scholarly journals Dispersive and hyperbolic models for non-hydrostatic shallow water flows and their application to steep forced waves modelling

2020 ◽  
Vol 1666 ◽  
pp. 012064
Author(s):  
A V Chebotnikov ◽  
A A Chesnokov ◽  
A K Khe ◽  
V Yu Liapidevskii
Keyword(s):  
Shallow Water ◽  
Water Flows ◽  
Shallow Water Flows ◽  
Forced Waves

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

Simulation of resonant gravity waves in shallow water flows using a depth-averaged URANS model

2020 ◽  
pp. 1097-1103
Author(s):  
A. Navas-Montilla ◽  
C. Juez ◽  
M.J. Franca ◽  
J. Murillo
Keyword(s):  
Shallow Water ◽  
Gravity Waves ◽  
Water Flows ◽  
Shallow Water Flows

Unstructured spectral/hp element methods for shallow water flows

Shallow Flows ◽  
2004 ◽  
pp. 593-600
Author(s):  
Lars Bergdahl ◽  
Claes Eskilsson ◽  
Spencer Sherwin
Keyword(s):  
Shallow Water ◽  
Water Flows ◽  
Shallow Water Flows
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