Ole Secher Madsen

SPECTRAL WAVE ATTENUATION BY BOTTOM FRICTION: THEORY

The Labrador Sea Extreme Waves Experiment (LEWEX), is an international basic research programme concerned with full-scale measurements, analysis, modelling and simulation in test basins of 3-dimensional seas. The research is carried out in order to assess the significance of 3-dimensional sea states in engineering applications. The first phase of the programme full scale wave measurements in the North Atlantic Ocean was performed at a site and time that had a high probability of encountering severe sea states. The present publication shows examples of measured bi-modal directional sea spectra obtained with the WAVESCAN buoy and directional sea spectra measured with an airborne Synthetic Aperture Radar (SAR). Directional spectra of gravity waves are obtained with the SAR both in open waters and below an ice cover. Further work is needed in order to verify SAR-measurements with in-situ observations. In-situ measured directional spectra are also compared with hindcast spectra from the 3G-WAM model. Hindcast significant wave heights were found to be lower than the in-situ measurements.The littoral drift model developed at DHI and ISVA, see Deigaard et al. (1986b) has been extended to include the effects of the irregularity of the waves, of a coastal current and a wind acting on the surf zone. Further, a mathematical model to simulate the near-shore current pattern along a barred coast with rip channels has been developed. The influence on the littoral drift of the irregularity of waves, wind, coastal current, and rip channels is discussed. It is concluded that irregularity of waves and presence of rip channels must be considered while coastal current and wind action are of minor importance.At present, the Prodhoe Bay oil field in Alaska contributes a substantial amount of the domestic oil production of the United States. Oil is also expected to be present on the continental shelf of Alaska, and it is estimated that approximatedly 28 percent of the total U. S. reserve is located beneath the shallow ice covered seas of the Alaskan continental shelf. To expolre and to exploit these oil rich resources, engineers are confronted with hostile oceanographic conditions such as high tides, waves, strong currents and sea ice. The same area is also rich in fishery resources. Being one of the most productive fishing grounds in the nothern Pacific, the potential ecological impact due to an oil spill is of a major concern. This paper describes the methologies used for the development of a modeling system for the oil risk analysis. The system is designed with generality in mind so it can be used for other coastal areas. The development of three dimensional models used in the modeling system described here have been published in the earlier International Coastal Engineering Conferences (Liu and Leendertse, 1982, 1984, 1986) and a report published recently by RAND (Liu and Leendertse, 1987). In the oil-spill risk analysis, these three dimensional hydrodynamic models are coupled to a two-dimensional stochastic weather model and an oil weathering model.The entrainment phenomena have been investigated across an interface between two-layered stratified flow induced by wind shear stress. The velocities of mean flow, turbulence and entrainment have been measured under three different conditions of water surface by using a wind-wave tank. When the entrainment velocity ue is expressed on the basis of the turbulent quantities at the interface, the turbulent entrainment coefficient E ( = ue/u) is given by E = A-(egl/u2)-3I1 ( A = 0.7). Here Eg, u and 1 are the effective buoyancy, the turbulence intensity and the integral lengthscale of turbulence at the interface, respectively. This result coincides with the relationship of entrainment due to oscillating grid turbulence, in which the mean flow does not exist. When, for the practical purpose, the estimation of ue is made by using the mean velocity Um and the depth h of mixed layer, Em ( - Ue/Um ) = Am•(egh/Um 2)3/2 is derived from the transformation of E = A-(egl/u2)-3/2. There holds Am = A-Tf between Am and Tf, Tf being a turbulence factor given by (u/Um)4•(1/h)-3/2. It has been found that this relationship is also valid in various types of two-layered stratified flows as well as the wind-induced two-layered flows.The two projects (LUBIATOWO 79 and LUBIATOWO 86) were aimed at study pore pressure behaviour in natural sand bed in the coastal zone of the Baltic sea under the action of storm waves. During both projects, the wave induced pore pressures at the various levels in the sea bed were measured. The collected data were used to verify the applicability of the various theoretical approaches. In the conclusion, the range of the application of the particular analytical method is given.The rapid recession of the shingle bank of Hurst Beach (up to 3.5m/yr) makes it an excellent natural laboratory for the study of the factors which influence the stability of shingle beaches. Studies have included: the significance of long period, high energy, swell waves the classification and quantification of overwash processes run-up and seepage characteristics the effect of settlement of the underlying strata and the implications for practices in shingle nourishment. The studies have revealed the distinctive character of shingle beaches as compared with the more fully researched sand beaches. More detailed research on shingle beaches is justified particularly in relation to (i) the run-up characteristics including its interaction with swash cusps and (ii) the influence of the subsidiary sand fraction on the beach characteristics.This paper presents a technique to reproduce, by a twodimensional moveable-bed model, beach change due to the timedependent storm waves which are generated by the passage of an atmospheric depression. In the model test, scaling conditions for sand grain-size, vertical and horizontal lengths, and wave height and period characteristics were established by applying the authors scale-model relationship which was reported; and wave duration time also was decided. A method of employing regular waves in the model to represent irregular waves in the field is proposed. From the results, it was shown that the model can reproduce well the beach change in the field using the regular waves having the mean wave properties in the irregular waves.Environmental assessment, engineering studies and designs were completed for a new 26.5 m3/s seawater intake system in the Persian Gulf. The original intake facility consisted of a curved, 60m breakwater with one end attached to the shoreline, a settling basin immediately adjacent to the shoreline and dredged to a maximum depth of approximately 5m, and a pumphouse structure located on shore such that the seaward wall formed one side of the settling basin. The facility located on an island in the Gulf, which served multiple seawater uses, had experienced both structural and operational problems, the latter consisting principally of excessive ingestion of sediment and seaweed. These factors plus the requirement for additional demands for seawater beyond plant capacity caused the owner to initiate a study of alternative intake systems, produce a design for the most effective solution and construct the new intake system.A total of eleven new types of blocks are developed for this project. After performing a series of model tests for them and having a consideration of easy casting, two types of blocks are selected and presented here in this paper. They are named Double U block and I block, respectively. The two have been compared with several existing types which have been widely used in Taiwan. It is shown that the Double U block is an excellent type of block with high stability and low reflection coefficient. The I block has an advantage of easy casting, although it is not outstanding in other characteristics.A two-dimensional wave prediction model suitable for use on personal computers is described. The model requires the twodimensional time-dependent wind field as input. Output consists of wave height, wave period, and wave direction estimates at all grid points on a computational grid representing an enclosed or semi-closed basin. Model predictions compare favorably with observations from a wave research tower in Lake Erie. A formula is provided to estimate how long a model simulation would take on a personal computer given the surface area of the computational domain, the grid size, and the computer clock speed.Cullera Bay is a neritic ecosystem placed on the Spanish Mediterranean Littoral largely influenced by the Jucar River, that brings about lower salinities than surrounding waters, and broad variations of its values. An extensive research, with 9 samplings throughout the year, was carried out, measuring both physical and chemical parameters, and the planktonic communities. The trophic status of the ecosystem, the spatial and temporal variations of the nutrients and the planktonic communities were studied, evaluating the influence of the river loads and the littoral dynamics. Some essential basis to allow a suitable emplacement of waste waters disposals along the Valencian littoral are set up in order to minimize the gradual eutrophication of this coast.In the last two years a whole of studies was realized in order to determine precise solutions to the regeneration of Villajoyosas beach, in the Spanish mediterranean coast. Investigations were carried out to the surrounding coastal areas based in field investigations and laboratory analyses of the beaches materials.

A Realistic Model of the Wind-Induced Ekman Boundary Layer

Abstract A physically realistic and general model for the vertical eddy viscosity in a homogeneous fluid is proposed. For an infinitely deep ocean the vertical eddy viscosity increases linearly with depth from a value of zero at the free surface. Based on this model a general theory is developed for the drift current resulting from a time-varying surface shear stress. Explicit expressions are given for the temporal development of the drift current in the vicinity of the free surface and for the steady-state response to a suddenly applied uniform shear stress. The steady-state solution predicts the effective Ekman layer depth to be proportional to the square root of the wind shear stress and reproduces the experimentally observed logarithmic velocity deficit near the free surface. The angle between the surface drift current and the wind stress is found to be somewhat smaller (of the order 10°) than predicted by Ekmans classical solution. For the unsteady response to a suddenly applied wind stress the pres...

Waves and currents over a fixed rippled bed: 1. Bottom roughness experienced by waves in the presence and absence of currents

Several theoretical models have been advanced for turbulent boundary layers associated with wave and current flows over a rough bed. Although these models differ, particularly in the sophistication with which turbulence is modeled, they all share one common feature: the bottom roughness is characterized by a single roughness length scale kn. However, no experimental data have been presented which accurately characterize the bottom roughnesses for wave and current boundary layers such that this basic assumption can be considered verified. This paper and a companion paper [Mathisen and Madsen, this issue] present results of an experimental study to verify this basic assumption. In this paper, wave roughnesses (i.e., bottom roughnesses experienced by pure waves and waves in the presence of a current) are compared with the roughness experienced by a pure current. The roughnesses for pure currents and pure waves are shown to be the same if determination of the pure wave roughness from measurements of wave energy dissipation includes the phase difference between the near-bottom horizontal orbital velocity and bottom shear stress. When these analysis procedures are extended to combined wave-current flows, the roughness experienced by waves in the presence of a current is shown to be that obtained for pure waves.

Waves and currents over a fixed rippled bed: 2. Bottom and apparent roughness experienced by currents in the presence of waves

This paper is the second of two papers which present the results of an experimental study to verify the use of a single bottom roughness length scale to characterize wave and current boundary layer flows over a rough bed. While the first paper [Mathisen and Madsen, this issue] included analysis of wave attenuation measurements to estimate the bottom roughness experienced by waves in the presence and absence of a current, this paper includes the analysis of time-averaged velocity profiles to estimate the bottom and apparent roughness experienced by a current in the presence of waves. In this paper, velocity profiles predicted by the Grant and Madsen [1986] model are compared with measured velocity profiles. Apparent hydraulic roughness predictions of the Grant and Madsen [1986] model are shown to underpredict the apparent hydraulic roughnesses experienced by the current. This difference is shown to be a result of an underprediction of the wave boundary layer thickness and of a steady streaming or mass transport which is induced by the wave motion within the wave boundary layer of the combined wave-current flow. By modifying the wave boundary layer thickness and estimating the wave-induced mass transport from pure wave experiments, the bottom roughness for pure current, pure wave, and combined wave-current boundary layer flows is shown to be characterized by a single roughness scale.

LONGSHORE SEDIMENT TRANSPORT DATA: A REVIEW

Numerical modelling of rivers, estuaries and shallow seas has attracted increasing interest over the last two decades. The models have developed from one dimensional (ID) applications to tidal propagation and flood routing through two and, finally, three dimensional applications to motions ranging from pseudo-turbulence to annual mean residual flows. The present account describes the development, over the last five years, of the modelling studies carried out by the author concerning the hydrodynamics of the southern North Sea and River Thames. The objective is to identify those major points which have emerged that may have a wider significance.The equations describing conservation of mass, momentum and energy in a turbulent free surface flow are derived for a controle volume extending over the whole depth. The effect of the turbulent surface oscillations are discussed but neglected in the following analysis, where the equations are applied to the energy balance in a surf zone wave motion. This leads to results for the wave height variation and the velocity of propagation. The results cannot be reconciled completely with measurements and the concluding discussion is aimed at revealing how the model can be improved.A three-dimensional morphodynamic model of sequential beach changes Is presented. The model Is based on variations in breaker wave power generating a predictable sequence of beach conditions. The spectrum of beach conditions from fully eroded-dissipatlve to fully accreted reflective is characterised by ten beach-stages. Using the breaker wave power to beach-stage relationship the model Is applied to explain temporal, spatial and global variations In beach morphodynamlcs.Fast-response electromagnetic flowmeters were used in a marginal flood channel of an ebb tidal delta to assess the importance of wave contributions to the flood dominance of these channels. Measurements were made at a single point in the channel in both ebb and flood currents. The oscillatory motion of waves was a very significant feature of the velocity records, and its magnitude was comparable with the mean flow at all stages of the tide. This observation shows that flowmeters capable of responding accurately to wave velocities are needed to obtain accurate values of mean flow. Some earlier measurements made with slow response flowmeters are probably unreliable. Wave contributions to the mean flow were assessed by looking at the correlation between the low frequency (>17.5s) oscillations of the along-channel current and the low frequency envelope of the wave velocities. Surprisingly little correlation was found for any time lag, suggesting that wave effects were not important in the mean tidal currents in the channel studied. However, close to low tide on the ebb, conditions existed which appear to have been favourable for the wave pump mechanism suggested by Bruun andViggisson (1973). Significant correlation between the wave envelope and low frequency fluctuations was observed at this time. It is therefore suggested that wave effects can be important to the mean flow in marginal channels with rapidly converging and shoaling mouths which are oriented towards the dominant incident wave direction.The agents of initial damage to the dunes are water, which undermines them, and animals (including man) which damage the protective vegetation by grazing or trampling. Of these, man has recently assumed predominant local importance because of the popularity of sea-side holidays and of the land-falls of certain marine engineering works such as oil and gas pipelines and sewage outfalls. The need is therefore increasing for active dune management programmes to ensure that under these accentuated pressures, the coast retain an equilibrium comparable with that delicately balanced equilibrium which obtains naturally at a particular location.

Waves and currents over a fixed rippled bed: 3. Bottom and apparent roughness for spectral waves and currents

This paper is the third in a series of three that presents the results of experiments designed to verify the use of a single bottom roughness length scale for waves and currents over a rough bed. While the first two papers concentrated on the bottom roughnesses experienced by monochromatic wave and current boundary layer flows, this paper presents the results of additional experiments that investigate the use of an equivalent wave representation to extend these results to spectral wave and current boundary layer flows. Spectral waves, simulated by five components, and currents were generated in a 20-m-long wave flume with a fixed rippled bottom. Attenuation due to bottom friction is determined from total attenuation measurements for individual wave components by removing the effects of sidewall dissipation and wave-wave interactions. These attenuation estimates are used to establish representative friction factors, which are used in conjunction with an existing eddy viscosity model to determine bottom roughnesses. The bottom roughnesses experienced by spectral waves (in the presence and absence of a current) match the bottom roughnesses for monochromatic waves. When these experimentally determined bottom roughnesses are used in conjunction with the eddy viscosity model, predictions of attenuation for individual wave components closely match measurements. When the wave boundary layer thickness is defined to be the height at which the predicted velocity deficit in the wave boundary layer is within 5% of the free stream velocity, excellent agreement is obtained between predicted and measured velocity profiles for currents in the presence of codirectional waves. Therefore these experiments show that a single bottom roughness, when used in conjunction with an equivalent wave representation, adequately characterizes both monochromatic and spectral wave-current boundary layer flows over a fixed rippled bed.

A Finite-Depth Wind-Wave Model. Part I: Model Description

Abstract A parametric windsea model for arbitrary water depths is presented. The model is derived from a conservation of energy flux formulation and includes shoaling, refraction, dissipation by bottom friction, as well as finite-depth modifications of the atmospheric input and nonlinear wave–wave interaction source terms. The importance of dissipation due to a rough ocean floor on the migration of the spectral peak frequency is discussed and compared with that caused by nonlinear energy transfer. Numerical simulations are used to systematically examine wave growth and the development of the spectral peak in a depth-limited ocean. Two idealized situations of wave growth and propagation are considered to further understand the influence of bottom friction on the spectral dynamics. The first case studies the characteristics of fetch-limited wave growth in a steady, uniform wind as function of depth and bottom roughness. The second case examines the role of bottom dissipation on a fully developed deep-water ...

MOVABLE BED FRICTION FACTORS FOR SPECTRAL WAVES

Tanah Lot Temple is situated in Tabanan Regency - Bali, on the coast of the Indonesian Ocean. Due to continuous wave attack, wind force, and weathering of the rock bank where the Temple stands, abrasion has occured which is more and more threatening the existence of the Temple. Considering that Tanah Lot Temple is a sacred place for the Hindu Balinese people and a place of high cultural value, and also an important tourism, steps to save the Temple are imperative. The Central as well as the Regional Authorities, and also the Bali nese community are very much interested in the effort to keep the Temple intact. Measures have been undertaken to protect both the seaside and land-side banks of the Temple rock bank. This paper only discusses counter measures of the sea —side bank of the Temple.

Bottom Stress in Wind-Driven Depth-Averaged Coastal Flows

Abstract The relationship between depth-averaged velocity and bottom stress for purely wind-driven flows in unstratified coastal waters is examined using a one-dimensional (vertically resolving) current model. Results indicate that conventional drag laws employed in depth-averaged coastal circulation models may produce large directional errors in bottom stress estimated. A drag tensor is suggested as an alternative to conventional drag coefficient formulations. The drag tensor allows for variation in direction between depth-averaged velocity and bottom stress. Two physically relevant cases are studied in order to quantify drag tensor variation as a function of water depth, wind stress and bottom roughness. The drag tensor allows for phenomena excluded by drag coefficient formulations. Results indicate that the drag tensor is a simple and physically pleasing alternative to dray coefficients.

Near-bottom flow and flow resistance for currents obliquely incident to two-dimensional roughness elements

Measurements of the three components of the velocity when a steady current is flowing over a rippled bottom are presented. The bottom consisted of equally spaced triangular bars placed at angles of 0°, 30°, 45°, and 60° to the incident flow. The experiments show that close to the bottom, there is a transverse component of the velocity, which, for the larger angles of incidence, can be of the same order of magnitude as the main flow. The spatial average velocity profiles obtained from the measurements performed between two ripple crests show that close to the bottom, there is a well-defined logarithmic region. The bottom roughness obtained by fitting a logarithmic law in the near-bottom region to the longitudinal component of the flow depends strongly on the angle of incidence. In contrast, the analysis of the near-bottom velocity component in the direction perpendicular to the ripple axis shows that the bottom roughness is independent of the angle of incidence. These experimental observations support the concept of a direction-dependent equivalent bottom roughness when currents are obliquely incident to two-dimensional bottom roughness elements, such as wave-generated ripples.