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Table Of Integrals Series And Products

The global decline in estuarine and coastal ecosystems (ECEs) is affecting a number of critical benefits, or ecosystem services. We review the main ecological services across a variety of ECEs, including marshes, mangroves, nearshore coral reefs, seagrass beds, and sand beaches and dunes. Where possible, we indicate estimates of the key economic values arising from these services, and discuss how the natural variability of ECEs impacts their benefits, the synergistic relationships of ECEs across seascapes, and management implications. Although reliable valuation estimates are beginning to emerge for the key services of some ECEs, such as coral reefs, salt marshes, and mangroves, many of the important benefits of seagrass beds and sand dunes and beaches have not been assessed properly. Even for coral reefs, marshes, and mangroves, important ecological services have yet to be valued reliably, such as cross-ecosystem nutrient transfer (coral reefs), erosion control (marshes), and pollution control (mangroves). An important issue for valuing certain ECE services, such as coastal protection and habitat-fishery linkages, is that the ecological functions underlying these services vary spatially and temporally. Allowing for the connectivity between ECE habitats also may have important implications for assessing the ecological functions underlying key ecosystems services, such coastal protection, control of erosion, and habitat-fishery linkages. Finally, we conclude by suggesting an action plan for protecting and/or enhancing the immediate and longer-term values of ECE services. Because the connectivity of ECEs across land-sea gradients also influences the provision of certain ecosystem services, management of the entire seascape will be necessary to preserve such synergistic effects. Other key elements of an action plan include further ecological and economic collaborative research on valuing ECE services, improving institutional and legal frameworks for management, controlling and regulating destructive economic activities, and developing ecological restoration options.

https://esajournals.onlinelibrary.wiley.com/doi/pdf/10.1890/10-1510.1

The value of estuarine and coastal ecosystem services

The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Followingare chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.

Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book

Social and ecological vulnerability to disasters and outcomes of any particular extreme event are influenced by buildup or erosion of resilience both before and after disasters occur. Resilient social-ecological systems incorporate diverse mechanisms for living with, and learning from, change and unexpected shocks. Disaster management requires multilevel governance systems that can enhance the capacity to cope with uncertainty and surprise by mobilizing diverse sources of resilience.

/pdf/social-ecological-resilience-to-coastal-disasters-4l1v0vsqf5.pdf

Social-Ecological Resilience to Coastal Disasters

This paper describes the development of a numerical model for studying the evolution of a wave train, shoaling and breaking in the surf zone. The model solves the Reynolds equations for the mean (ensemble average) flow field and the k–e equations for the turbulent kinetic energy, k, and the turbulence dissipation rate, e. A nonlinear Reynolds stress model (Shih, Zhu & Lumley 1996) is employed to relate the Reynolds stresses and the strain rates of the mean flow. To track free-surface movements, the volume of fluid (VOF) method is employed. To ensure the accuracy of each component of the numerical model, several steps have been taken to verify numerical solutions with either analytical solutions or experimental data. For non-breaking waves, very accurate results are obtained for a solitary wave propagating over a long distance in a constant depth. Good agreement between numerical results and experimental data has also been observed for shoaling and breaking cnoidal waves on a sloping beach in terms of free-surface profiles, mean velocities, and turbulent kinetic energy. Based on the numerical results, turbulence transport mechanisms under breaking waves are discussed.

A numerical study of breaking waves in the surf zone

This is a study of the interactions of solitary waves climbing up a circular island. A series of large-scale laboratory experiments with waves of different incident height-to-depth ratios and different crest lengths is described. Detailed two-dimensional run-up height measurements and time histories of surface elevations around the island are presented. A numerical model based on the two-dimensional shallow-water wave equations including runup calculations was developed. Numerical model predictions agreed very well with the laboratory data and the model was used to study wave trapping and the effect of slope. Under certain conditions, enhanced runup and wave trapping on the lee side of the island were observed, suggesting a possible explanation for the devastation reported by field surveys in Babi Island off Flores, Indonesia, and in Okushiri Island, Japan.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112095004095

Runup of solitary waves on a circular Island

http://coastal.usc.edu/plynett/publications/Lynett%20-%20Modeling%20Wave%20Runup%202002%20CE.pdf

Modeling wave runup with depth-integrated equations

The Boundary Integral Equation Method for Porous Media Flow

This paper presents a numerical model for simulating wave interaction with porous structures. The model calculates the mean flow outside of porous structures based on the Reynolds averaged Navier-S...

Philip L.-F. Liu

Papers

A numerical study of breaking waves in the surf zone

Runup of solitary waves on a circular Island

Modeling wave runup with depth-integrated equations

The Boundary Integral Equation Method for Porous Media Flow

Numerical Modeling of Wave Interaction with Porous Structures