scholarly journals Shallow water model for pollutant distribution in the Ypacarai Lake

2021 ◽  
Vol 26 (2) ◽  
pp. 54-76
Author(s):  
Diego Bareiro ◽  
Enrique O’Durnin ◽  
Laura Oporto ◽  
Christian Schaerer
Keyword(s):  
Shallow Water ◽  
Stokes Equations ◽  
Water Model ◽  
Navier Stokes ◽  
Shallow Water Model ◽  
Navier Stokes Equations ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Wind Velocities ◽  
The Impact

In this paper, we analyze the distribution of a non-reactive contaminant in Ypacarai Lake. We propose a shallow-water model that considers wind-induced currents, inflow and outflow conditions in the tributaries, and bottom effects due to the lakebed. The hydrodynamic is based on the depth-averaged Navier-Stokes equations considering wind stresses as force terms which are functions of the wind velocity. Bed (bottom) stress is based on Manning's equation, the lakebed characteristics, and wind velocities. The contaminant transportation is modeled by a 2D convection-diffusion equation taking into consideration water level. Comparisons between the simulation of the model, analytical solutions, and laboratory results confirm that the model captures the complex dynamic phenomenology of the lake. In the simulations, one can see the regions with the highest risk of accumulation of contaminants. It is observed the effect of each term and how it can be used them to mitigate the impact of the pollutants.    

scholarly journals Fluid-kinetic modelling for respiratory aerosols with variable size and temperature

2020 ◽  
Vol 67 ◽  
pp. 100-119 ◽  
Author(s):  
Laurent Boudin ◽  
Céline Grandmont ◽  
Bérénice Grec ◽  
Sébastien Martin ◽  
Amina Mecherbet ◽  
...  
Keyword(s):  
Stokes Equations ◽  
Kinetic Modelling ◽  
Type Equation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Aerosol Dynamics ◽  
Convection Diffusion Equation ◽  
Time Marching ◽  
Branched Structure ◽  
The Impact

In this paper, we propose a coupled fluid-kinetic model taking into account the radius growth of aerosol particles due to humidity in the respiratory system. We aim to numerically investigate the impact of hygroscopic effects on the particle behaviour. The air flow is described by the incompressible Navier-Stokes equations, and the aerosol by a Vlasov-type equation involving the air humidity and temperature, both quantities satisfying a convection-diffusion equation with a source term. Conservations properties are checked and an explicit time-marching scheme is proposed. Twodimensional numerical simulations in a branched structure show the influence of the particle size variations on the aerosol dynamics.

A stationary circular hydraulic jump, the limits of its existence and its gasdynamic analogue

2008 ◽  
Vol 601 ◽  
pp. 189-198 ◽  
Author(s):  
ASLAN R. KASIMOV
Keyword(s):  
Surface Tension ◽  
Hydraulic Jump ◽  
Stokes Equations ◽  
Critical Value ◽  
Water Model ◽  
Navier Stokes ◽  
Jump Conditions ◽  
Shallow Water Model ◽  
Finite Radius ◽  
Navier Stokes Equations

We propose a theory of a steady circular hydraulic jump based on the shallow-water model obtained from the depth-averaged Navier–Stokes equations. The flow structure both upstream and downstream of the jump is determined by considering the flow over a plate of finite radius. The radius of the jump is found using the far-field conditions together with the jump conditions that include the effects of surface tension. We show that a steady circular hydraulic jump does not exist if the surface tension is above a certain critical value. The solution of the problem provides a basis for the hydrodynamic stability analysis of the hydraulic jump. An analogy between the hydraulic jump and a detonation wave is pointed out.

Geometrically intrinsic modeling of shallow water flows

2020 ◽  
Vol 54 (6) ◽  
pp. 2125-2157 ◽  
Author(s):  
Elena Bachini ◽  
Mario Putti
Keyword(s):  
Shallow Water ◽  
Stokes Equations ◽  
Order Approximation ◽  
Bottom Topography ◽  
Water Model ◽  
Navier Stokes ◽  
Bottom Surface ◽  
Finite Volume Scheme ◽  
Navier Stokes Equations ◽  
Mountain Landscape

Shallow water models of geophysical flows must be adapted to geometric characteristics in the presence of a general bottom topography with non-negligible slopes and curvatures, such as a mountain landscape. In this paper we derive an intrinsic shallow water model from the Navier–Stokes equations defined on a local reference frame anchored on the bottom surface. The equations resulting are characterized by non-autonomous flux functions and source terms embodying only the geometric information. We show that the proposed model is rotational invariant, admits a conserved energy, is well-balanced, and it is formally a second order approximation of the Navier–Stokes equations with respect to a geometry-based order parameter. We then derive a numerical discretization by means of a first order upwind Godunov finite volume scheme intrinsically defined on the bottom surface. We study convergence properties of the resulting scheme both theoretically and numerically. Simulations on several synthetic test cases are used to validate the theoretical results as well as more experimental properties of the solver. The results show the importance of taking into full consideration the bottom geometry even for relatively mild and slowly varying curvatures.

scholarly journals CALCULATIONS OF WAVES FORMED FROM SURFACE CAVITIES

1976 ◽  
Vol 1 (15) ◽  
pp. 63 ◽  
Author(s):  
Charles L. Mader
Keyword(s):  
Water Waves ◽  
Wave Motion ◽  
Stokes Equations ◽  
Water Model ◽  
Navier Stokes ◽  
Critical Depth ◽  
Shallow Water Model ◽  
Navier Stokes Equations ◽  
Tsunami Waves ◽  
Long Wave

The wave motion resulting from cavities in the ocean surface was investigated using both the long wave, shallow water model and the incompressible Navier-Stokes equations. The fluid flow resulting from the calculated collapse of the cavities is significantly different for the two models. The experimentally observed flow resulting from explosively formed cavities is in better agreement with the flow calculated using the incompressible Navier-Stokes model. The resulting wave motions decay rapidly to deep water waves. Large cavities located under the surface of the ocean will be more likely to result in Tsunami waves than cavities on the surface. This is contrary to what has been suggested by the upper critical depth phenomenon.

On the Flow Fields of Inertial Impactors

1974 ◽  
Vol 96 (4) ◽  
pp. 394-400 ◽  
Author(s):  
V. A. Marple ◽  
B. Y. H. Liu ◽  
K. T. Whitby
Keyword(s):  
Flow Field ◽  
Stokes Equations ◽  
Relaxation Method ◽  
Water Model ◽  
Navier Stokes ◽  
Visualization Technique ◽  
Navier Stokes Equations ◽  
Theoretical Results ◽  
Plate Distance ◽  
Good Agreement

The flow field in an inertial impactor was studied experimentally with a water model by means of a flow visualization technique. The influence of such parameters as Reynolds number and jet-to-plate distance on the flow field was determined. The Navier-Stokes equations describing the laminar flow field in the impactor were solved numerically by means of a finite difference relaxation method. The theoretical results were found to be in good agreement with the empirical observations made with the water model.

scholarly journals Measuring the Impact of Observations on the Predictability of the Kuroshio Extension in a Shallow-Water Model

2012 ◽  
Vol 42 (1) ◽  
pp. 3-17 ◽  
Author(s):  
Werner Kramer ◽  
Henk A. Dijkstra ◽  
Stefano Pierini ◽  
Peter Jan van Leeuwen
Keyword(s):  
Shallow Water ◽  
Particle Filtering ◽  
Predictive Power ◽  
Kuroshio Extension ◽  
Water Model ◽  
Ensemble Prediction ◽  
Shallow Water Model ◽  
One Year ◽  
The Impact ◽  
The Kuroshio

Abstract In this paper, sequential importance sampling is used to assess the impact of observations on an ensemble prediction for the decadal path transitions of the Kuroshio Extension. This particle-filtering approach gives access to the probability density of the state vector, which allows the predictive power—an entropy-based measure—of the ensemble prediction to be determined. The proposed setup makes use of an ensemble that, at each time, samples the climatological probability distribution. Then, in a postprocessing step, the impact of different sets of observations is measured by the increase in predictive power of the ensemble over the climatological signal during one year. The method is applied in an identical-twin experiment for the Kuroshio Extension using a reduced-gravity shallow-water model. This study investigates the impact of assimilating velocity observations from different locations during the elongated and the contracted meandering states of the Kuroshio Extension. Optimal observation locations correspond to regions with strong potential vorticity gradients. For the elongated state the optimal location is in the first meander of the Kuroshio Extension. During the contracted state it is located south of Japan, where the Kuroshio separates from the coast.

scholarly journals Flow Pressure Behavior Downstream of Ski Jumps

Fluids ◽  
2020 ◽  
Vol 5 (4) ◽  
pp. 168 ◽  
Author(s):  
Agostino Lauria ◽  
Giancarlo Alfonsi ◽  
Ali Tafarojnoruz
Keyword(s):  
High Speed ◽  
Stokes Equations ◽  
Dynamic Pressure ◽  
Pressure Head ◽  
Navier Stokes ◽  
Maximum Pressure ◽  
Navier Stokes Equations ◽  
Free Jet ◽  
Jet Characteristics ◽  
The Impact

Ski jump spillways are frequently implemented to dissipate energy from high-speed flows. The general feature of this structure is to transform the spillway flow into a free jet up to a location where the impact of the jet creates a plunge pool, representing an area for potential erosion phenomena. In the present investigation, several tests with different ski jump bucket angles are executed numerically by means of the OpenFOAM® digital library, taking advantage of the Reynolds-averaged Navier–Stokes equations (RANS) approach. The results are compared to those obtained experimentally by other authors as related to the jet length and shape, obtaining physical insights into the jet characteristics. Particular attention is given to the maximum pressure head at the tailwater. Simple equations are proposed to predict the maximum dynamic pressure head acting on the tailwater, as dependent upon the Froude number, and the maximum pressure head on the bucket. Results of this study provide useful suggestions for the design of ski jump spillways in dam construction.

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