scholarly journals Modelling turbulence generation in solitary waves on shear shallow water flows

2015 ◽  
Vol 773 ◽  
pp. 49-74 ◽  
Author(s):  
G. L. Richard ◽  
S. L. Gavrilyuk
Keyword(s):  
Shallow Water ◽  
Solitary Waves ◽  
Velocity Fluctuation ◽  
Small Region ◽  
Vertical Coordinate ◽  
Water Flows ◽  
Shallow Water Flows ◽  
Dispersive Model ◽  
Wave Profiles ◽  
Turbulence Generation

We derive a dispersive model of shear shallow water flows which takes into account a non-uniform horizontal velocity. This model generalizes the Green–Naghdi model to the case of shear flows. Besides the classical dispersion term in the Green–Naghdi model related to the acceleration of the free surface, it also contains a new dispersion parameter related to the flow structure. This parameter is related to the second moment of the velocity fluctuation with respect to the vertical coordinate. The distinction between shearing and turbulence based on the scale of variation of the velocity fluctuation is proposed. In particular, an equation for the turbulence generation is derived. Solitary waves for this model are obtained in explicit form. Comparison of solitary wave profiles with experimental ones is also performed. The agreement is very good apart from the small region near the top of the wave.

scholarly journals Pseudo-compressibility, Dispersive Model and Acoustic Waves in Shallow Water Flows

2021 ◽  
pp. 209-250
Author(s):  
Anne-Sophie Bonnet-Ben Dhia ◽  
Marie-Odile Bristeau ◽  
Edwige Godlewski ◽  
Sébastien Impériale ◽  
Anne Mangeney ◽  
...  
Keyword(s):  
Shallow Water ◽  
Acoustic Waves ◽  
Water Flows ◽  
Shallow Water Flows ◽  
Dispersive Model

Assessing the Numerical Accuracy of Complex Spherical Shallow-Water Flows

2007 ◽  
Vol 135 (11) ◽  
pp. 3876-3894 ◽  
Author(s):  
Ali R. Mohebalhojeh ◽  
David G. Dritschel
Keyword(s):  
Shallow Water ◽  
Fourth Order ◽  
Large Scale ◽  
Numerical Accuracy ◽  
Conservation Of Energy ◽  
Water Flows ◽  
Shallow Water Flows ◽  
Low Froude Number ◽  
Contour Advection ◽  
High Reynolds

Abstract The representation of nonlinear shallow-water flows poses severe challenges for numerical modeling. The use of contour advection with contour surgery for potential vorticity (PV) within the contour-advective semi-Lagrangian (CASL) algorithm makes it possible to handle near-discontinuous distributions of PV with an accuracy beyond what is accessible to conventional algorithms used in numerical weather and climate prediction. The emergence of complex distributions of the materially conserved quantity PV, in the absence of forcing and dissipation, results from large-scale shearing and deformation and is a common feature of high Reynolds number flows in the atmosphere and oceans away from boundary layers. The near-discontinuous PV in CASL sets a limit on the actual numerical accuracy of the Eulerian, grid-based part of CASL. For the spherical shallow-water equations, the limit is studied by comparing the accuracy of CASL algorithms with second-order-centered, fourth-order-compact, and sixth-order-supercompact finite differencing in latitude in conjunction with a spectral treatment in longitude. The comparison is carried out on an unstable midlatitude jet at order one Rossby number and low Froude number that evolves into complex vortical structures with sharp gradients of PV. Quantitative measures of global conservation of energy and angular momentum, and of imbalance as diagnosed using PV inversion by means of Bolin–Charney balance, indicate that fourth-order differencing attains the highest numerical accuracy achievable for such nonlinear, advectively dominated flows.

scholarly journals Formation and coarsening of roll-waves in shear shallow water flows down an inclined rectangular channel

2017 ◽  
Vol 159 ◽  
pp. 189-203 ◽  
Author(s):  
K.A. Ivanova ◽  
S.L. Gavrilyuk ◽  
B. Nkonga ◽  
G.L. Richard
Keyword(s):  
Shallow Water ◽  
Rectangular Channel ◽  
Water Flows ◽  
Roll Waves ◽  
Shallow Water Flows
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