An Implicit Nonlinearly Consistent Method for the Two-Dimensional Shallow-Water Equations with Coriolis Force

Mousseau, V. A.; Knoll, D. A.; Reisner, J. M.
November 2002
Monthly Weather Review;Nov2002, Vol. 130 Issue 11, p2611
Academic Journal
An implicit and nonlinearly consistent (INC) solution technique is presented for the two-dimensional shallow-water equations. Since the method is implicit, and therefore unconditionally stable, time steps may be used that result in both gravity wave Courant-Friedrichs-Lewy (CFL) numbers and advection CFL numbers being larger than one. By nonlinearly consistent it is meant that all of the unknown variables appear at the same time level in the equations and are solved for simultaneously in an iterative manner (i.e., no splitting errors intime). The INC method is compared to a more traditional semi-implicit method for stepping over the gravity wave stability constraint. Results are presented that show that the second-order-in-time INC method can maintain a high level of accuracy if the dynamical timescale of the system is resolved by the time step. To investigate this difference in temporal integration accuracy between the nonlinearly consistent method and the semi-implicit method an approximate modified equation analysis was performed. The INC solution technique employed is the Jacobian-free Newton-Krylov (JFNK) method, Preconditioning of the JFNK method is achieved via a semi-implicit solution method. The height matrix from the semi-implicit algorithm is solved using a multigrid linear solver to provide efficiency and scalability.


Related Articles

  • An Explication of the Coriolis Effect. Phillips, Norman A. // Bulletin of the American Meteorological Society;Feb2000, Vol. 81 Issue 2, p299 

    Studies the Coriolis force. Interpretation of how motion on the rotating earth is affected by the Coriolis force; Explanation on the principal properties of the Coriolis force using dynamical principles valid in nonrotating space.

  • Measure the Coriolis effect.  // Current Science;2/12/99, Vol. 84 Issue 11, p6 

    Presents an activity of measuring the Coriolis effect. Theory on why water spinning down a bathtub drain turns in different directions in the Northern and Southern hemispheres.

  • The Effect of Tilted Rotation on Shear Instabilities at Low Stratifications. Jeffery, Nicole; Wingate, Beth // Journal of Physical Oceanography;Dec2009, Vol. 39 Issue 12, p3147 

    A linear stability analysis of the inviscid stratified Boussinesq equations is presented given a steady zonal flow with constant vertical shear in a tilted f plane. Full nonhydrostatic terms are included: 1) acceleration of vertical velocity and 2) Coriolis force terms arising from the...

  • Convective Behavior Of Low Prandtl Number Fluid Heated On Centrifuge. Yuko Inatomi // AIP Conference Proceedings;2/15/2008, Vol. 973 Issue 1, p482 

    It has been shown by numerical simulations and by analysis of crystals that buoyancy convection in liquid might be suppressed at a particular rotation rate on a centrifuge. In the present study a damping effect that the Coriolis force has on buoyancy convection in low Prandtl number on a...

  • Flow through a rotating helical pipe with a wide range of the Dean number. Alam, M. M.; Ota, M.; Ferdows, M.; Islamv, M. N.; Wahiduzzaman, M.; Yamamoto, K. // Archives of Mechanics;2008, Vol. 59 Issue 6, p501 

    THE INCOMPRESSIBLE VISCOUS steady flow through a helical pipe of circular cross- section, rotating at a constant angular velocity about the center of curvature is investigated numerically to examine the combined effects of rotation (Coriolis force), torsion and curvature (centrifugal force) on...

  • Experimental investigation of natural convective flows in slowly rotating wide spherical shells. Antje Brucks // Archive of Applied Mechanics;Jan2008, Vol. 78 Issue 1, p33 

    Abstract  Experimental results are presented on natural convection in a spherical shell of inner and outer radii r 1 = 14 mm and r 2 = 35 mm, with the inner sphere cooled and the outer sphere heated. The fluids filling the shell are...

  • Vestibular contribution to the planning of reach trajectories. Bockisch, Christopher J.; Haslwanter, Thomas // Experimental Brain Research;Sep2007, Vol. 182 Issue 3, p387 

    Reaching for an object while simultaneously rotating induces Coriolis and centrifugal inertial forces on the arm that require compensatory actions to maintain accuracy. We investigated whether the nervous system uses vestibular signals of head rotation to predict inertial forces. Human subjects...

  • Adjustment to Injections of Mass, Momentum, and Heat in a Compressible Atmosphere. Chagnon, Jeffrey M.; Bannon, Peter R. // Journal of the Atmospheric Sciences;8/1/2005, Vol. 62 Issue 8, p2749 

    This study compares the response to injections of mass, heat, and momentum during hydrostatic and geostrophic adjustment in a compressible atmosphere. The sensitivity of the adjustment to these different injection types is examined at varying spatial and temporal scales through analysis of the...

  • The Effects of the Full Coriolis Force on the Structure and Motion of a Tropical Cyclone. Part I: Effects due to Vertical Motion. Xudong Liang; Chan, Johnny C. L. // Journal of the Atmospheric Sciences;10/1/2005, Vol. 62 Issue 10, p3825 

    In most dynamical studies of synoptic-scale phenomena, only the components of the Coriolis force contributed by the horizontal motion are considered, and only in the horizontal momentum equation. The other components are neglected based on a scale analysis. However, it is shown that such an...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics