THE MECHANICS OF DEEP WATER, SHALLOW WATER, AND BREAKING WAVES

NOTE: This article was published in a former series of GEUS Bulletin. Please use the original series name when citing this article, for example: Ineson, J. R., & Peel, J. S. (1997). Cambrian shelf stratigraphy of North Greenland. Geology of Greenland Survey Bulletin, 173, 1-120. https://doi.org/10.34194/ggub.v173.5024 _______________ The Lower Palaeozoic Franklinian Basin is extensively exposed in northern Greenland and the Canadian Arctic Islands. For much of the early Palaeozoic, the basin consisted of a southern shelf, bordering the craton, and a northern deep-water trough; the boundary between the shelf and the trough shifted southwards with time. In North Greenland, the evolution of the shelf during the Cambrian is recorded by the Skagen Group, the Portfjeld and Buen Formations and the Brønlund Fjord, Tavsens Iskappe and Ryder Gletscher Groups; the lithostratigraphy of these last three groups forms the main focus of this paper. The Skagen Group, a mixed carbonate-siliciclastic shelf succession of earliest Cambrian age was deposited prior to the development of a deep-water trough. The succeeding Portfjeld Formation represents an extensive shallow-water carbonate platform that covered much of the shelf; marked differentiation of the shelf and trough occurred at this time. Following exposure and karstification of this platform, the shelf was progressively transgressed and the siliciclastics of the Buen Formation were deposited. From the late Early Cambrian to the Early Ordovician, the shelf showed a terraced profile, with a flat-topped shallow-water carbonate platform in the south passing northwards via a carbonate slope apron into a deeper-water outer shelf region. The evolution of this platform and outer shelf system is recorded by the Brønlund Fjord, Tavsens Iskappe and Ryder Gletscher Groups. The dolomites, limestones and subordinate siliciclastics of the Brønlund Fjord and Tavsens Iskappe Groups represent platform margin to deep outer shelf environments. These groups are recognised in three discrete outcrop belts - the southern, northern and eastern outcrop belts. In the southern outcrop belt, from Warming Land to south-east Peary Land, the Brønlund Fjord Group (Lower-Middle Cambrian) is subdivided into eight formations while the Tavsens Iskappe Group (Middle Cambrian - lowermost Ordovician) comprises six formations. In the northern outcrop belt, from northern Nyeboe Land to north-west Peary Land, the Brønlund Fjord Group consists of two formations both defined in the southern outcrop belt, whereas a single formation makes up the Tavsens Iskappe Group. In the eastern outcrop area, a highly faulted terrane in north-east Peary Land, a dolomite-sandstone succession is referred to two formations of the Brønlund Fjord Group. The Ryder Gletscher Group is a thick succession of shallow-water, platform interior carbonates and siliciclastics that extends throughout North Greenland and ranges in age from latest Early Cambrian to Middle Ordovician. The Cambrian portion of this group between Warming Land and south-west Peary Land is formally subdivided into four formations.The Lower Palaeozoic Franklinian Basin is extensively exposed in northern Greenland and the Canadian Arctic Islands. For much of the early Palaeozoic, the basin consisted of a southern shelf, bordering the craton, and a northern deep-water trough; the boundary between the shelf and the trough shifted southwards with time. In North Greenland, the evolution of the shelf during the Cambrian is recorded by the Skagen Group, the Portfjeld and Buen Formations and the Brønlund Fjord, Tavsens Iskappe and Ryder Gletscher Groups; the lithostratigraphy of these last three groups forms the main focus of this paper. The Skagen Group, a mixed carbonate-siliciclastic shelf succession of earliest Cambrian age was deposited prior to the development of a deep-water trough. The succeeding Portfjeld Formation represents an extensive shallow-water carbonate platform that covered much of the shelf; marked differentiation of the shelf and trough occurred at this time. Following exposure and karstification of this platform, the shelf was progressively transgressed and the siliciclastics of the Buen Formation were deposited. From the late Early Cambrian to the Early Ordovician, the shelf showed a terraced profile, with a flat-topped shallow-water carbonate platform in the south passing northwards via a carbonate slope apron into a deeper-water outer shelf region. The evolution of this platform and outer shelf system is recorded by the Brønlund Fjord, Tavsens Iskappe and Ryder Gletscher Groups. The dolomites, limestones and subordinate siliciclastics of the Brønlund Fjord and Tavsens Iskappe Groups represent platform margin to deep outer shelf environments. These groups are recognised in three discrete outcrop belts - the southern, northern and eastern outcrop belts. In the southern outcrop belt, from Warming Land to south-east Peary Land, the Brønlund Fjord Group (Lower-Middle Cambrian) is subdivided into eight formations while the Tavsens Iskappe Group (Middle Cambrian - lowermost Ordovician) comprises six formations. In the northern outcrop belt, from northern Nyeboe Land to north-west Peary Land, the Brønlund Fjord Group consists of two formations both defined in the southern outcrop belt, whereas a single formation makes up the Tavsens Iskappe Group. In the eastern outcrop area, a highly faulted terrane in north-east Peary Land, a dolomite-sandstone succession is referred to two formations of the Brønlund Fjord Group. The Ryder Gletscher Group is a thick succession of shallow-water, platform interior carbonates and siliciclastics that extends throughout North Greenland and ranges in age from latest Early Cambrian to Middle Ordovician. The Cambrian portion of this group between Warming Land and south-west Peary Land is formally subdivided into four formations.

Download Full-text

Development and Validation of Quasi-Eulerian Mean Three-Dimensional Equations of Motion Using the Generalized Lagrangian Mean Method

Journal of Marine Science and Engineering ◽

10.3390/jmse9010076 ◽

2021 ◽

Vol 9 (1) ◽

pp. 76

Author(s):

Duoc Nguyen ◽

Niels Jacobsen ◽

Dano Roelvink

Keyword(s):

Surface Waves ◽

Deep Water ◽

Surf Zone ◽

Equations Of Motion ◽

Three Dimensional ◽

Breaking Waves ◽

Successful Implementation ◽

Random Waves ◽

Mean Motion ◽

Generalized Lagrangian

This study aims at developing a new set of equations of mean motion in the presence of surface waves, which is practically applicable from deep water to the coastal zone, estuaries, and outflow areas. The generalized Lagrangian mean (GLM) method is employed to derive a set of quasi-Eulerian mean three-dimensional equations of motion, where effects of the waves are included through source terms. The obtained equations are expressed to the second-order of wave amplitude. Whereas the classical Eulerian-mean equations of motion are only applicable below the wave trough, the new equations are valid until the mean water surface even in the presence of finite-amplitude surface waves. A two-dimensional numerical model (2DV model) is developed to validate the new set of equations of motion. The 2DV model passes the test of steady monochromatic waves propagating over a slope without dissipation (adiabatic condition). This is a primary test for equations of mean motion with a known analytical solution. In addition to this, experimental data for the interaction between random waves and a mean current in both non-breaking and breaking waves are employed to validate the 2DV model. As shown by this successful implementation and validation, the implementation of these equations in any 3D model code is straightforward and may be expected to provide consistent results from deep water to the surf zone, under both weak and strong ambient currents.

Download Full-text

Tubarão Martelo Field Riser System: Shallow Water Challenging

Volume 5A: Pipeline and Riser Technology ◽

10.1115/omae2015-41864 ◽

2015 ◽

Author(s):

Elton J. B. Ribeiro ◽

Zhimin Tan ◽

Yucheng Hou ◽

Yanqiu Zhang ◽

Andre Iwane

Keyword(s):

Shallow Water ◽

Deep Water ◽

Oil And Gas ◽

Vertical Motion ◽

Oil And Gas Industry ◽

System Configuration ◽

Wave Load ◽

Gas Industry ◽

Campos Basin ◽

Water Problem

Currently the oil and gas industry is focusing on challenging deep water projects, particularly in Campos Basin located coast off Brazil. However, there are a lot of prolific reservoirs located in shallow water, which need to be developed and they are located in area very far from the coast, where there aren’t pipelines facilities to export oil production, in this case is necessary to use a floating production unit able to storage produced oil, such as a FPSO. So, the riser system configuration should be able to absorb FPSO’s dynamic response due to wave load and avoid damage at touch down zone, in this case is recommended to use compliant riser configuration, such as Lazy Wave, Tethered Wave or Lazy S. In addition to, the proposed FPSO for Tubarão Martelo development is a type VLCC (Very Large Crude Carrier) using external turret moored system, which cause large vertical motion at riser connection and it presents large static offset. Also are expected to install 26 risers and umbilicals hanging off on the turret, this large number of risers and umbilicals has driven the main concerns to clashing and clearance requirement since Lazy-S configuration was adopted. In this paper, some numerical model details and recommendations will be presented, which became a feasible challenging risers system in shallow water. For instance, to solve clashing problem it is strictly recommended for modeling MWA (Mid Water Arch) gutter and bend stiffener at top I-tube interface, this recommendation doesn’t matter in deep water, but for shallow water problem is very important. Also is important to use ballast modules in order to solve clashing problems.

Download Full-text

Salmon and Eel Movement in Constant Circular Current

Journal of the Fisheries Research Board of Canada ◽

10.1139/f47-035 ◽

1949 ◽

Vol 7c (7) ◽

pp. 432-448 ◽

Cited By ~ 6

Author(s):

Viola M. Davidson

Keyword(s):

Light Intensity ◽

Shallow Water ◽

Deep Water ◽

Sudden Change ◽

Circular Current

Underyearling salmon in a circular pond of moving water at 20–25 °C. swam during the day and rested on the bottom at night. Before feeding they translocated actively upstream in rapid shallow water and in all directions in slow deep water. During feeding they held position in slow water, but made short excursions to seize food. After feeding, most moved into rapid, shallow water, the largest into the most rapid water.Translocating salmon usually went upstream and swam faster in more rapid water so that the rate of translocation remained constant. The rate of translocation increased with the size of the fish, more than doubling from 3 to 4 cm. in length.While steady illumination caused the salmon to swim up in the water from the bottom, a sudden change in light intensity when they were swimming, as by an object moving against the sky, caused them to swim quickly from shallow to deep water.Eels translocated upstream regularly only in the more rapid water, the swimming rate increasing with current rate. Eels 7 cm. long translocated almost twice as rapidly as salmon 3.5 cm. long. Eels burrowed in the gravel in bright daylight, came out in the evening and translocated rapidly even at night when the salmon were resting.

Download Full-text

Resistance Tests of an Articulated Pusher Barge System in Deep and Shallow Water

10.1115/omae2021-61754 ◽

2021 ◽

Author(s):

Li Zhang ◽

Lei Xing ◽

Mingyu Dong ◽

Weimin Chen

Keyword(s):

Shallow Water ◽

Water Depth ◽

Deep Water ◽

Water Resistance ◽

Model Tests ◽

System 2 ◽

Changing Trend ◽

The Difference ◽

Transport Vessel ◽

Resistance Performance

Abstract Articulated pusher barge vessel is a short-distance transport vessel with good economic performance and practicability, which is widely used in the Yangtze River of China. In this present work, the resistance performance of articulated pusher barge vessel in deep water and shallow water was studied by model tests in the towing tank and basin of Shanghai Ship and Shipping Research Institute. During the experimental investigation, the articulated pusher barge vessel was divided into three parts: the pusher, the barge and the articulated pusher barge system. Firstly, the deep water resistance performance of the articulated pusher barge system, barge and the pusher at design draught T was studied, then the water depth h was adjusted, and the shallow water resistance at h/T = 2.0, 1.5 and 1.2 was tested and studied respectively, and the difference between deep water resistance and shallow water resistance at design draught were compared. The results of model tests and analysis show that: 1) in the study of deep water resistance, the total resistance of the barge was larger than that of the articulated pusher barge system. 2) for the barge, the shallow water resistance increases about 0.4–0.7 times at h/T = 2.0, 0.5–1.1 times at h/T = 1.5, and 0.7–2.3 times at h/T = 1.2. 3) for the pusher, the shallow water resistance increases about 1.0–0.4 times at h/T = 2.7, 1.2–0.9 times at h/T = 2.0, and 1.7–2.4 times at h/T = 1.6. 4) for the articulated pusher barge system, the shallow water resistance increases about 0.2–0.3 times at h/T = 2.0, 0.5–1.3 times at h/T = 1.5, and 1.0–3.5 times at h/T = 1.2. Furthermore, the water depth Froude number Frh in shallow water was compared with the changing trend of resistance in shallow water.

Download Full-text

Marine late Saalian to Eemian environments and climatic variability in the Danish shelf area

Netherlands Journal of Geosciences – Geologie en Mijnbouw ◽

10.1017/s0016774600023696 ◽

2000 ◽

Vol 79 (2-3) ◽

pp. 335-343 ◽

Cited By ~ 23

Author(s):

Marit-Solveig Seidenkrantz ◽

Karen Luise Knudsen ◽

Peter Kristensen

Keyword(s):

Climate Variability ◽

Shallow Water ◽

Oxygen Isotope ◽

Deep Water ◽

Climatic Variability ◽

Shelf Area ◽

North East ◽

The North ◽

Mis 5E

AbstractThe marine Eemian (marine oxygen-isotope substage 5e: MIS 5e) is represented by shallow-water deposits in southern and western Denmark, while relatively deep-water environments occurred to the north and north-east, where complete interglacial successions seem to be present. We present an overview of the marine Eemian deposits in Denmark, and discuss in more detail indications of climate variability, both for the late Saalian and within the Eemian.

Download Full-text

A Coupled-Mode Technique for the Run-Up of Non-Breaking Dispersive Waves on Plane Beaches

Volume 2: Ocean Engineering and Polar and Arctic Sciences and Technology ◽

10.1115/omae2006-92162 ◽

2006 ◽

Author(s):

K. A. Belibassakis ◽

G. A. Athanassoulis

Keyword(s):

Shallow Water ◽

Water Waves ◽

Wave Equations ◽

Neumann Boundary ◽

Breaking Waves ◽

Numerical Results ◽

Coupled Mode Theory ◽

Mode Theory ◽

Coupled Mode ◽

Run Up

A coupled-mode model is developed and applied to the transformation and run-up of dispersive water waves on plane beaches. The present work is based on the consistent coupled-mode theory for the propagation of water waves in variable bathymetry regions, developed by Athanassoulis & Belibassakis (1999) and extended to 3D by Belibassakis et al (2001), which is suitably modified to apply to a uniform plane beach. The key feature of the coupled-mode theory is a complete modal-type expansion of the wave potential, containing both propagating and evanescent modes, being able to consistently satisfy the Neumann boundary condition on the sloping bottom. Thus, the present approach extends previous works based on the modified mild-slope equation in conjunction with analytical solution of the linearised shallow water equations, see, e.g., Massel & Pelinovsky (2001). Numerical results concerning non-breaking waves on plane beaches are presented and compared with exact analytical solutions; see, e.g., Wehausen & Laitone (1960, Sec. 18). Also, numerical results are presented concerning the run-up of non-breaking solitary waves on plane beaches and compared with the ones obtained by the solution of the shallow-water wave equations, Synolakis (1987), Li & Raichlen (2002), and experimental data, Synolakis (1987).

Download Full-text