Internal Tide Generation at the Continental Shelf Modeled Using a Modal Decomposition: Two-Dimensional Results

2007 ◽  
Vol 37 (3) ◽  
pp. 428-451 ◽  
Author(s):  
Stephen D. Griffiths ◽  
R. H. J. Grimshaw
Keyword(s):  
Continental Shelf ◽  
Fluid Motion ◽  
Tidal Flow ◽  
Three Dimensional ◽  
Internal Tide ◽  
Basis Functions ◽  
Horizontal Structure ◽  
Simple Boundary ◽  
Flow Over Topography ◽  
Time Periodic

Abstract Stratified flow over topography is studied, with oceanic applications in mind. A model is developed for a fluid with arbitrary vertical stratification and a free surface, flowing over three-dimensional topography of arbitrary size and steepness, with background rotation, in the linear hydrostatic regime. The model uses an expansion of the flow fields in terms of a set of basis functions, which efficiently capture the vertical dependence of the flow. The horizontal structure may then be found by solving a set of coupled partial differential equations in two horizontal directions and time, subject to simple boundary conditions. In some cases, these equations may be solved analytically, but, in general, simple numerical procedures are required. Using this formulation, the internal tide generated by a time-periodic barotropic tidal flow over a continental shelf and slope is calculated in various idealized configurations. The topography and fluid motion are taken to be independent of one coordinate direction and the fluid to be either two-layer or uniformly stratified. For the two-layer case, expressions for the shoreward and oceanward energy fluxes associated with the internal tide are derived. For the uniformly stratified case, it is studied numerically how the accuracy of the solutions depends upon the number of basis functions used, and it is shown that good solutions and energy flux estimates can often be obtained with only a few basis functions. In both cases, the results show that the position of the coastline, through its effect on the form of the barotropic tide, significantly influences the strength of the internal tide generation.

scholarly journals Limiting amplitudes of fully nonlinear interfacial tides and solitons

2016 ◽  
Author(s):  
Borja Aguiar-González ◽  
Theo Gerkema
Keyword(s):  
Numerical Solutions ◽  
Fluid Layer ◽  
Tidal Flow ◽  
Internal Tide ◽  
Boussinesq Equations ◽  
Fully Nonlinear ◽  
Soliton Theory ◽  
Weakly Nonlinear ◽  
Flow Over Topography ◽  
Model Equations

Abstract. A new two-fluid layer model consisting of forced rotation-modified Boussinesq equations is derived for studying tidally-generated fully nonlinear, weakly nonhydrostatic dispersive interfacial waves. This set is a generalization of the Choi-Camassa equations, extended here with forcing terms and Coriolis effects. The forcing is represented by a horizontally oscillating sill, mimicking a barotropic tidal flow over topography. Solitons are generated by a disintegration of the interfacial tide. Because of strong non-linearity, solitons in some cases attain a limiting table-shaped form, in accordance with soliton theory. More generally, we use the model equations to investigate the role of the initial stages of the internal tide on the limiting amplitudes of solitons under fully nonlinear conditions. Numerical solutions reveal that the tide-generated solitons are primarily limited by the underlying quasi-nonlinear internal tide. We show the decisive factor is the generation of higher harmonics, which already limit the growth of the initial internal tide. As a consequence, and contrary to predictions by classical KdV theory alone, we find that tidally generated solitons are subjected to limiting amplitudes even under weakly nonlinear conditions. This implies that under strongly nonlinear conditions, amplitudes of solitons may be limited before attaining a table-shaped form.

scholarly journals Limiting amplitudes of fully nonlinear interfacial tides and solitons

2016 ◽  
Vol 23 (4) ◽  
pp. 285-305
Author(s):  
Borja Aguiar-González ◽  
Theo Gerkema
Keyword(s):  
Numerical Solutions ◽  
Fluid Layer ◽  
Tidal Flow ◽  
Internal Tide ◽  
Boussinesq Equations ◽  
Strong Nonlinearity ◽  
Fully Nonlinear ◽  
Soliton Theory ◽  
Flow Over Topography ◽  
Linear Version

Abstract. A new two-fluid layer model consisting of forced rotation-modified Boussinesq equations is derived for studying tidally generated fully nonlinear, weakly nonhydrostatic dispersive interfacial waves. This set is a generalization of the Choi–Camassa equations, extended here with forcing terms and Coriolis effects. The forcing is represented by a horizontally oscillating sill, mimicking a barotropic tidal flow over topography. Solitons are generated by a disintegration of the interfacial tide. Because of strong nonlinearity, solitons may attain a limiting table-shaped form, in accordance with soliton theory. In addition, we use a quasi-linear version of the model (i.e. including barotropic advection but linear in the baroclinic fields) to investigate the role of the initial stages of the internal tide prior to its nonlinear disintegration. Numerical solutions reveal that the internal tide then reaches a limiting amplitude under increasing barotropic forcing. In the fully nonlinear regime, numerical experiments suggest that this limiting amplitude in the underlying internal tide extends to the nonlinear case in that internal solitons formed by a disintegration of the internal tide may not reach their table-shaped form with increased forcing, but appear limited well below that state.

scholarly journals Internal Tides in the Southwestern Atlantic off Brazil: Observations and Numerical Modeling

2007 ◽  
Vol 37 (6) ◽  
pp. 1512-1526 ◽  
Author(s):  
Adriene F. Pereira ◽  
Belmiro M. Castro
Keyword(s):  
Continental Shelf ◽  
Three Dimensional ◽  
Internal Tide ◽  
Equation Model ◽  
Shelf Break ◽  
Internal Tides ◽  
Southwestern Atlantic ◽  
Model Response ◽  
Southwestern Atlantic Ocean ◽  
Vertical Displacements

Abstract Data collected from moored instruments, deployed over the southeastern Brazilian continental shelf during the summer and winter months of 2001, show internal tide activity near the shelf break. To help to elucidate the observations, a fully three-dimensional nonlinear primitive equation model is applied to simulate the regional barotropic and baroclinic tides. Two semidiurnal (M2 and S2) and two diurnal (K1 and O1) tidal frequencies are considered. Tidal surface elevations are relatively small over the whole modeled area, reaching maximum values of about 0.40 m for M2 and 0.11 m for O1. Comparison between observed and computed tide elevation and Greenwich phase shows reasonable agreement. When the baroclinic response of the model is investigated, stratification is prescribed using summer and winter climatology data of potential density. In this case, the model response to summer and winter stratifications is very similar and internal tides are generated over the shelf break and slope, with vertical displacements up to 25 m, and seaward propagation. Modeled semidiurnal tidal ellipses agree well with winter and summer observations. Observed diurnal tidal ellipses in the middle of the continental shelf and close to the shelf break during summer show an intensification through the water column that could not be represented by the model. Estimates of the total baroclinic M2 offshore energy flux are about 3.5 and 0.5 MW considering winter and summer stratifications, respectively. Although these quantities are three orders of magnitude less than that estimated for regions known for intense internal tides, they refer to offshore fluxes computed for a very small section of the southeastern Brazilian shelf. This is the first published investigation into internal tides in the southwestern Atlantic Ocean off Brazil.

A Real-Time Mathematical Model for Three-Dimensional Tidal Flow and Water Quality

1991 ◽  
Vol 24 (6) ◽  
pp. 171-177 ◽  
Author(s):  
Zeng Fantang ◽  
Xu Zhencheng ◽  
Chen Xiancheng
Keyword(s):  
Mathematical Model ◽  
Water Quality ◽  
Real Time ◽  
Control Volume ◽  
Tidal Flow ◽  
Three Dimensional ◽  
River Estuary ◽  
Pearl River Estuary ◽  
Practical Application ◽  
The Pearl River

A real-time mathematical model for three-dimensional tidal flow and water quality is presented in this paper. A control-volume-based difference method and a “power interpolation distribution” advocated by Patankar (1984) have been employed, and a concept of “separating the top-layer water” has been developed to solve the movable boundary problem. The model is unconditionally stable and convergent. Practical application of the model is illustrated by an example for the Pearl River Estuary.

scholarly journals A Three-Dimensional Numerical and Multi-Objective Optimal Design of Wavy Plate-Fins Heat Exchangers

Processes ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 9
Author(s):  
Chao Yu ◽  
Xiangyao Xue ◽  
Kui Shi ◽  
Mingzhen Shao
Keyword(s):  
Heat Exchangers ◽  
Cfd Simulation ◽  
Three Dimensional ◽  
Basis Functions ◽  
Approximation Model ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Multi Objective Genetic Algorithm ◽  
Colburn Factor ◽  
Heat Exchange Efficiency

This paper presents a method for optimizing wavy plate-fin heat exchangers accurately and efficiently. It combines CFD simulation, Radical Basis Functions (RBF) with multi-objective optimization to improve the performance. The optimization of the Colburn factor j and the friction coefficient f is regarded as a multi-objective optimization problem, due to the existence of two contradictory goals. The approximation model was obtained by Radical Basis Functions, and the shape of the heat exchanger was optimized by multi-objective genetic algorithm (MOGA). The optimization results showed that j increased by 17.62% and f decreased by 20.76%, indicating that the heat exchange efficiency was significantly enhanced and the fluid structure resistance reduced. Then, from the aspects of field synergy and tubulence energy, the performance advantage of the optimized structure was further confirmed.

Energetics of Barotropic and Baroclinic Tides in the Monterey Bay Area

2012 ◽  
Vol 42 (2) ◽  
pp. 272-290 ◽  
Author(s):  
Dujuan Kang ◽  
Oliver Fringer
Keyword(s):  
Energy Flux ◽  
Three Dimensional ◽  
Internal Tide ◽  
Submarine Canyon ◽  
Tidal Energy ◽  
Energy Partitioning ◽  
Navier Stokes ◽  
Monterey Bay ◽  
Topographic Features ◽  
Bay Area

Abstract A detailed energy analysis of the barotropic and baroclinic M2 tides in the Monterey Bay area is performed. The authors first derive a theoretical framework for analyzing internal tide energetics based on the complete form of the barotropic and baroclinic energy equations, which include the full nonlinear and nonhydrostatic energy flux contributions as well as an improved evaluation of the available potential energy. This approach is implemented in the Stanford Unstructured Nonhydrostatic Terrain-Following Adaptive Navier–Stokes Simulator (SUNTANS). Results from three-dimensional, high-resolution SUNTANS simulations are analyzed to estimate the tidal energy partitioning among generation, radiation, and dissipation. A 200 km × 230 km domain including all typical topographic features in this region is used to represent the Monterey Bay area. Of the 152-MW energy lost from the barotropic tide, approximately 133 MW (88%) is converted into baroclinic energy through internal tide generation, and 42% (56 MW) of this baroclinic energy radiates away into the open ocean. The tidal energy partitioning depends greatly on the topographic features. The Davidson Seamount is most efficient at baroclinic energy generation and radiation, whereas the Monterey Submarine Canyon acts as an energy sink. Energy flux contributions from nonlinear and nonhydrostatic effects are also examined. In the Monterey Bay area, the nonlinear and nonhydrostatic contributions are quite small. Moreover, the authors investigate the character of internal tide generation and find that in the Monterey Bay area the generated baroclinic tides are mainly linear and in the form of internal tidal beams. Comparison of the modeled tidal conversion to previous theoretical estimates shows that they are consistent with one another.

Diesel Droplet Diffusion in Isotropic Turbulence With Digital Holographic Cinematography

2005 ◽  
Author(s):  
Balaji Gopalan ◽  
Edwin Malkiel ◽  
Jian Sheng ◽  
Joseph Katz
Keyword(s):  
Time Series ◽  
High Speed ◽  
Isotropic Turbulence ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Time History ◽  
Sample Volume ◽  
Velocity Autocorrelation Function ◽  
Digital Cameras ◽  
Velocity Autocorrelation

High-speed in-line digital holographic cinematography was used to investigate the diffusion of droplets in locally isotropic turbulence. Droplets of diesel fuel (0.3–0.9mm diameter, specific gravity of 0.85) were injected into a 37×37×37mm3 sample volume located in the center of a 160-liter tank. The turbulence was generated by 4 spinning grids, located symmetrically in the corners of the tank, and was characterized prior to the experiments. The sample volume was back illuminated with two perpendicular collimated beams of coherent laser light and time series of in-line holograms were recorded with two high-speed digital cameras at 500 frames/sec. Numerical reconstruction generated a time series of high-resolution images of the droplets throughout the sample volume. We developed an algorithm for automatically detecting the droplet trajectories from each view, for matching the two views to obtain the three-dimensional tracks, and for calculating the time history of velocity. We also measured the mean fluid motion using 2-D PIV. The data enabled us to calculate the Lagrangian velocity autocorrelation function.

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