment, is shown to prograde at rates intermediate between those of mudflats and normal beaches, even though geometrical relationships would suggest retrogradation. Consideration of the interaction of various partially dependent sedimentary processes outlined in this paper can be used to characterize rates of progradation as well as to predict sediment type and geometry.