Ivar G. Jonsson

WAVE BOUNDARY LAYERS AMD FRICTION FACTORS

INTRODUCTION For the design of a coastal structure, the height of its crown must be determined rationally and economically, taking into consideration the water level of the sea and its occurence probability. The water level in the sea is mainly referred to the astronomical tide, the meteorological effect and the short period wave. If component height according to these elements are given as; 3c, ; the tidal level, xr ; the level rise caused by meteorological origin, and x, ; the half height of wave, the level of the wave crest X at a certain tidal condition is shown by following equation under several assumption: I a i + X, + X, (1)

Bed friction and dissipation in a combined current and wave motion

Abstract Two simple two-layer eddy viscosity models, which facilitate analytical solutions, are presented in order to describe the velocity field and associated shear stress in a combined current wave motion. The models, which have the same eddy viscosity in the current boundary layer, but different eddy viscosities in the wave boundary layer, cover together the whole rough turbulent regime. Straightforward definitions are made for the wave friction factor and the current friction factor for the combined motion, which are in accordance with the results for pure waves and pure currents. In this way one avoids the fictitious reference velocities and elliptic integrals which e.g. Grant and Madsen (1978, 1979) experienced. The two friction factors turn out to be functions of four dimensionless parameters. A detailed calculation procedure is presented. Comparison with laboratory experiments yields promising results. A new relation connecting dissipation and bed shear stress is also developed.

A new approach to oscillatory rough turbulent boundary layers

Abstract Velocity measurements have been performed in an oscillatory turbulent boundary layer over a rough wall, using a large oscillating water tunnel. These together with measurements by Kalkanis (1964) over an oscillating wall indicate the existence of universal wall and defect laws for velocity. A logarithmic overlap layer is predicted and observed as in a steady turbulent boundary layer, and this results in a new relationship between friction factor and relative boundary layer thickness. The phase lead of the defect velocity relative to the wall ditto seems to follow a universal law over the whole defect layer. A method is suggested for the calculation of the phase lead of wall shear stress over velocity in the free stream for large amplitude to roughness ratios. Apart from the inner layer, it is in principle possible to construct the velocity profiles in a turbulent oscillatory boundary layer at a rough wall, using the findings of this report. A review of experimental and theoretical investigations of the stability of the oscillatory boundary layer is also given.

INTERACTION BETWEEN WAVES AMD CURRENTS

The wave-induced longshore current variation across the surf zone is described for a simplified model The basic assumptions are that the conditions are steady, the bottom contours are straight and parallel but allow for an arbitrary bottom profile, the waves are adequately described by linear theory, and that spilling breakers exist across the surf zone Conservation equations of mass, momentum, and energy, separated into the steady and unsteady components, are used to describe second order-wave-induced phenomena of shoaling waves approaching at an angle to the beach An expression for the longshore current is developed, based on the alongshore component of excess momentum flux due to the presence of unsteady wave motion Wave set-down and set-up have been included in the formulation Emphasis in the analysis is placed on formulating usable predictive equations for engineering practice Comparison with experimental results from the laboratory and field show that if the assumed conditions are approximately fulfilled, the predicted results compare quite favorably

Edge waves revisited

Abstract For edge waves on an infinite beach of constant slope comparison is made between the full linear solution and the shallow water approximation. Modifications to the shallow-water edge-wave dispersion relation accounting for an offshore shelf are obtained and compared with an earlier approximation. A physically comprehensible description of edge waves is given, using a geometrical optics approach, leading to approximate expressions for their dispersion relation. Both shallow water and general depth are considered. For the shallow water case comparison is made with the exact relation for an exponentially seaward decreasing slope. Finally the maximum possible edge wave amplitude is estimated by heuristic arguments.

ENERGY FLUX AND WAVE ACTION IN GRAVITY WAVES PROPAGATING ON A CURRENT

The total energy flux with the mean energy level as a datum is shown to be proportional to the wave action flux for waves on steady irrotational currents. This leads directly to the wave action conservation principle. The set-down of the mean water surface is calculated in a new and simple way. In addition the mean Eulerian current velocity profile is discussed, and the myth of a non-zero mass transport in a pure wave motion is reconsidered. Dissipative effects are neglected.

COMPUTATION OF LONGSHORE CURRENTS

The steady state profile of the longshore current induced by regular, obliquely incident, breaking waves, over a bottom with arbitrary parallel bottom contours, is predicted. A momentum approach is adopted. The wave parameters must be given at a depth outside the surf zone, where the current velocity is very small. The variation of the bottom roughness along the given bottom profile must be prescribed in advance. Depth refraction is included also in the calculation of wave set-down and set-up. Current refraction and rip-currents are excluded. The model includes two new expressions, one for the calculation of the turbulent lateral mixing, and one for the turbulent bottom friction. The term for the bottom friction is non-linear. Rapid convergent numerical algorithms are described for the solution of the governing equations. The predicted current profiles are compared with laboratory experiments and field measurements. For a plane sloping bottom, the influence of different eddy viscosities and constant values of bottom roughness is examined.The calculation of turbulent flow using Naviers equations assumes the introduction of a turbulent viscosity coefficient the value of which is normally constant, conforming with Boussinesqs hypothesis. It was shown that setting aside this hypothesis, a velocity profile quite different to that resulting from the classic theory is obtained in the case of flow induced by wind. This result appears to be confirmed by the tests carried out in the Mediterranean. The advantage of this method is that it gives the vertical turbulent diffusion which is of particular interest to pollution studies.In the numerical method of prediction of wind waves in deep water, Hasselmanns nonlinear interaction theory is applied. This method assumes the energy balance of individual component waves. However, the total energy balance must exist in the transformation of irregular waves in shoaling water. In this investigation, experiments were carried out on the transformations in shoaling water of composite waves having two components and random waves having one or two main peaks. It was found that the elementary component wave height of the composite waves and the elementary peak power of the random waves decrease with decrease in the water depth. This reason can be explained qualitatively by the theory of the elementary component wave height change of finite amplitude waves in shoaling water. The secondary component wave height of the composite waves and the secondary peak power of the random waves increase with decrease in the water depth. This can be explained qualitatively by Hamadas theory of nonlinear interaction in uniform depth.Experiments have been carried out by using non-breaking waves and breaking waves to investigate the wave forces on a vertical circular cell located in the shallow water. Based on the experimental data, the drag coefficient and the inertia coefficient of a circular cylinder and the curling factor of breaking waves are estimated, and the computation methods of wave forces are examined. As a result, it is shown that the phase lag of inertia forces behind the accelerations of water particles should be considered for the estimation of the drag coefficient as well as the inertia coefficient. In addition the previous formula of the maximum breaking wave forces acting on a cell or a pile is revised by introducing the effects of the above-mentioned phase lag and another phase difference, both of which are functions of the ratio of the cell diameter to the wave length. • It is confirmed that the proposed formula is applicable even to the large cell with the diameter comparable to the wave length. INTRODUCTION Many studies have been done on the impulsive pressures acting on a vertical wall, but there has been very little investigation of breaking wave forces on a cell-type structure. The breaking wave forces should be taken into consideration all the same in the design of pile-type or cell-type structures in nearshore area, because breaking waves cause extreme shock pressures on a cell structure asThe air bubble plume induced by the steady release of air into water has been analyzed with an integral technique based on the equations for conservation of mass, momentum and buoyancy. This approach has been widely used to study the behavior of submerged turbulent jets and plumes. The case of air-bubble induced flow, however, includes additional features. In this study the compressibility of the air and the differential velocity between the rising air bubbles ,and the water are introduced as basic propertie s of the air bubble plume in addition to a fundamental coefficient of entrainment and a turbulent Schmidt number characterizing the lateral spreading of the air bubbles. Theoretical solutions for twoand three-dimensional air-bubble systems in homogeneous, stagnant water are presented in both dimensional and normalized form and compared to existing experimental data. The further complication of a stratified environment is briefly discussed since this case is of great practical interest. This paper is to be considered as a progress report, as future experimental verification of various hypotheses is needed.

VARIATION OF SEDIMENT SUSPENSION IN OSCILLATORY FLOW

This report will update the coastal zone practitioner on the National Flood Insurance Program (NFIP) as it affects the implementation of manmade changes along the coastline. It is our intent to place in proper perspective this fast-changing and often difficult to interpret national program. Readers will achieve an overall understanding of the NFIP on the coast, and will be in a position to apply the programs requirements in their efforts. We will begin with a history of the application of the NFIP to the coastal zone. The history of the problems encountered will lead into current regulations, methodologies, and the changes the Federal Emergency Management Agency plans for the future.The spatial variability of the nearshore wave field is examined in terms of the coherence functions found between five closely spaced wave gages moored off the North Carolina coast in 17 meters depth. Coherence was found to rapidly decrease as the separation distance increased, particularly in the along-crest direction. This effect is expressed as nondimensional coherence contours which can be used to provide an estimate of the wave coherence expected between two spatial positions.Prediction of depositional patterns in estuaries is one of the primary concerns to coastal engineers planning major hydraulic works. For a well-mixed estuary where suspended load is the dominant transport mode, we propose to use the divergence of the distribution of the net suspended load to predict the depositional patterns. The method is applied to Hangzhou Bay, and the results agree well qualitatively with measured results while quantitatively they are also of the right order of magnitude.

Current-depth refraction of water waves

Abstract Surface gravity waves propagating on large-scale currents over a gently sloping sea bed are considered. Assuming irrotational flow a general proof is given of the existence of a mean energy level, leading directly to the current wave set-down. The complete set of conservation equations describing combined current-depth refraction is presented and solved in two special ssituations. Also a case with a rotational current is considered. Dissipation is neglected.

A mild‐slope wave equation and its application to tsunami calculations

A wave equation correct to first order in wave amplitude and bottom slope is used to calculate the wave field around an island. This is of circular cylindrical shape, and is situated on a paraboloidal shoal in an ocean of constant depth (Figure 1). The sides of the island are assumed fully reflecting. The incident waves are plane, periodic, and of small amplitude. Periods up to 30 min are investigated, and the Coriolis force is neglected. The wave equation is solved analytically, and a great number of numerical computations are carried through. The total wave field over the shoal is presented for two discrete periods in the upper end of the tsunami frequency range. The amplitudes at the middle of the front face of the island, and at the middle of the lee face, are given as functions of the wave period, and the existence of “resonance”; periods is thus demonstrated. Comparison with solutions to the linearized long‐wave equation is made, and the validity range of the shallow water theory is estimated. The g...