Hugo B. Fischer

The dilution of an undersea sewage cloud by salt fingers

Abstract A qualitative experiment is described showing that when sewage effluent is released from an undersea diffuser to form a submerged cloud salt fingers will form at the interface between the top of the cloud and the ocean water above. Calculations based on previous laboratory experiments show that in a typical practical example the flux through the interface due to the fingers may cause substantial dilution to an effluent cloud during the time that it drifts from the site of the diffuser towards the coast.

A NUMERICAL MODEL OF ESTUARINE POLLUTANT TRANSPORT

The data for the spectra of wind-generated waves measured in a laboratory tank and in a bay are analyzed using the similarity theory of Kitaigorodski, and the one-dimensional spectra of fetch-limited wind waves are determined from the data. The combined field and laboratory data cover such a wide range of dimensionless fetch F (= gF/u ) as F : 10 ~ 10 . The fetch relations for the growthes of spectral peak frequency u)m and of total energy E of the spectrum are derived from the proposed spectra, which are consistent with those derived directly from the measured spectra.A solution of finite amplitude long waves on constant sloping beaches is obtained by solving the equations of the shallow water theory of the lowest order. Non-linearity of this theory is taken into account, using the perturbation method. Bessel functions involved in the solution are approximated with trigonometric functions. The applicable range of this theory is determined from the two limit conditions caused by the hydrostatic pressure assumption and the trigonometric function approximation of Bessel functions. The shoaling of this finite amplitude long waves on constant sloping beaches is discussed. Especially, the effects of the beach slope on the wave height change and the asymmetric wave profile near the breaking point are examined, which can not be explained by the concept of constancy of wave energy flux based on the theory of progressive waves in uniform depth. These theoretical results are presented graphically, and compared with curves of wave shoaling based on finite amplitude wave theories. On the other hand, the experiments are conducted with respect to the transformation of waves progressing on beaches of three kinds of slopes ( 1/30, 1/2.0 and 1/10 ) . The experimental results are compared with the theoretical curves to confirm the validity of the theory.Measurements of drift were made in a wind and wave facility at different elevations below the mean water level. The drift profiles were obtained for reference wind speeds, Ur = 3.1, 5.7 and 9.6 m/sec. The measurement technique involved tracing the movement of small paper discs which were soaked in water to become neutrally buoyant at the elevation of release. A logarithmic drift profile is proposed. The water shear velocity, U*w, predicts a surface stress, TS = pw U*S, in agreement with that obtained from the wind shear velocity, s = Pa U*li where pa and pw refer to air and water densities, respectively.The paper describes a procedure for obtaining field data on the mean concentration of sediments in combination of waves and currents outside the breaker zone, as well as some results of such measurements. It is assumed that the current turbulence alone is responsible for the maintenance of the concentration profile above a thin layer close to the bottom, in which pick-up of sediments due to wave agitation takes place. This assumption gives a good agreement between field data and calculated concentration profiles.A section of beach on the south coast of England has been under surveillance for five years, from March 1966 until March 1971. During this period, two permeable groynes of the Makepeace Wood type were constructed. Beach cross sectional areas and rates of accretion were compared before and after groyne construction. The groynes caused a buildup in beach levels updrift.The results of model tests, carried out to evaluate the stability of submarine slopes under wave action are presented. A Bentonite clay was sedimented in a glass walled tank 6 feet long by 0.5 feet wide by 2.5 feet deep. The sedimentation and consolidation processes were studied and sediment densities were measured at various depths in the profile. Vane shear strength profiles were also measured afvarious average degrees of consolidation. Plastic markers were placed in the sediment adjacent to a glass wall so that the soil movements under both gravity and wave induced slides could be documented by photography. Dimensional similitude is discussed and the model test data are presented in a dimensionless form. All instabilities were observed to be of the infinite slope type. Analysis of the data shows that wave action is instrumental in initiating downslope mass movements in gently to steeply sloping off-shore sediments. General lack of agreement between the model test results and published theoretical analyses was found but there was close similarity in the depths and form of failure under wave action and under gravity stresses alone. The loss of stability under wave action is analyzed on the concept that failure is gravity controlled and the soil strength is reduced to a value commensurate with gravity sliding by the cyclic shearing stresses imposed by progressive waves. A method of evaluating the stability of prototype slopes using a model test correlation and field vane strength measurements is proposed. INTRODUCTION Instabilities in submarine slopes have been observed or have been inferred over a wide range of slope angles from less than half a degree up to about 30°. These subaqueous landslides are believed to have caused rupture of submarine cables and to have generated many of the geomorphological features on the ocean bottom. There are numerous records describing these landslides but very few publications discuss the application of the principles of soil mechanics to the analysis of the stability of submarine slopes. Associate Professor of Civil Engineering, Queens University at Kingston, Canada 2 Soils Engineer, Geocon Ltd., Toronto, Canada 3 Associate Professor of Civil Engineering, Cornell University, Ithaca, N.Y.Several mathematical models have been lately presented which describe the tidal wave propagation within an estuary. The existing models derived from the method for damped co-oscillating tides are based on sinusoidal wave profile. Meanwhile a tidal wave which moves upstream, generally exhibits a progressive deformation which tends to unbalance the length of time between flood and ebb tides. The actual profile is therefore no longer sinusoidal. Our investigation uses the potential method, and takes into account the wave amplitude which is usually neglected compared with the water depth. Finally, the velocity potential is obtained explicitely, using a double iterative method. Tidal elevation, particle velocities and trajectories are given by the same computer programmed algorithm. Our study shows that l) the phenomenon can be clearly visualized on the theoretical curves and 2) the magnitude of this deformation is inversely proportional to the water depth, becoming significant when the ratio f|/h reaches the critical value of 1/10. Damping and geometrical effects are also considered and the theory was applied to the St.Lawrence Estuary. A partial positive reflection of the incoming tidal wave is assumed at the narrow section near Quebec, whereas a complete negative reflection is assumed at the entrance to Lake St.Peter. The calculated and observed wave profiles, velocity distributions, and phase shifts are in good agreement.A numerical model is presented to describe the hydromechanics of lagoons connected to the ocean by relatively narrow inlets. Because special attention is given to the flushing, all second order terms in the hydrodynamic equations are retained. The study is restricted to lagoons with a onedimensional flow pattern and water of uniform density. In designing a numerical solution to the equations, the inlet equations are regarded as implicit boundary conditions to the equations describing the flow in the lagoon proper. The advantages of this approach are: (1) the size of the computational grid in the lagoon can be chosen independently of the relatively small dimensions of the inlets and (2) the flow at branching inlets (an inlet connecting a lagoon to the ocean such that branching of the inlet flow can occur) still can be described by a one-dimensional tidal model. The predictive capability of the numerical model is confirmed by favorable comparison between measured and computed particle paths and net transport for a series of laboratory experiments. In the experiments a canal of uniform width and depth is freely connected to a tidal basin at one end and at the other end is connected to the same basin by a submerged weir.