NUMERICAL MODELLING OF MARINE HYDRODYNAMICS
CONTENTS CHAPTER OUR HOME – THE EARTH THE BASICS THE OCEANS – AN INTRODUCTION SPATIAL AND TEMPORAL SCALES OCEANS – THE REGULATOR OF TEMPERATURE CARRIERS OF HEAT – CYCLONES AND CURRENTS FRANKLIN TO SATELLITES CHAPTER RESPONSES AND FORCES INTRODUCTION THE RESPONSE VARIABLES THE FORCING FUNCTION NEWTON’S LAWS RATE OF CHANGE FORCES ON FLUID THE PRESSURE-GRADIENT FORCES AND HYDRO- STATIC BALANCE VISCOUS FORCE THE CORIOLIS FORCE THE CONSERVATION EQUATIONS THE CONSERVATION OF MASS CONSERVATION OF HEAT AND SALT GOVERNING EQUATIONS GEOSTROPHIC EQUILIBRIUM THE GEOSTROPHIC BALANCE DYNAMIC HEIGHT AND GEOSTROPHIC VELOCITY GEOSTROPHIC VELOCITY SPECIFIC VOLUME ANOMALY VELOCITY ACROSS A SECTION ABSOLUTE VELOCITIES LARGE-SCALE GEOSTROPHIC BALANCE INERTIAL MOTION THERMAL WIND WIND-DRIVEN CIRCULATION WIND STRESS AND EDDY VISCOSITY THE EKMAN BALANCE THE INTEGRATED EKMAN TRANSPORT UPWELLING (COASTAL AND EQUATORIAL) SVERDRUP DYNAMICS VORTICITY RELATIVE VORTICITY PLANETARY VORTICITY ABSOLUTE VORTICITY POTENTIAL VORTICITY STOMMEL’S SOLUTION MUNK’S MODEL AND FUTURE DIRECTIONS THE ABYSSAL CONNECTION THE SINKING REGIONS THE CONVEYOR BELT MERIDIONAL OVERTURNING CIRCULATION (MOC) ATLANTIC MOC (AMOC) A SIMPLE MODEL FOR THE THC WIND-DRIVEN AND THERMOHALINE TIME–DEPENDENT CIRCULATION TIME-DEPENDENCE AND WAVES THE INERTIA-GRAVITY WAVE EQUATIONS SURFACE GRAVITY WAVES WHAT EXACTLY IS A WAVE? EXAMPLES OF WAVES IN OTHER MEDIA FOURIER DECOMPOSITION AN EXAMPLE OF FOURIER DECOMPOSITION THE DISPERSION RELATIONSHIP THE DISPERSION DIAGRAM KELVIN WAVES ROSSBY WAVES THE LAYERING OF OCEANS THE IDEA OF LAYERS THE 2-LAYER OCEAN BUOYANCY FREQUENCY STRATIFICATION AND VERTICAL MIXING STRATIFICATION AND HORIZONTAL MIXING ENERGY EXTRACTION FROM STRATIFICATION BARRIER LAYER AND INVERSION LAYER EL NI˜NO AND LA NI˜NA A BRIEF HISTORY THE PHYSICAL SETUP TWO-LAYER MODEL THE EQUATORIAL JET EQUATORIAL KELVIN AND ROSSBY WAVES THE INDIAN NI˜NO (IOD) INSTABILITY BAROTROPIC INSTABILITY BAROCLINIC INSTABILITY EXAMPLES OF BT/BC INSTABILITIES INTRODUCTION TO MODELING CONTEXT OF MODELING WHAT IS A MODEL? PURPOSE OF MODELING WHAT DO WE MODEL? HOW DO YOU MODEL? GENERAL APPROACH TO MODELING DOMAIN AND GRID-RESOLUTION INITIAL CONDITION BOUNDARY CONDITIONS AND FORCING PARAMETERS AN EARLY OCEAN MODEL NUMERICAL METHODS FINITE DIFFERENCE THE BASIC EQUATIONS THE MODEL EQUATIONS THE COMPUTER ALGORITHM CONCLUSION TURBULENCE AND EDDIES TURBULENCE AND EDDY VISCOSITY TURBULENCE THE CLOSURE PROBLEM A SIMPLE EDDY VISCOSITY KOLMOGOROV THEORY APPROACHES TO CLOSURE MODELING RELATION TO VERTICAL MIXING TURBULENCE AND MIXED LAYER PWP MODEL MULTISCALE OCEAN MODELS 10 1 A BRIEF BACKGROUND 10 2 MULTISCALE MODELS 10 3 GENERALIZED VERTICAL COORDINATES 10 4 HARVARD OCEAN PREDICTION SYSTEM (HOPS) 10 5 THE PRINCETON OCEAN MODEL (POM) 10 5 1 VERTICAL MIXING IN POM MELLOR-YAMADA 2 5 CLOSURE SCHEME 10 6 REGIONAL OCEAN MODELING SYSTEM (ROMS) 10 6 1 VERTICAL MIXING IN ROMS PHILANDER AND PACANOWSKI – PPMIX K-PROFILE PARAMETERIZATION – LMD94 GENERIC LENGTH SCALE 10 7 MITGCM 10 8 HYCOM 10 9 MIT – MSEAS 10 10MOM6 SIMULATION AND PREDICTION 11 1 CONTEXT OF SIMULATION AND PREDICTION 11 2 GRID AND MODEL SETUP 11 3 MODEL INITIALIZATION 11 3 1 CLIMATOLOGY 11 3 2 OBSERVATIONS FOR MODELING SYSTEMS IN SITU OBSERVATIONS BUOYS GLOBAL ARRAYS REGIONAL ARRAYS ARGO FLOATS DRIFTERS SURVEY DATA SATELLITE OBSERVATIONS NEW OBSERVATIONAL PLATFORMS 11 3 3 FORCING FIELDS AND REANALYSES 11 4 OPTIMAL INTERPOLATION 11 4 1 THE CORRECTION METHOD 11 4 2 KRIGING 11 4 3 OBJECTIVE ANALYSIS 11 5 DATA ASSIMILATION 11 6 EXAMPLE SIMULATIONS 11 6 1 THE NORTH ATLANTIC SIMULATION 11 6 2 A BAY OF BENGAL SIMULATION 11 6 3 BRAZIL CURRENT GENESIS REGION 11 7 PREDICTION 11 8 IOOS 11 9 APPLICATIONS 11 9 1 CLIMATE CHANGE AND MACHINE LEARNING 11 9 2 TECHNOLOGY AND SOCIETY SYNOPTIC OCEAN MODELING 12 1 THE SYNOPTIC OCEAN 12 2 FORMS 12 3 FORMS – WESTERN NORTH ATLANTIC 12 3 1 GSMR – DEEPER REGIONS 12 3 2 FEATURE MODELS – GULF STREAM AND RINGS A KINEMATIC SYNTHESIS 12 3 3 GOMGB – COASTAL FORMS WATER-MASS FRONT FM SHELF-SLOPE FRONT (AND UP- WELLING) FM COASTAL EDDY AND GYRE T/S FEATURE MODELS 12 3 4 INITIALIZATION WITH FORMS – WNA 12 3 5 A FORECASTING SYSTEM FOR WNA 12 4 PROCESS STUDIES WITH FORMS 12 4 1 THE STRAIT OF SICILY 12 4 2 BRAZIL CURRENT 12 5 A WORLD OF FORMS INTERDISCIPLINARY MODELING 13 1 INTRODUCTION 13 2 THE BASICS 13 3 THE BIOGEOCHEMICAL CYCLES 13 4 VERTICAL DISTRIBUTION OF DISSOLVED GASES 13 5 MERIDIONAL DISTRIBUTION OF DISSOLVED GASES 13 6 SIMPLE BIOGEOCHEMICAL MODELING 13 7 BIOGEOCHEMICAL MODELS – TWO EXAMPLES 13 8 BIOGEOCHEMICAL PROCESSES 13 8 1 OCEAN ACIDIFICATION 13 8 2 DENITRIFICATION 13 8 3 HARMFUL ALGAL BLOOMS 13 8 4 HYPOXIA 13 9 MODELING FISH – STOCKS AND RECRUITS 13 9 1 STOCK–RECRUITMENT RELATIONSHIP MODELING OF THE CLIMATE SYSTEM 14 1 ATMOSPHERIC MODELING 14 2 TEMPERATURE AND CO2 14 3 CLIMATE SYSTEM MODELS 14 4 SCENARIO MODELING 14 5 CLIMATE PROJECTION, DOWNSCALING, AND GOVERNANCE