Validation of the nonhydrostatic General Curvilinear Coastal Ocean Model (GCCOM) for stratified flows

Abstract While global- and basin-scale processes can be captured quite well with computationally-inexpensive hydrostatic models, smaller-scale features such as shoaling nonlinear internal waves and bores, coastal fronts, and other convective processes require the use of a nonhydrostatic model to accurately capture dynamics. Here the nonhydrostatic capabilities of the General Curvilinear Coastal Ocean Model (GCCOM) in a stratified environment are introduced. GCCOM is a three-dimensional, nonhydrostatic Large Eddy Simulation (LES), rigid lid model that has the ability to run in a fully three-dimensional general curvilinear coordinate system. This model was previously validated for unstratified flows with curvilinear coordinates. Here, recent advances of the model to simulate stratified flows are presented, focusing on sigma coordinate grids with both flat bottom geometry and a local gently sloping seamount. In particular, a suite of test cases widely used as benchmarks for assessing the nonhydrostatic capabilities for gravity-driven flows and internal waves is presented: an internal seiche in a flat bottom tank, the classic lock release and gravity current experiment, and a field-scale internal wave beam experiment consisting of an oscillating tidal flow over a topographic ridge. GCCOM shows excellent agreement with the benchmark test cases and is able to accurately resolve complex nonhydrostatic phenomena in stratified flows. Future studies will utilize the model capabilities for realistic field-scale internal wave simulations.

[1]  Mary P. Thomas,et al.  Nesting nonhydrostatic GCCOM within hydrostatic ROMS for multiscale Coastal Ocean Modeling , 2016, OCEANS 2016 MTS/IEEE Monterey.

[2]  J. Berntsen,et al.  Assessment of non-hydrostatic ocean models using laboratory scale problems , 2006 .

[3]  Eckart Meiburg,et al.  Analysis and direct numerical simulation of the flow at a gravity-current head. Part 1. Flow topology and front speed for slip and no-slip boundaries , 2000, Journal of Fluid Mechanics.

[4]  A. Mccarthy.  Development , 1996, Current Opinion in Neurobiology.

[5]  Mark W. Denny,et al.  Pulsed delivery of subthermocline water to Conch Reef (Florida Keys) by internal tidal bores , 1996 .

[6]  Louis J. Wicker,et al.  Time-Splitting Methods for Elastic Models Using Forward Time Schemes , 2002 .

[7]  Daniel L. Rudnick,et al.  Development, implementation, and validation of a California coastal ocean modeling, data assimilation, and forecasting system , 2017 .

[8]  Y. Notay.  An aggregation-based algebraic multigrid method , 2010 .

[9]  Serge Gratton,et al.  Conjugate gradients versus multigrid solvers for diffusion‐based correlation models in data assimilation , 2013 .

[10]  Robert L. Haney,et al.  On the Pressure Gradient Force over Steep Topography in Sigma Coordinate Ocean Models , 1991 .

[11]  J. Berntsen.  Internal Pressure Errors in Sigma-Coordinate Ocean Models , 2002 .

[12]  William Gropp,et al.  Efficient Management of Parallelism in Object-Oriented Numerical Software Libraries , 1997, SciTools.

[13]  O. Fringer,et al.  Physical vs. numerical dispersion in nonhydrostatic ocean modeling , 2011 .

[14]  C. Ai,et al.  A 3D unstructured non-hydrostatic ocean model for internal waves , 2016, Ocean Dynamics.

[15]  G. Stelling,et al.  Numerical Modeling of Wave Propagation, Breaking and Run-Up on a Beach , 2009 .

[16]  B. Jones,et al.  Cross-shelf transport into nearshore waters due to shoaling internal tides in San Pedro Bay, CA. , 2009 .

[17]  S. Monismith,et al.  Observations of nonlinear internal waves at a persistent coastal upwelling front , 2016 .

[18]  José E. Castillo,et al.  Solving Poisson equation with Robin boundary condition on a curvilinear mesh using high order mimetic discretization methods , 2017, Math. Comput. Simul..

[19]  Oliver B. Fringer,et al.  Moving grid method for numerical simulation of stratified flows , 2013 .

[20]  A. Lucas,et al.  Physical and biological processes underlying the sudden surface appearance of a red tide in the nearshore , 2011 .

[21]  S. Sarkar,et al.  SOMAR-LES: A framework for multi-scale modeling of turbulent stratified oceanic flows , 2017 .

[22]  José E. Castillo,et al.  Unified Curvilinear Ocean Atmosphere Model (UCOAM): A vertical velocity case study , 2013, Math. Comput. Model..

[23]  T. Benjamin.  Gravity currents and related phenomena , 1968, Journal of Fluid Mechanics.

[24]  Carlos R. Torres,et al.  Stratified rotating flow over complex terrain , 2003 .

[25]  A. Agrawal,et al.  Evaluation of SIFOM-FVCOM system for high-fidelity simulation of small-scale coastal ocean flows , 2016 .

[26]  Alexander F. Shchepetkin,et al.  Algorithm for non-hydrostatic dynamics in the Regional Oceanic Modeling System , 2007 .

[27]  I. S. Ertesvåg,et al.  Large eddy simulation in generalized curvilinear coordinates using conventional approach: Theory and validation , 2012 .

[28]  R. Street,et al.  The dynamics of breaking progressive interfacial waves , 2003, Journal of Fluid Mechanics.

[29]  Carlos R. Torres,et al.  Flow past a sphere moving vertically in a stratified diffusive fluid , 2000, Journal of Fluid Mechanics.

[30]  A. M. Davies,et al.  Numerical studies of flow over a sill: sensitivity of the non-hydrostatic effects to the grid size , 2009 .

[31]  Sutanu Sarkar,et al.  Tidal flow over topography: effect of excursion number on wave energetics and turbulence , 2014, Journal of Fluid Mechanics.

[32]  L. Perelman,et al.  A finite-volume, incompressible Navier Stokes model for studies of the ocean on parallel computers , 1997 .

[33]  Ben R. Hodges,et al.  A hydrostatic/non-hydrostatic grid-switching strategy for computing high-frequency, high wave number motions embedded in geophysical flows , 2009, Environ. Model. Softw..

[34]  Vincenzo Casulli,et al.  A SEMI-IMPLICIT FINITE DIFFERENCE METHOD FOR NON-HYDROSTATIC, FREE-SURFACE FLOWS , 1999 .

[35]  S. A. Jordan.  A Large-Eddy Simulation Methodology in Generalized Curvilinear Coordinates , 1999 .

[36]  S. Monismith,et al.  Connecting wind‐driven upwelling and offshore stratification to nearshore internal bores and oxygen variability , 2014 .

[37]  James C. McWilliams,et al.  A method for computing horizontal pressure‐gradient force in an oceanic model with a nonaligned vertical coordinate , 2003 .

[38]  M. Parlange,et al.  Surface length scales and shear stress: Implications for land‐atmosphere interaction over complex terrain , 1999 .

[39]  Geoffrey C. Fox,et al.  Grid portal architectures for scientific applications , 2005 .

[40]  Interfacing an ensemble Data Assimilation system with a 3D nonhydrostatic Coastal Ocean Model, an OSSE experiment , 2016, OCEANS 2016 MTS/IEEE Monterey.

[42]  Eric Wolanski,et al.  Upwelling by internal tides and Kelvin waves at the continental shelf break on the Great Barrier Reef , 1983 .

[43]  Leonhard Kleiser,et al.  A direct Numerical Simulation Approach to the Study of Intrusion Fronts , 1997 .

[44]  P. Moin,et al.  Application of a Fractional-Step Method to Incompressible Navier-Stokes Equations , 1984 .

[45]  Peter Franks,et al.  Horizontal internal-tide fluxes support elevated phytoplankton productivity over the inner continental shelf , 2011 .

[46]  Edward Santilli,et al.  The Stratified Ocean Model with Adaptive Refinement (SOMAR) , 2015, J. Comput. Phys..

[47]  Sailkat Dey,et al.  Curvilinear Mesh Generation in 3D , 1999, IMR.

[48]  K. Kuwahara,et al.  Computation of high Reynolds number flow around a circular cylinder with surface roughness , 1984 .

[49]  Sean Vitousek,et al.  A nonhydrostatic, isopycnal-coordinate ocean model for internal waves , 2014 .

[50]  Chris Hill,et al.  Efficient ocean modeling using non-hydrostatic algorithms , 1998 .

[51]  Robert L. Street,et al.  A New Hybrid Model for Coastal Simulations , 2006 .

[52]  Carlos R. Torres,et al.  Three-dimensional stratified flow over Alarcón Seamount, Gulf of California entrance , 2004 .

[53]  A. E. Gill.  Atmosphere-Ocean Dynamics , 1982 .

[54]  L. Perelman,et al.  Hydrostatic, quasi‐hydrostatic, and nonhydrostatic ocean modeling , 1997 .

[55]  R. Walter,et al.  Internal bore seasonality and tidal pumping of subthermocline waters at the head of the Monterey submarine canyon , 2015 .

[56]  Geoffrey W. Cowles,et al.  A nonhydrostatic version of FVCOM: 1. Validation experiments , 2010 .

[57]  M. Gerritsen,et al.  An unstructured-grid, finite-volume, nonhydrostatic, parallel coastal ocean simulator , 2006 .

[58]  Lei Lin,et al.  Partially implicit finite difference scheme for calculating dynamic pressure in a terrain-following coordinate non-hydrostatic ocean model , 2016 .

[59]  J. Smagorinsky,et al.  GENERAL CIRCULATION EXPERIMENTS WITH THE PRIMITIVE EQUATIONS , 1963 .