Bottom friction models for shallow water equations: Manning’s roughness coefficient and small-scale bottom heterogeneity

Appropriate methods and tools accessibility for bi-dimensional flow simulation leads to their weak use for floods assessment and forecasting in West African countries, particularly in urban areas where huge losses of life and property are recorded. To mitigate flood risks or to elaborate flood adaptation strategies, there is a need for scientific information on flood events. This paper focuses on a numerical tool developed for urban inundation extent simulation due to extreme tropical rainfall in Ouagadougou city. Two-dimensional (2D) shallow-water equations are solved using a finite volume method with a Harten, Lax, Van Leer (HLL) numerical fluxes approach. The Digital Elevation Model provided by NASA’s Shuttle Radar Topography Mission (SRTM) was used as the main input of the model. The results have shown the capability of the numerical tool developed to simulate flow depths in natural watercourses. The sensitivity of the model to rainfall intensity and soil roughness coefficient was highlighted through flood spatial extent and water depth at the outlet of the watershed. The performance of the model was assessed through the simulation of two flood events, with satisfactory values of the Nash–Sutcliffe criterion of 0.61 and 0.69. The study is expected to be useful for flood managers and decision makers in assessing flood hazard and vulnerability.

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On the Spectral Convergence of the Supercompact Finite-Difference Schemes for the f-Plane Shallow-Water Equations

Monthly Weather Review ◽

10.1175/2009mwr2824.1 ◽

2009 ◽

Vol 137 (7) ◽

pp. 2393-2406 ◽

Cited By ~ 5

Author(s):

S. Ghader ◽

A. R. Mohebalhojeh ◽

V. Esfahanian

Keyword(s):

Finite Difference ◽

Shallow Water ◽

Potential Vorticity ◽

Shallow Water Equations ◽

Small Scale ◽

Finite Difference Schemes ◽

Vorticity Field ◽

Eighth Order ◽

Spectral Convergence ◽

Nonlinear Flows

For the f-plane shallow-water equations, the convergence properties of the supercompact finite-difference method (SCFDM) are examined during the evolution of complex, nonlinear flows spawned by an unstable jet. The second-, fourth-, sixth-, and eighth-order SCFDMs are compared with a standard pseudospectral (PS) method. To control the buildup of small-scale activity and thus the potential for numerical instability, the vorticity field is damped explicitly by the application of a triharmonic hyperdiffusion operator acting on the vorticity field. The global distribution of mass between isolevels of potential vorticity, called mass error, and the representation of the balance and imbalance are used to assess numerical accuracy. In each of the quantitative measures, a clear convergence of the SCFDM to the PS method is observed. There is no saturation in accuracy up to the eighth order examined. Taking the PS solution as the reference, for the fundamental quantity of potential vorticity the rate of convergence to PS turns out to be algebraic and near-quadratic.

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Asymmetry of Free Circulations in Closed Ocean Gyres

Journal of Physical Oceanography ◽

10.1175/2007jpo3789.1 ◽

2008 ◽

Vol 38 (2) ◽

pp. 517-526 ◽

Cited By ~ 8

Author(s):

J. H. LaCasce ◽

O. A. Nøst ◽

P. E. Isachsen

Keyword(s):

Shallow Water ◽

Shallow Water Equations ◽

Cyclonic Circulation ◽

Wind Forcing ◽

Small Scale ◽

Steady Flows ◽

Anticyclonic Circulation ◽

Ocean Gyres ◽

Scale Structures ◽

Small Scale Structures

Abstract Steady flows in regions of closed geostrophic contours, such as in ocean basins or over seamounts, are examined by calculating solutions to the nonlinear quasigeostrophic and shallow-water equations with topography. For oceanically realistic choices of parameters, the solutions are asymmetric in that those with cyclonic circulation resemble the topography while those with anticyclonic circulation exhibit small-scale structure and cross-isobath flow. These small-scale structures reflect topographic wave modes, which are stationary with the anticyclonic circulation. The implication of the asymmetry is that random wind forcing is much more likely to excite persistent cyclonic than anticyclonic flow. This may explain why the circulation in the Norwegian and Greenland Gyres is most often cyclonic.

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Consistent section-averaged shallow water equations with bottom friction

European Journal of Mechanics - B/Fluids ◽

10.1016/j.euromechflu.2020.12.005 ◽

2021 ◽

Vol 86 ◽

pp. 123-149

Author(s):

Victor Michel-Dansac ◽

Pascal Noble ◽

Jean-Paul Vila

Keyword(s):

Shallow Water ◽

Shallow Water Equations ◽

Bottom Friction

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Calibration of the 1D shallow water equations: a comparison of Monte Carlo and gradient-based optimization methods

Journal of Hydroinformatics ◽

10.2166/hydro.2017.021 ◽

2017 ◽

Vol 19 (2) ◽

pp. 282-298 ◽

Cited By ~ 2

Author(s):

Asier Lacasta ◽

Mario Morales-Hernández ◽

Javier Burguete ◽

Pilar Brufau ◽

Pilar García-Navarro

Keyword(s):

Monte Carlo ◽

Shallow Water ◽

Shallow Water Equations ◽

Stochastic Approach ◽

Optimization Methods ◽

Computational Effort ◽

Roughness Coefficient ◽

Advantages And Disadvantages ◽

Gradient Based ◽

The One

The calibration of parameters in complex systems usually requires a large computational effort. Moreover, it becomes harder to perform the calibration when non-linear systems underlie the physical process, and the direction to follow in order to optimize an objective function changes depending on the situation. In the context of shallow water equations (SWE), the calibration of parameters, such as the roughness coefficient or the gauge curve for the outlet boundary condition, is often required. In this work, the SWE are used to simulate an open channel flow with lateral gates. Due to the uncertainty in the mathematical modeling that these lateral discharges may introduce into the simulation, the work is focused on the calibration of discharge coefficients. Thus, the calibration is performed by two different approaches. On the one hand, a classical Monte Carlo method is used. On the other hand, the development and application of an adjoint formulation to evaluate the gradient is presented. This is then used in a gradient-based optimizer and is compared with the stochastic approach. The advantages and disadvantages are illustrated and discussed through different test cases.

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Propagation of a finite-amplitude potential vorticity front along the wall of a stratified fluid

Journal of Fluid Mechanics ◽

10.1017/s0022112002001520 ◽

2002 ◽

Vol 468 ◽

pp. 179-204 ◽

Cited By ~ 5

Author(s):

MELVIN E. STERN ◽

KARL R. HELFRICH

Keyword(s):

Laboratory Experiment ◽

Shallow Water ◽

Potential Vorticity ◽

Shallow Water Equations ◽

Numerical Solutions ◽

Similarity Theory ◽

Wave Structure ◽

Small Scale ◽

Reduced Gravity ◽

Coriolis Parameter

A similarity solution to the long-wave shallow-water equations is obtained for a density current (reduced gravity = g′, Coriolis parameter = f) propagating alongshore (y = 0). The potential vorticity q = f/H1 is uniform in −∞ < x [les ] xnose(t), 0 < y [les ] L(x, t), and the nose of this advancing potential vorticity front displaces fluid of greater q = f/H0, which is located at L < y < ∞. If L0 = L(−∞, t), the nose point with L(xnose(t), t) = 0 moves with velocity Unose = √g′H0 φ, where φ is a function of H1/H0, f2L20/g′H0. The assumptions made in the similarity theory are verified by an initial value solution of the complete reduced-gravity shallow-water equations. The latter also reveal the new effect of a Kelvin shock wave colliding with a potential vorticity front, as is confirmed by a laboratory experiment. Also confirmed is the expansion wave structure of the intrusion, but the observed values of Unose are only in qualitative agreement; the difference is attributed to the presence of small-scale (non-hydrostatic) turbulence in the laboratory experiment but not in the numerical solutions.

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MAPPING TIDAL CURRENTS AND RESIDUAL CURRENTS BY USE OF COASTAL ACOUSTIC TOMOGRAPHY

Proceedings of International Conference "Managinag risks to coastal regions and communities in a changinag world" (EMECS'11 - SeaCoasts XXVI) ◽

10.31519/conferencearticle_5b1b94407213d3.12732916 ◽

2017 ◽

Author(s):

Xiao-Hua Zhu ◽

Ze-Nan Zhu ◽

Xinyu Guo ◽

...

Keyword(s):

Shallow Water ◽

Shallow Water Equations ◽

Mean Amplitude ◽

Momentum Equation ◽

Tidal Currents ◽

Acoustic Tomography ◽

Mean Values ◽

Residual Currents ◽

Water Depths ◽

Deep Area

A coastal acoustic tomography (CAT) experiment for mapping the tidal currents in the Zhitouyang Bay was successfully carried out with seven acoustic stations during July 12 to 13, 2009. The horizontal distributions of tidal current in the tomography domain are calculated by the inverse analysis in which the travel time differences for sound traveling reciprocally are used as data. Spatial mean amplitude ratios M2 : M4 : M6 are 1.00 : 0.15 : 0.11. The shallow-water equations are used to analyze the generation mechanisms of M4 and M6. In the deep area, velocity amplitudes of M4 measured by CAT agree well with those of M4 predicted by the advection terms in the shallow water equations, indicating that M4 in the deep area where water depths are larger than 60 m is predominantly generated by the advection terms. M6 measured by CAT and M6 predicted by the nonlinear quadratic bottom friction terms agree well in the area where water depths are less than 20 m, indicating that friction mechanisms are predominant for generating M6 in the shallow area. Dynamic analysis of the residual currents using the tidally averaged momentum equation shows that spatial mean values of the horizontal pressure gradient due to residual sea level and of the advection of residual currents together contribute about 75% of the spatial mean values of the advection by the tidal currents, indicating that residual currents in this bay are induced mainly by the nonlinear effects of tidal currents.

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