Application of a two-dimensional hydrodynamic reservoir model to Lake Erie

2001 ◽  
Vol 58 (5) ◽  
pp. 858-869 ◽  
Author(s):  
L Boegman ◽  
M R Loewen ◽  
P F Hamblin ◽  
D A Culver
Keyword(s):  
Lake Erie ◽  
Nutrient Loading ◽  
Thermal Structure ◽  
Domain Model ◽  
Water Level Fluctuations ◽  
Two Dimensional ◽  
Large Lakes ◽  
Physical Forcing ◽  
Model Predictions ◽  
Averaged Model

The relative impacts of changes in nutrient loading and zebra mussel establishment on plankton in large lakes are strongly influenced by hydrodynamics, yet adequately modelling the temporal-spatial complexity of physical and biological processes has been difficult. We adapted a two-dimensional public domain model, CE-QUAL-W2, to test whether it could provide a hydrodynamically accurate simulation of the seasonal variation in the vertical-longitudinal thermal structure of Lake Erie. The physical forcing for the model is derived from surface meteorological buoys and measurements of precipitation, inflows, and outflows. To calibrate and validate the model, predictions were compared with an extensive set of field data collected during May through September 1994. The model accurately predicted water-level fluctuations without adjustment. However, significant modifications to the eddy coefficient turbulence algorithm were required to simulate acceptable longitudinal currents. The thermal structure was accurately predicted in all three basins, even though this laterally averaged model cannot simulate Coriolis effects. We are currently extending the model's water-quality module to include the effects of nutrient loading and zebra mussels on the plankton.

scholarly journals Two-dimensional modeling of density and thermal structure of dense circumstellar outflowing disks

2018 ◽  
Vol 613 ◽  
pp. A75 ◽  
Author(s):  
P. Kurfürst ◽  
A. Feldmeier ◽  
J. Krtička
Keyword(s):  
Mass Loss ◽  
Optical Depth ◽  
Massive Stars ◽  
Thermal Structure ◽  
Time Dependent ◽  
Navier Stokes ◽  
Viscous Heating ◽  
Two Dimensional ◽  
Dense Region ◽  
Loss Rates

Context. Evolution of massive stars is affected by a significant loss of mass either via (nearly) spherically symmetric stellar winds or by aspherical mass-loss mechanisms, namely the outflowing equatorial disks. However, the scenario that leads to the formation of a disk or rings of gas and dust around massive stars is still under debate. It is also unclear how various forming physical mechanisms of the circumstellar environment affect its shape and density, as well as its kinematic and thermal structure. Aims. We study the hydrodynamic and thermal structure of optically thick, dense parts of outflowing circumstellar disks that may be formed around various types of critically rotating massive stars, for example, Be stars, B[e] supergiant (sgB[e]) stars or Pop III stars. We calculate self-consistent time-dependent models of temperature and density structure in the disk’s inner dense region that is strongly affected by irradiation from a rotationally oblate central star and by viscous heating. Methods. Using the method of short characteristics, we specify the optical depth of the disk along the line-of-sight from stellar poles. Within the optically thick dense region with an optical depth of τ > 2∕3 we calculate the vertical disk thermal structure using the diffusion approximation while for the optically thin outer layers we assume a local thermodynamic equilibrium with the impinging stellar irradiation. For time-dependent hydrodynamic modeling, we use two of our own types of hydrodynamic codes: two-dimensional operator-split numerical code based on an explicit Eulerian finite volume scheme on a staggered grid, and unsplit code based on the Roe’s method, both including full second-order Navier-Stokes shear viscosity. Results. Our models show the geometric distribution and contribution of viscous heating that begins to dominate in the central part of the disk for mass-loss rates higher than Ṁ ≳ 10−10 M⊙ yr−1. In the models of dense viscous disks with Ṁ > 10−8 M⊙ yr−1, the viscosity increases the central temperature up to several tens of thousands of Kelvins, however the temperature rapidly drops with radius and with distance from the disk midplane. The high mass-loss rates and high viscosity lead to instabilities with significant waves or bumps in density and temperature in the very inner disk region. Conclusions. The two-dimensional radial-vertical models of dense outflowing disks including the full Navier-Stokes viscosity terms show very high temperatures that are however limited to only the central disk cores inside the optically thick area, while near the edge of the optically thick region the temperature may be low enough for the existence of neutral hydrogen, for example.

Two-dimensional depth-averaged model simulation

2015 ◽  
Author(s):  
Anna Avramenko ◽  
Jari Hamalainen
Keyword(s):  
Model Simulation ◽  
Two Dimensional ◽  
Averaged Model

Climate Change and Nutrient Loading in the Western Lake Erie Basin: Warming Can Counteract a Wetter Future

2019 ◽  
Vol 53 (13) ◽  
pp. 7543-7550 ◽  
Author(s):  
Margaret M. Kalcic ◽  
Rebecca Logsdon Muenich ◽  
Samantha Basile ◽  
Allison L. Steiner ◽  
Christine Kirchhoff ◽  
...  
Keyword(s):  
Climate Change ◽  
Lake Erie ◽  
Nutrient Loading ◽  
Western Lake ◽  
Western Lake Erie

A new model of shoaling and breaking waves. Part 2. Run-up and two-dimensional waves

2019 ◽  
Vol 867 ◽  
pp. 146-194 ◽  
Author(s):  
G. L. Richard ◽  
A. Duran ◽  
B. Fabrèges
Keyword(s):  
Large Scale ◽  
Turbulent Viscosity ◽  
Breaking Waves ◽  
Small Scale ◽  
Two Dimensional ◽  
Numerical Resolution ◽  
Wide Range ◽  
Scale Turbulence ◽  
Run Up ◽  
Averaged Model

We derive a two-dimensional depth-averaged model for coastal waves with both dispersive and dissipative effects. A tensor quantity called enstrophy models the subdepth large-scale turbulence, including its anisotropic character, and is a source of vorticity of the average flow. The small-scale turbulence is modelled through a turbulent-viscosity hypothesis. This fully nonlinear model has equivalent dispersive properties to the Green–Naghdi equations and is treated, both for the optimization of these properties and for the numerical resolution, with the same techniques which are used for the Green–Naghdi system. The model equations are solved with a discontinuous Galerkin discretization based on a decoupling between the hyperbolic and non-hydrostatic parts of the system. The predictions of the model are compared to experimental data in a wide range of physical conditions. Simulations were run in one-dimensional and two-dimensional cases, including run-up and run-down on beaches, non-trivial topographies, wave trains over a bar or propagation around an island or a reef. A very good agreement is reached in every cases, validating the predictive empirical laws for the parameters of the model. These comparisons confirm the efficiency of the present strategy, highlighting the enstrophy as a robust and reliable tool to describe wave breaking even in a two-dimensional context. Compared with existing depth-averaged models, this approach is numerically robust and adds more physical effects without significant increase in numerical complexity.

A 2D Numerical Model for Simulation of Two-Dimensional Circular Dam-Break

2011 ◽  
Vol 130-134 ◽  
pp. 2993-2996
Author(s):  
Ming Qin Liu ◽  
Y.L. Liu
Keyword(s):  
Solution Procedure ◽  
Dam Break ◽  
Curvilinear Coordinates ◽  
Two Dimensional ◽  
Proposed Model ◽  
Curvilinear Coordinate ◽  
Orthogonal Curvilinear Coordinate System ◽  
Orthogonal Curvilinear Coordinates ◽  
Averaged Model ◽  
The Mathematical Model

The purpose of this paper is to present a 2D depth-averaged model under orthogonal curvilinear coordinates for simulating two-dimensional circular dam-break flows. The proposed model uses an orthogonal curvilinear coordinate system efficiently and accurately to simulate the flow field with irregular boundaries. As for the numerical solution procedure, The SIMPLEC solution procedure has been used for the transformed governing equations in the transformed domain. Practical application of the model is illustrated by an example, which demonstrates that the mathematical model can capture hydraulic discontinuities accurately such as steep fronts, hydraulic jump and drop, etc.

scholarly journals Relative effects of biotic and abiotic factors during early life history on recruitment dynamics: a case study

2017 ◽  
Vol 74 (7) ◽  
pp. 1125-1134 ◽  
Author(s):  
Fan Zhang ◽  
Kevin B. Reid ◽  
Thomas D. Nudds
Keyword(s):  
Life History ◽  
Yellow Perch ◽  
Lake Erie ◽  
Abiotic Factors ◽  
Zooplankton Abundance ◽  
Biotic Factors ◽  
Large Lakes ◽  
Middle Term ◽  
Biotic And Abiotic Factors ◽  
Juvenile Stages

The relative effects of biotic and abiotic factors, and the life-history stages upon which they act to affect fish recruitment, vary among species and ecosystems. We compared the effects of spawning stock biomass, and factors operating at early-term (encompassing the egg, yolk-sac larval, and first few days of swim-up larval stages), middle-term (including the swim-up larval and pelagic juvenile stages), and late-term (over the benthic juvenile stage) on recruitment by yellow perch (Perca flavescens) in the western basin of Lake Erie between 1999 and 2013. Variation of recruitment was mainly driven by middle-term effects. Then, abiotic factors, such as warming rate and wind speed, more strongly affected recruitment than did biotic factors. Among middle-term biotic factors, the top-down effect of yearling walleye (Sander vitreus) abundance was stronger than the bottom-up effect of zooplankton abundance. Similar to marine species, physical processes appear to strongly affect recruitment dynamics of Lake Erie yellow perch over its pelagic larval and juvenile stages, demonstrating the importance of physical and biological processes in understanding fish population dynamics in large lakes.

Vernier Image Processing: Model and Experiments

Perception ◽  
1997 ◽  
Vol 26 (1_suppl) ◽  
pp. 110-110
Author(s):  
A V Chihman ◽  
V N Chihman ◽  
Y E Shelepin
Keyword(s):  
Fourier Analysis ◽  
Visual Processing ◽  
Fourier Spectrum ◽  
Field Size ◽  
Two Dimensional ◽  
Frequency Range ◽  
Additional Line ◽  
Point Spread ◽  
Model Predictions ◽  
Spread Function

Earlier we proposed a model for visual processing of the optical image of Vernier targets (1996 Perception25 Supplement, 115 – 116) based on Fourier analysis of the image. Our model comprises blurring of the thin Vernier bars by the optical point-spread function followed by calculation of the two-dimensional Fourier spectrum. In our model the processing area for Fourier analysis (the receptive field size) is 5 min arc. For a Vernier target, the contrast energy in the low-spatial-frequency range is different in different orientations, and magnification of the Vernier shift changes the orientation of the oblique Fourier components. To test the model, we carried out experiments in which the stimuli were Vernier lines with additional line distractors orthogonal to the orientation of the oblique Fourier components. Thresholds for detecting Vernier displacements were determined by a 2AFC paradigm and compared with model predictions. The results are consistent with our modelling of Vernier performance as a measurement of oblique components of the 2-D Fourier spectrum.

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