scholarly journals A Tsunami Ball Approach to Storm Surge and Inundation: Application to Hurricane Katrina, 2005

2009 ◽  
Vol 2009 ◽  
pp. 1-13 ◽  
Author(s):  
Steven N. Ward
Keyword(s):  
Finite Element ◽  
Finite Difference ◽  
Hurricane Katrina ◽  
Storm Surge ◽  
Volume Density ◽  
Momentum Equation ◽  
Cape Cod ◽  
Laptop Computer ◽  
New Approach ◽  
Advection Term

Most analyses of storm surge and inundation solve equations of continuity and momentum on fixed finite-difference/finite-element meshes. I develop a completely new approach that uses a momentum equation to accelerate bits or balls of water over variable depth topography. The thickness of the water column at any point equals the volume density of balls there. In addition to being more intuitive than traditional methods, the tsunami ball approach has several advantages. (a) By tracking water balls of fixed volume, the continuity equation is satisfied automatically and the advection term in the momentum equation becomes unnecessary. (b) The procedure is meshless in the finite-difference/finite-element sense. (c) Tsunami balls care little if they find themselves in the ocean or inundating land. (d) Tsunami ball calculations of storm surge can be done on a laptop computer. I demonstrate and calibrate the method by simulating storm surge and inundation around New Orleans, Louisiana caused by Hurricane Katrina in 2005 and by comparing model predictions with field observations. To illustrate the flexibility of the tsunami ball technique, I run two “What If” hurricane scenarios—Katrina over Savannah, Georgia and Katrina over Cape Cod, Massachusetts.

THE 1958 LITUYA BAY LANDSLIDE AND TSUNAMI — A TSUNAMI BALL APPROACH

2010 ◽  
Vol 04 (04) ◽  
pp. 285-319 ◽  
Author(s):  
STEVEN N. WARD ◽  
SIMON DAY
Keyword(s):  
Finite Element ◽  
Finite Difference ◽  
Volume Density ◽  
Momentum Equation ◽  
Normal Faults ◽  
Western Slope ◽  
Variable Depth ◽  
New Approach ◽  
Advection Term ◽  
The Impact

Many analyses of tsunami generation and inundation solve equations of continuity and momentum on fixed finite difference/finite element meshes. We develop a new approach that uses a momentum equation to accelerate bits or balls of water over variable depth topography. The thickness of the water column at any point equals the volume density of balls there. The new approach has several advantages over traditional methods: (1) by tracking water balls of fixed volume, the continuity equation is satisfied automatically and the advection term in the momentum equation becomes unnecessary. (2) The procedure is meshless in the finite difference/finite element sense. (3) Tsunami balls care little if they find themselves in the ocean or inundating land. We demonstrate and validate the tsunami ball method by simulating the 1958 Lituya Bay landslide and tsunami. We find that a rockslide of dimension and volume (3 - 6 × 107m3) generally consistent with observations can indeed tumble from 200–900 m height on the east slope of Gilbert Inlet, splash water up to ~ 500 m on the western slope, and make an impressive tsunami running down the length of the fiord. A closer examination of eyewitness accounts and trimline maps, however, finds a "rockslide only" tsunami somewhat lacking in size outside of Gilbert Inlet. This discrepancy, coupled with fact that ~ 3 × 108 m3 of sediment infilled the deepest parts of Lituya Bay between 1926 and 1959, suggests that the source of the 1958 tsunami was not one landslide, but two. The initial rockslide generated the famous big splash and cratered the floor in front of Lituya Glacier. We propose that the impact of the rockslide destabilized the foundation of the Glacier and triggered a second larger, but slower moving subglacier slide. The subglacier slide induced the fresh normal faults on the collapsed glacier above, helped to bulk up the rockslide tsunami outside of Gilbert Inlet, and supplied most of the infill evident in post-1958 bathymetric charts.

A New Approach to the Rigid Finite Element Method in Modeling Spatial Slender Systems

2018 ◽  
Vol 18 (02) ◽  
pp. 1850017 ◽  
Author(s):  
Iwona Adamiec-Wójcik ◽  
Łukasz Drąg ◽  
Stanisław Wojciech
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Dynamic Analysis ◽  
Equations Of Motion ◽  
Nonlinear Dynamic Analysis ◽  
New Approach ◽  
Static And Dynamic Analysis ◽  
Rigid Finite Element Method ◽  
Longitudinal Flexibility ◽  
Element Method

The static and dynamic analysis of slender systems, which in this paper comprise lines and flexible links of manipulators, requires large deformations to be taken into consideration. This paper presents a modification of the rigid finite element method which enables modeling of such systems to include bending, torsional and longitudinal flexibility. In the formulation used, the elements into which the link is divided have seven DOFs. These describe the position of a chosen point, the extension of the element, and its orientation by means of the Euler angles Z[Formula: see text]Y[Formula: see text]X[Formula: see text]. Elements are connected by means of geometrical constraint equations. A compact algorithm for formulating and integrating the equations of motion is given. Models and programs are verified by comparing the results to those obtained by analytical solution and those from the finite element method. Finally, they are used to solve a benchmark problem encountered in nonlinear dynamic analysis of multibody systems.

scholarly journals Hurricane Gustav (2008) Waves and Storm Surge: Hindcast, Synoptic Analysis, and Validation in Southern Louisiana

2011 ◽  
Vol 139 (8) ◽  
pp. 2488-2522 ◽  
Author(s):  
J. C. Dietrich ◽  
J. J. Westerink ◽  
A. B. Kennedy ◽  
J. M. Smith ◽  
R. E. Jensen ◽  
...  
Keyword(s):  
Gulf Of Mexico ◽  
Hurricane Katrina ◽  
Storm Surge ◽  
Unstructured Mesh ◽  
Wind Waves ◽  
Wave Model ◽  
Small Scale ◽  
Research Division ◽  
Time Histories ◽  
Southern Louisiana

AbstractHurricane Gustav (2008) made landfall in southern Louisiana on 1 September 2008 with its eye never closer than 75 km to New Orleans, but its waves and storm surge threatened to flood the city. Easterly tropical-storm-strength winds impacted the region east of the Mississippi River for 12–15 h, allowing for early surge to develop up to 3.5 m there and enter the river and the city’s navigation canals. During landfall, winds shifted from easterly to southerly, resulting in late surge development and propagation over more than 70 km of marshes on the river’s west bank, over more than 40 km of Caernarvon marsh on the east bank, and into Lake Pontchartrain to the north. Wind waves with estimated significant heights of 15 m developed in the deep Gulf of Mexico but were reduced in size once they reached the continental shelf. The barrier islands further dissipated the waves, and locally generated seas existed behind these effective breaking zones.The hardening and innovative deployment of gauges since Hurricane Katrina (2005) resulted in a wealth of measured data for Gustav. A total of 39 wind wave time histories, 362 water level time histories, and 82 high water marks were available to describe the event. Computational models—including a structured-mesh deepwater wave model (WAM) and a nearshore steady-state wave (STWAVE) model, as well as an unstructured-mesh “simulating waves nearshore” (SWAN) wave model and an advanced circulation (ADCIRC) model—resolve the region with unprecedented levels of detail, with an unstructured mesh spacing of 100–200 m in the wave-breaking zones and 20–50 m in the small-scale channels. Data-assimilated winds were applied using NOAA’s Hurricane Research Division Wind Analysis System (H*Wind) and Interactive Objective Kinematic Analysis (IOKA) procedures. Wave and surge computations from these models are validated comprehensively at the measurement locations ranging from the deep Gulf of Mexico and along the coast to the rivers and floodplains of southern Louisiana and are described and quantified within the context of the evolution of the storm.

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