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  • 1
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    A continental shelf bottom boundary layer model : the effects of waves, currents, and a movable bed (2009)
    Massachusetts Institute of Technology and Woods Hole Oceanographic Institution
    Details
    Publication Date: 2022-05-25
    Description: Submitted in partial fulfillment of the requirements for the degree of Doctor of Science at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution January 1983
    Description: A simple model for the bottom boundary layer on the continental shelf is presented. The governing equations are developed for a stratified, turbulent Ekman layer in a combined wave and current flow over a moveable sediment bed. An eddy diffusivity closure scheme that includes the effect of suspended sediment, temperature, and salinity induced stratification on the vertical turbulent diffusion of mass and momentum couples the resulting unsteady conservation equations for fluid momentum, fluid mass, and suspended sediment mass. The wave velocity, current velocity, and suspended sediment concentration profiles predicted by the simultaneous solution of the conservation equations require the physical bottom roughness and a sediment reference concentrati on to be specified as boundary conditions. The physical bottom roughness associated with biologically generated bedforms, wave generated ripples, and near bed sediment transport are calculated as functions of the flow and sediment conditions. Using expressions for the height of sediment transporting layer and the sediment velocity, an expression for the sediment reference concentration is developed by matching laboratory measurements of sediment transport rates in oscillatory flow. The model predicts that the bottom flow field is highly dependent on (1) the nonlinear wave and current interaction, which increases the boundary shear stress and enhances vertical turbulent diffusion, (2) the effect of the boundary shear stress on a moveable sediment bed, which determines the physical bottom roughness and the amount of sediment in suspension, and (3) the effect of stable stratification, which inhibits vertical turbulent transport and couples the flow to the suspended sediment and fluid density profiles. The validity of the theoretical approach is supported by model predictions that are in excellent agreement with high quality data collected during two continental shelf bottom boundary layer experiments for a wide range of flow and bottom conditions.
    Description: Funding for the work resulting in this Thesis has been provided by the American Gas Association (Project No. PR-153-126), the National Science Foundation (Grant No. OCE~8014930), and NOAA-Sea Grant (NA-79AA-D-0010l; NA 79AA-D-00102).
    Keywords: Boundary layer ; Sediment transport ; Stratified flow
    Repository Name: Woods Hole Open Access Server
    Type: Thesis
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  • 2
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    Long nonlinear internal waves (2006)
    Annual Reviews
    Details
    Publication Date: 2022-05-25
    Description: Author Posting. © Annual Reviews, 2006. This article is posted here by permission of Annual Reviews for personal use, not for redistribution. The definitive version was published in Annual Review of Fluid Mechanics 38 (2006): 395-425, doi:10.1146/annurev.fluid.38.050304.092129.
    Description: Over the past four decades, the combination of in situ and remote sensing observations has demonstrated that long nonlinear internal solitary-like waves are ubiquitous features of coastal oceans. The following provides an overview of the properties of steady internal solitary waves and the transient processes of wave generation and evolution, primarily from the point of view of weakly nonlinear theory, of which the Korteweg-de Vries equation is the most frequently used example. However, the oceanographically important processes of wave instability and breaking, generally inaccessible with these models, are also discussed. Furthermore, observations often show strongly nonlinear waves whose properties can only be explained with fully nonlinear models.
    Description: KRH acknowledges support from NSF and ONR and an Independent Study Award from the Woods Hole Oceanographic Institution. WKM acknowledges support from NSF and ONR, which has made his work in this area possible, in close collaboration with former graduate students at Scripps Institution of Oceanography and MIT.
    Keywords: Solitary waves ; Nonlinear waves ; Stratified flow ; Physical Oceanography
    Repository Name: Woods Hole Open Access Server
    Type: Article
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  • 3
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    Internal tide and nonlinear internal wave behavior at the continental slope in the northern south China Sea (2006)
    IEEE
    Details
    Publication Date: 2022-05-25
    Description: Author Posting. © IEEE, 2004. This article is posted here by permission of IEEE for personal use, not for redistribution. The definitive version was published in IEEE Journal of Oceanic Engineering 29 (2004): 1105-1130, doi:10.1109/JOE.2004.836998.
    Description: A field program to measure acoustic propagation characteristics and physical oceanography was undertaken in April and May 2001 in the northern South China Sea. Fluctuating ocean properties were measured with 21 moorings in water of 350- to 71-m depth near the continental slope. The sea floor at the site is gradually sloped at depths less than 90 m, but the deeper area is steppy, having gradual slopes over large areas that are near critical for diurnal internal waves and steep steps between those areas that account for much of the depth change. Large-amplitude nonlinear internal gravity waves incident on the site from the east were observed to change amplitude, horizontal length scale, and energy when shoaling. Beginning as relatively narrow solitary waves of depression, these waves continued onto the shelf much broadened in horizontal scale, where they were trailed by numerous waves of elevation (alternatively described as oscillations) that first appeared in the continental slope region. Internal gravity waves of both diurnal and semidiurnal tidal frequencies (internal tides) were also observed to propagate into shallow water from deeper water, with the diurnal waves dominating. The internal tides were at times sufficiently nonlinear to break down into bores and groups of high-frequency nonlinear internal waves.
    Description: This work was supported in part by grants from the U.S. Office of Naval Research, Physical Oceanography and Ocean Acoustics Programs, and by the National Science Council of Taiwan.
    Keywords: Baroclinic tides ; Internal waves ; Nonlinear waves
    Repository Name: Woods Hole Open Access Server
    Type: Article
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  • 4
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    Nonlinear adjustment of a localized layer of buoyant, uniform potential vorticity fluid against a vertical wall (2007)
    Details
    Publication Date: 2022-05-25
    Description: Author Posting. © Elsevier B.V., 2006. This is the author's version of the work. It is posted here by permission of Elsevier B.V. for personal use, not for redistribution. The definitive version was published in Dynamics of Atmospheres and Oceans 41 (2006): 149-171, doi:10.1016/j.dynatmoce.2006.02.001.
    Description: The nonlinear evolution of a localized layer of buoyant, uniform potential vorticity fluid of uniform depth H, width w0 and length L released adjacent to a wall in a rotating system is studied using reduced-gravity shallow-water theory and numerical modeling. In the interior, far from the two ends of the layer, the initial adjustment gives, after ignoring inertia-gravity waves, a geostrophic flow of width w∞ and layer velocities parallel to the wall directed in the downstream direction (defined by Kelvin wave propagation). This steady geostrophic flow serves as the initial condition for a semigeostrophic solution using the method of characteristics. At the downstream end, the theory shows that the fluid intrudes along the wall as rarefaction terminating at a nose of vanishing width and depth. However, in a real fluid the presence of the lower layer leads to a blunt gravity current head. The theory is amended by introducing a gravity current head condition that has a blunt bore joined to the rarefaction by a uniform gravity current. The upstream termination of the initial layer produces a Kelvin rarefaction that propagates downstream, decreasing the layer depth along the wall, and initiating upstream flow adjacent to the wall. The theoretical solution compares favorably to numerical solutions of the reduced-gravity shallow-water equations. The agreement between theory and numerical solutions occurs regardless of whether the numerical runs are initiated with an adjusted geostrophic solution or with the release of a stagnant layer. The latter case excites inertia-gravity waves that, despite their large amplitude and breaking, do not significantly affect the evolution of the geostrophic flow. At times beyond the validity of the semigeostrophic theory, the numerical solutions evolve into a stationary arrays of vortices. The vortex formation can be interpreted as the finite-amplitude manifestation of a linear instability of the new flow established by the passage of the Kelvin wave. The Kelvin wave ultimately reduces the flux into the downstream gravity current and the vortices retain buoyant in the neighborhood of the initial layer.
    Description: This work was supported by NSF Grant OCE-0325102.
    Keywords: Geostrophic adjustment ; Gravity currents ; Kelvin waves ; Nonlinear waves ; Vortices
    Repository Name: Woods Hole Open Access Server
    Type: Preprint
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  • 5
    Electronic Resource
    Electronic Resource
    Stability of magnetohydrodynamic stratified shear flows (1991)
    Springer
    Il nuovo cimento della Società Italiana di Fisica 13 (1991), S. 765-778 
    Details
    ISSN: 0392-6737
    Keywords: Instabilities of shear flows ; Stratified flow ; a-Magnetohydrodynamics and electrohydrodynamics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Summary The linear stability of a stratified shear flow of a perfectly conducting bounded fluid in the presence of a magnetic field aligned with the flow and buoyancy forces has been studied under Boussinesq approximation. A new upper bound has been obtained for the range of real and imaginary parts of the complex wave velocity for growing perturbations. The upper bound depends on minimum Richardson number, wave number, Alfvén velocity and basic flow velocity. Höiland's necessary criterion for instability of hydrodynamic stratified homogeneous shear flow is modified and its analog for nonhomogeneous magnetohydrodynamic cases is derived. Finally the upper bound for the growth rate ofKC i and its variants, whereK is the wave number andC i the imaginary part of complex wave velocity, is derived as the necessary condition of instability. All estimates remain valid even when the minimum richardson numberJ 1, for some practical problems, exceeds 1/4 for growing perturbations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02452222
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  • 6
    Electronic Resource
    Electronic Resource
    A comparison of second-order and fourth-order pressure gradient algorithms in a σ-co-ordinate ocean model (1994)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 18 (1994), S. 361-383 
    Details
    ISSN: 0271-2091
    Keywords: Boundary-fitted co-ordinates ; Stratified flow ; Hydrostatic pressure ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In stratified three-dimensional models the use of a boundary-fitted vertical co-ordinate is known to produce errors in the horizontal pressure gradient calculation near steep topography. The error is due to the splitting of the horizontal pressure gradient term in each of the momentum equations into two parts and the subsequent incomplete cancellation of the truncation errors of those parts. In order to minimize these pressure gradient errors, a fourth-order-accurate pressure gradient calculation has been implemented and installed in SPEM, a three-dimensional primitive equation ocean model. The stability and accuracy of the new scheme are compared with those of the original second-order-accurate model in a series of calculations of unforced flow in the vicinity of an isolated seamount. The new scheme is shown to have much smaller pressure gradient errors over a wide range of parameter space as well as a greater parametric domain of numerical stability.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650180404
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  • 7
    Electronic Resource
    Electronic Resource
    Stratified flow under an ice keel - a numerical approach (1993)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 16 (1993), S. 353-364 
    Details
    ISSN: 0271-2091
    Keywords: Ice keels ; Drag ; Stratified flow ; Marker and cell ; SOLA-VOF ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A numerical investigation of the flow of two immiscible stratified fluids under an isolated keel has been undertaken. The investigation utilized the two-dimensional Euler equations for incompressible flow, and the solution of these equations has been obtained by using the well-known finite volume marker and cell approach. Experimental drag-force measurements are also presented for a family of two-dimensional topographic models of fixed height with increasing surface slopes in a two-layer density system. The range of flow speeds explored covers the Froude number range from subcritical to fully supercritical. The drag force measurements are augmented by detailed observations of the interface distortion. The results clearly show large drag increases arising from the internal wave systems generated in the stratified flow. Very good agreement has been found between the experimental and numerical results for both the interface shape between the two fluids and the drag force on a variety of keels.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650160502
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