Some mathematical problems associated with the development and use of marine models

“Science is now a tripartite endeavour with simulation added to the two classical components, experiment and theory (Robinson, 1987). The routine use of numerical “simulation in scientific research (numerical experimentation, sensitivity and process studies, etc.) is thought by many to represent the first major step forward in the basic scientific method since the seventeenth century”(Robinson, 1987).

[1]  J. Overland,et al.  Northward flow in the Bering and Chukchi seas , 1987 .

[2]  Robert M. Chervin,et al.  Ocean general circulation from a global eddy‐resolving model , 1992 .

[3]  R. V. Madala.  Efficient Time Integration Schemes for Atmosphere and Ocean Models , 1981 .

[4]  Andrew F. Bennett,et al.  Inverse Methods in Physical Oceanography: Frontmatter , 1992 .

[5]  C. Reason,et al.  The influence of the Bering Strait on the circulation in a coarse resolution global ocean model , 1994 .

[6]  J. Campin,et al.  On the computation of the barotropic mode of a free-surface world ocean model , 1995 .

[7]  J. Nihoul,et al.  Three-dimensional models of marine and estuarine dynamics , 1987 .

[8]  Harry L. Bryden,et al.  Direct estimates and mechanisms of ocean heat transport , 1982 .

[9]  P. Bradshaw,et al.  Turbulence Models and Their Application in Hydraulics. By W. RODI. International Association for Hydraulic Research, Delft, 1980. Paperback US $15. , 1983, Journal of Fluid Mechanics.

[10]  A. Rosati,et al.  A Quasi-equilibrium Turbulent Energy Model for Geophysical Flows , 1988 .

[11]  O. Reynolds.  III. An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels , 1883, Proceedings of the Royal Society of London.

[12]  C. Hirsch,et al.  Numerical Computation of Internal and External Flows. By C. HIRSCH. Wiley. Vol. 1, Fundamentals of Numerical Discretization. 1988. 515 pp. £60. Vol. 2, Computational Methods for Inviscid and Viscous Flows. 1990, 691 pp. £65. , 1991, Journal of Fluid Mechanics.

[13]  J Tonndorf,et al.  Cochlear prostheses. A state-of-the-art review. , 1977, The Annals of otology, rhinology & laryngology. Supplement.

[14]  S. Hastenrath.  On Meridional Heat Transports in the World Ocean , 1982 .

[15]  Eric Deleersnijder,et al.  Three-dimensional General Circulation Model of the Northern Bering Sea’s Summer Ecohydrodynamics , 1993 .

[16]  Frank O. Bryan,et al.  Parameter sensitivity of primitive equation ocean general circulation models , 1987 .

[17]  M. Endoh,et al.  A free surface general circulation model for the tropical Pacific Ocean , 1992 .

[18]  J. Houghton,et al.  Climate change : the IPCC scientific assessment , 1990 .

[19]  N. Heaps,et al.  Three-dimensional coastal ocean models , 1987 .

[20]  Salim Djenidi,et al.  Perspective in Three-Dimensional Modelling of the Marine System , 1987 .

[21]  R. Sani,et al.  On pressure boundary conditions for the incompressible Navier‐Stokes equations , 1987 .

[22]  G. Mellor,et al.  Development of a turbulence closure model for geophysical fluid problems , 1982 .

[23]  Jacques Nihoul.  Do not use a simple model when a complex one will do , 1994 .

[24]  Eric Deleersnijder,et al.  An Orthogonal Curvilinear System for a World Ocean Model , 1993 .

[25]  B. Cushman-Roisin.  Introduction to Geophysical Fluid Dynamics , 1994 .

[26]  D. Book,et al.  Finite-difference techniques for vectorized fluid dynamics calculations , 1981 .

[27]  J. Beckers.  Application of the GHER 3D general circulation model to the Western Mediterranean , 1991 .

[28]  Peter D. Killworth,et al.  Tests of a two-grid world ocean model , 1994 .

[29]  S. Levitus.  Climatological Atlas of the World Ocean , 1982 .

[30]  Peter D. Killworth,et al.  Deep convection in the World Ocean , 1983 .

[31]  A. Hirst,et al.  Sensitivity of a World Ocean GCM to Changes in Subsurface Mixing Parameterization , 1994 .

[32]  G. Mellor,et al.  Similarity Solutions for the Stratified Turbulent Rayleigh Problem , 1980 .

[33]  H. C. Longuet-Higgins.  Planetary waves on a rotating sphere , 1964, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[34]  J. Beckers,et al.  Analytical linear numerical stability conditions for an anisotropic three-dimensional advection-diffusion equation , 1992 .

[35]  A. Arakawa,et al.  Numerical methods used in atmospheric models , 1976 .

[36]  J. Klinck,et al.  The physics of the Antarctic Circumpolar Current , 1986 .

[37]  The assimilation of altimetric data into the barotropic mode of a rigid lid ocean model , 1994 .

[38]  M. England.  Representing the global-scale water masses in ocean general circulation models , 1993 .

[39]  Sol Hellerman,et al.  Normal Monthly Wind Stress Over the World Ocean with Error Estimates , 1983 .

[40]  T. Taylor,et al.  Computational methods for fluid flow , 1982 .

[41]  K. W. Bedford,et al.  preparation of Estuary and Marine Model Equations by Generalized Filtering Methods , 1987 .

[42]  M. Boussinesq.  Essai sur la théorie des eaux courantes , 1873 .

[43]  L. Mysak,et al.  Waves in the ocean , 1978 .

[44]  O. Reynolds.  On the dynamical theory of incompressible viscous fluids and the determination of the criterion , 1995, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[45]  K. Bryan.  A Numerical Method for the Study of the Circulation of the World Ocean , 1997 .

[46]  R. B. Tripp,et al.  Bering Strait the Regional Physical Oceanography , 1975 .

[47]  J. Dukowicz,et al.  Implicit free‐surface method for the Bryan‐Cox‐Semtner ocean model , 1994 .

[48]  Klaus Hasselmann,et al.  Mean Circulation of the Hamburg LSG OGCM and Its Sensitivity to the Thermohaline Surface Forcing , 1993 .

[49]  A. J. Gadd.  A split explicit integration scheme for numerical weather prediction , 1978 .

[50]  D. Webb,et al.  The Development of a Free-Surface Bryan–Cox–Semtner Ocean Model , 1991 .

[51]  Greg Holloway,et al.  Grid transformation for incorporating the Arctic in a global ocean model , 1994 .

[52]  Arnold L. Gordon,et al.  Interocean Exchange of Thermocline Water , 1986 .

[53]  A. Robinson.  Predicting Open Ocean Currents, Fronts and Eddies , 1987 .

[54]  R. Pacanowski,et al.  Parameterization of Vertical Mixing in Numerical Models of Tropical Oceans , 1981 .

[55]  M. England.  On the Formation of Antarctic Intermediate and Bottom Water in Ocean General Circulation Models , 1992 .

[56]  Alan F. Blumberg,et al.  Modeling vertical and horizontal diffusivities with the sigma coordinate system , 1985 .

[57]  A. Sielecki.  AN ENERGY-CONSERVING DIFFERENCE SCHEME FOR THE STORM SURGE EQUATIONS1 , 1968 .

[58]  I. Fung,et al.  Net diffusivity in ocean general circulation models with nonuniform grids , 1991 .

[59]  J. Labraga,et al.  Design of a Nonsingular Level 2.5 Second-Order Closure Model for the Prediction of Atmospheric Turbulence , 1988 .

[60]  Jane Hsiung,et al.  Estimates of Global Oceanic Meridional Heat Transport , 1985 .

[61]  V. Casulli,et al.  Stability, accuracy and efficiency of a semi-implicit method for three-dimensional shallow water flow☆ , 1994 .

[62]  J. Marotzke,et al.  Multiple Equilibria of the Global Thermohaline Circulation , 1991 .

[63]  Akio Arakawa,et al.  Computational Design of the Basic Dynamical Processes of the UCLA General Circulation Model , 1977 .

[64]  R. Ponte.  Variability in a homogeneous global ocean forced by barometric pressure , 1993 .

[65]  K. Döös,et al.  Interocean exchange of water masses , 1995 .

[66]  M. Batteen,et al.  On the computational noise of finite‐difference schemes used in ocean models , 1981 .

[67]  P. Delecluse,et al.  Comment [on “Net diffusivity in ocean general circulation models with nonuniform grids” by F. L. Yin and I. Y. Fung] , 1992 .

[68]  Eric Deleersnijder,et al.  On the practical advantages of the quasi-equilibrium version of the Mellor and Yamada level 2.5 turbulence closure applied to marine modelling , 1994 .

[69]  É. Deleersnijder.  An analysis of the vertical velocity field computed by a three-dimensional model in the region of the Bering Strait , 1994 .

[70]  R. Sambrotto,et al.  Large Yearly Production of Phytoplankton in the Western Bering Strait , 1984, Science.

[71]  J. Price,et al.  On the scaling of stress-driven entrainment experiments , 1979, Journal of Fluid Mechanics.

[72]  K. Aagaard,et al.  Transports through Bering Strait: Annual and interannual variability , 1988 .

[73]  K. Ruddick,et al.  Presentation of a family of turbulence closure models for stratified shallow water flows and preliminary application to the Rhine outflow region , 1996 .

[74]  Dennis A. Hansell,et al.  Carbon and nitrogen cycling within the Bering/Chukchi Seas: Source regions for organic matter effecting AOU demands of the Arctic Ocean , 1989 .

[75]  K. Aagaard,et al.  ON THE WATER EXCHANGE THROUGH BERING STRAIT1 , 1966 .

[76]  J. Toggweiler,et al.  Simulations of radiocarbon in a coarse-resolution world ocean model: 2. Distributions of bomb-produced carbon 14 , 1989 .

[77]  R. T. Cheng,et al.  SEMI-IMPLICIT FINITE DIFFERENCE METHODS FOR THREE-DIMENSIONAL SHALLOW WATER FLOW , 1992 .

[78]  O. M. Phillips,et al.  On the penetration of a turbulent layer into stratified fluid , 1969, Journal of Fluid Mechanics.

[79]  J. S. Godfrey.  A sverdrup model of the depth-integrated flow for the world ocean allowing for island circulations , 1989 .

[80]  J. Houghton,et al.  Climate change 1992 : the supplementary report to the IPCC scientific assessment , 1992 .

[81]  P. Killworth,et al.  Gradual instability of relaxation-extrapolation schemes , 1984 .

[82]  Pierre Brasseur,et al.  A variational inverse method for the reconstruction of general circulation fields in the northern Bering Sea , 1991 .

[83]  Pierre Brasseur,et al.  Application of a 3-D variational inverse model to the analysis of ecohydrodynamic data in the Northern Bering and Southern Chukchi Seas , 1991 .

[84]  A. Bennett.  Inverse Methods in Physical Oceanography , 1992 .

[85]  N. A. Phillips,et al.  A COORDINATE SYSTEM HAVING SOME SPECIAL ADVANTAGES FOR NUMERICAL FORECASTING , 1957 .

[86]  R. C. Malone,et al.  A Reformulation and Implementation of the Bryan-Cox-Semtner Ocean Model on the Connection Machine , 1993 .

[87]  Eric Deleersnijder,et al.  Stability of a FBTCS scheme applied to the propagation of shallow-water inertia-gravity waves on various space grids , 1993 .

[88]  B. Cushman-Roisin.  Analytical, linear stability criteria for the leap-frog, Dufort-Frankel method , 1984 .

[89]  Anthony Rosati,et al.  The sea surface pressure formulation of rigid lid models. Implications for altimetric data assimilation studies , 1995 .

[90]  S. Patankar.  Numerical Heat Transfer and Fluid Flow , 2018, Lecture Notes in Mechanical Engineering.

[91]  É. Deleersnijder.  Upwelling and upsloping in three-dimensional marine models , 1989 .

[92]  Wallace Broeker,et al.  The Great Ocean Conveyor , 1991 .