Baroclinic stability for a family of two‐level, semi‐implicit numerical methods for the 3D shallow water equations

Rueda, Francisco J.; Sanmiguel‐Rojas, E.; Hodges, Ben R.

doi:10.1002/fld.1391

Cited by 18 publications

(10 citation statements)

References 31 publications

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“…The hydrodynamic model Si3D is based on Computational Fluid Dynamics and adopts an implicit finite‐difference method for numerical solution of the Navier‐Stokes equations. It has been comprehensively described [ Casulli and Cheng , ; Casulli and Cattani , ; Rueda et al ., ; Smith , ] and applied in many investigations of water flow in natural water bodies [e.g., Rueda et al ., ; Singleton et al ., ].…”

Section: Numerical Model Formulationmentioning

confidence: 99%

A coupled three‐dimensional hydrodynamic model for predicting hypolimnetic oxygenation and epilimnetic mixing in a shallow eutrophic reservoir

Chen

Lei

Carey

et al. 2017

Water Resources Research

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Artificial mixing and hypolimnetic oxygenation are two common methods for improving water quality in reservoirs. To examine the effects of their operation on the thermal structure of the water column, we used a three‐dimensional hydrodynamic model coupled with a newly developed water‐jet model and an existing linear bubble‐plume model in conjunction with whole‐reservoir in situ mixing experiments in a drinking‐water reservoir. This reservoir has a side‐stream supersaturation (SSS) hypolimnetic oxygenation system and a bubble‐plume epilimnetic mixing (EM) system installed to reduce hypolimnetic hypoxia and algal blooms. The results show that the SSS successfully adds dissolved oxygen to the hypolimnion without destratifying the reservoir, whereas the EM, located at the lower metalimnetic boundary, deepens this boundary and partially mixes the metalimnion and epilimnion. The newly developed water‐jet model coupled with the hydrodynamic model can successfully predict the variation of the thermal structure in the reservoir. The extent to which the SSS and EM systems affect the thermal structure of the reservoir is also quantified by further application of the coupled hydrodynamic model.

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Section: Numerical Model Formulationmentioning

confidence: 99%

A coupled three‐dimensional hydrodynamic model for predicting hypolimnetic oxygenation and epilimnetic mixing in a shallow eutrophic reservoir

Chen

Lei

Carey

et al. 2017

Water Resources Research

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“…The backward Euler time stepping in TRIM‐like methods has been shown to be baroclinically stable for baroclinic flow [ Rueda et al , 2007] but barotropically dissipative [ Casulli and Cattani , 1994]. It can be shown that the ratio of the reflected or transmitted surface wave energy to that of internal waves scales to sβ 1/2 for Ω 2 ≪ β [e.g., Hurley and Imberger , 1969].…”

Section: Comparison Between the Numerical And Analytical Resultsmentioning

confidence: 99%

Effect of stair‐step and piecewise linear topography on internal wave propagation in a geophysical flow model

2009

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[1] The paper describes the effect of a stair-step representation of bottom topography, common in most numerical models, on the propagation of internal waves in a geophysical flow. An analytical solution was used to predict the effect of stair-step and piecewise linear representations of topography on the reflection and transmission of internal waves. The Estuary Lake and Coastal Model (ELCOM) was used to simulate the transmission of a train of small-amplitude internal gravity waves propagated along a variable depth rectangular channel containing a linearly stratified fluid. The effect of the different obstacle approximations was examined in terms of the interference of the resulting wave number content, and hence the associated reflection coefficients, which could be directly compared to the analytical theory. It was shown that for Gaussian obstacles of varying lengths and heights, the full bottom cells and partial bottom cells solutions from ELCOM agree with the stair-step and piecewise linear solutions from the theory, respectively. It was shown that when Gaussian obstacles with weak slopes are represented by stair steps, an aliasing that is similar to that in discrete Fourier transform can occur, resulting in reflection coefficients that are much higher than the exact solution. On the other hand, piecewise linear approximations produce significantly attenuated aliasing. An immersed boundary technique that enforces a no-flux condition at the actual sloping bottom, similar to that of the analytical solution, is found not to produce better numerical results.Citation: Simanjuntak, M. A., J. Imberger, and K. Nakayama (2009), Effect of stair-step and piecewise linear topography on internal wave propagation in a geophysical flow model,

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“…The Si3D hydrodynamic model, a semi‐implicit 3‐D computational fluid dynamics code, was adopted in this study. The code employs a finite‐difference method for numerical solution of the Navier‐Stokes equations (Rueda & Schladow, ; Rueda et al, ). The governing equations include continuity equation, momentum equations, and scalar transport equations, which can be found in (Smith, ).…”

Section: Methodsmentioning

confidence: 99%

Three‐Dimensional Effects of Artificial Mixing in a Shallow Drinking‐Water Reservoir

Chen

Little

Carey

et al. 2018

Water Resources Research

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Studies that examine the effects of artificial mixing for water‐quality mitigation in lakes and reservoirs often view a water column with a one‐dimensional (1‐D) perspective (e.g., homogenized epilimnetic and hypolimnetic layers). Artificial mixing in natural water bodies, however, is inherently three dimensional (3‐D). Using a 3‐D approach experimentally and numerically, the present study visualizes thermal structure and analyzes constituent transport under the influence of artificial mixing in a shallow drinking‐water reservoir. The purpose is to improve the understanding of artificial mixing, which may help to better design and operate mixing systems. In this reservoir, a side‐stream supersaturation (SSS) hypolimnetic oxygenation system and an epilimnetic bubble‐plume mixing (EM) system were concurrently deployed in the deep region. The present study found that, while the mixing induced by the SSS system does not have a distinct 3‐D effect on the thermal structure, epilimnetic mixing by the EM system causes 3‐D heterogeneity. In the experiments, epilimnetic mixing deepened the lower metalimnetic boundary near the diffuser by about 1 m, with 55% reduction of the deepening rate at 120 m upstream of the diffuser. In a tracer study using a 3‐D hydrodynamic model, the operational flow rate of the EM system is found to be an important short‐term driver of constituent transport in the reservoir, whereas the duration of the EM system operation is the dominant long‐term driver. The results suggest that artificial mixing substantially alters both 3‐D thermal structure and constituent transport, and thus needs to be taken into account for reservoir management.

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Baroclinic stability for a family of two‐level, semi‐implicit numerical methods for the 3D shallow water equations

Cited by 18 publications

References 31 publications

A coupled three‐dimensional hydrodynamic model for predicting hypolimnetic oxygenation and epilimnetic mixing in a shallow eutrophic reservoir

A coupled three‐dimensional hydrodynamic model for predicting hypolimnetic oxygenation and epilimnetic mixing in a shallow eutrophic reservoir

Effect of stair‐step and piecewise linear topography on internal wave propagation in a geophysical flow model

Three‐Dimensional Effects of Artificial Mixing in a Shallow Drinking‐Water Reservoir

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