On the use of combined compact scheme for numerical solution of the two-layer oceanic shallow water equations

Many types of oceanic physical phenomena have a wide range in both space and time. In general, simplified models, such as shallow water model, are used to describe these oceanic motions. The shallow water equations are widely applied in various oceanic and atmospheric extents. By using the two-layer shallow water equations, the stratification effects can be considered too. In this research, the sixth-order combined compact method is investigated and numerically implemented as a high-order method to solve the two-layer shallow water equations. The second-order centered, fourth-order compact and sixth-order super compact finite difference methods are also used to spatial differencing of the equations. The first part of the present work is devoted to accuracy assessment of the sixth-order super compact finite difference method (SCFDM) and the sixth-order combined compact finite difference method (CCFDM) for spatial differencing of the linearized two-layer shallow water equations on the Arakawa's A-E and Randall's Z numerical grids. Two general discrete dispersion relations on different numerical grids, for inertia-gravity and Rossby waves, are derived. These general relations can be used for evaluation of the performance of any desired numerical scheme. For both inertia-gravity and Rossby waves, minimum error generally occurs on Z grid using either the sixth-order SCFDM or CCFDM methods. For the Randall's Z grid, the sixth-order CCFDM exhibits a substantial improvement , for the frequency of the barotropic and baroclinic modes of the linear inertia-gravity waves of the two layer shallow water model, over the sixth-order SCFDM. For the Rossby waves, the sixth-order SCFDM shows improvement, for the barotropic and baroclinic modes, over the sixth-order CCFDM method except on Arakawa's C grid. In the second part of the present work, the sixth-order CCFDM method is used to solve the one-layer and two-layer shallow water equations in their nonlinear form. In one-layer model with periodic boundaries, the performance of the methods for mass conservation is compared. The results show high accuracy of the sixth-order CCFDM method to simulate a complex flow field. Furthermore, to evaluate the performance of the method in a non-periodic domain the sixth-order CCFDM is applied to spatial differencing of vorticity-divergence-mass representation of one-layer shallow water equations to solve a wind-driven current problem with no-slip boundary conditions. The results show good agreement with published works. Finally, the performance of different schemes for spatial differencing of two-layer shallow water equations on Z grid with periodic boundaries is investigated. Results illustrate the high accuracy of combined compact method.

A baseline survey of water quality, invertebrates, fisheries and socioeconomics on Lake Edward for proposed seismic surveys in block 4B : Final report

The National Fisheries Resources Research Institute (NaFIRRI) on behalf of OPEP Consult Ltd undertook a baseline survey of the transition zone (basically along the shoreline) and near shore habitats of the Uganda apart of Lake Edward and Kazinga channel during December 2007 to January 2008. A major objective of the baseline survey was to generate baseline information on the aquatic ecosystem features related to the fisheries and socio-economics of the fish catch including issues raised by residents in the fish landing sites. Therefore, the baseline survey captured information on water quality, the aquatic invertebrate fauna, aspects of fish biology and ecology, the fish catch including facilities at fish landings, value in the catch and related fisheries socio-economic issues perceived by residents in the settled areas along the shores.

Marine Vertebrates and Low Frequency Sound: Technical Report for LFA EIS

Over the past 50 years, economic and technological developments have dramatically increased the human contribution to ambient noise in the ocean. The dominant frequencies of most human-made noise in the ocean is in the low-frequency range (defined as sound energy below 1000Hz), and low-frequency sound (LFS) may travel great distances in the ocean due to the unique propagation characteristics of the deep ocean (Munk et al. 1989). For example, in the Northern Hemisphere oceans low-frequency ambient noise levels have increased by as much as 10 dB during the period from 1950 to 1975 (Urick 1986; review by NRC 1994). Shipping is the overwhelmingly dominant source of low-frequency manmade noise in the ocean, but other sources of manmade LFS including sounds from oil and gas industrial development and production activities (seismic exploration, construction work, drilling, production platforms), and scientific research (e.g., acoustic tomography and thermography, underwater communication). The SURTASS LFA system is an additional source of human-produced LFS in the ocean, contributing sound energy in the 100-500 Hz band. When considering a document that addresses the potential effects of a low-frequency sound source on the marine environment, it is important to focus upon those species that are the most likely to be affected. Important criteria are: 1) the physics of sound as it relates to biological organisms; 2) the nature of the exposure (i.e. duration, frequency, and intensity); and 3) the geographic region in which the sound source will be operated (which, when considered with the distribution of the organisms will determine which species will be exposed). The goal in this section of the LFA/EIS is to examine the status, distribution, abundance, reproduction, foraging behavior, vocal behavior, and known impacts of human activity of those species may be impacted by LFA operations. To focus our efforts, we have examined species that may be physically affected and are found in the region where the LFA source will be operated. The large-scale geographic location of species in relation to the sound source can be determined from the distribution of each species. However, the physical ability for the organism to be impacted depends upon the nature of the sound source (i.e. explosive, impulsive, or non-impulsive); and the acoustic properties of the medium (i.e. seawater) and the organism. Non-impulsive sound is comprised of the movement of particles in a medium. Motion is imparted by a vibrating object (diaphragm of a speaker, vocal chords, etc.). Due to the proximity of the particles in the medium, this motion is transmitted from particle to particle in waves away from the sound source. Because the particle motion is along the same axis as the propagating wave, the waves are longitudinal. Particles move away from then back towards the vibrating source, creating areas of compression (high pressure) and areas of rarefaction (low pressure). As the motion is transferred from one particle to the next, the sound propagates away from the sound source. Wavelength is the distance from one pressure peak to the next. Frequency is the number of waves passing per unit time (Hz). Sound velocity (not to be confused with particle velocity) is the impedance is loosely equivalent to the resistance of a medium to the passage of sound waves (technically it is the ratio of acoustic pressure to particle velocity). A high impedance means that acoustic particle velocity is small for a given pressure (low impedance the opposite). When a sound strikes a boundary between media of different impedances, both reflection and refraction, and a transfer of energy can occur. The intensity of the reflection is a function of the intensity of the sound wave and the impedances of the two media. Two key factors in determining the potential for damage due to a sound source are the intensity of the sound wave and the impedance difference between the two media (impedance mis-match). The bodies of the vast majority of organisms in the ocean (particularly phytoplankton and zooplankton) have similar sound impedence values to that of seawater. As a result, the potential for sound damage is low; organisms are effectively transparent to the sound – it passes through them without transferring damage-causing energy. Due to the considerations above, we have undertaken a detailed analysis of species which met the following criteria: 1) Is the species capable of being physically affected by LFS? Are acoustic impedence mis-matches large enough to enable LFS to have a physical affect or allow the species to sense LFS? 2) Does the proposed SURTASS LFA geographical sphere of acoustic influence overlap the distribution of the species? Species that did not meet the above criteria were excluded from consideration. For example, phytoplankton and zooplankton species lack acoustic impedance mis-matches at low frequencies to expect them to be physically affected SURTASS LFA. Vertebrates are the organisms that fit these criteria and we have accordingly focused our analysis of the affected environment on these vertebrate groups in the world’s oceans: fishes, reptiles, seabirds, pinnipeds, cetaceans, pinnipeds, mustelids, sirenians (Table 1).