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Physical Model(l)ing Marine sciences ‘SUPERCOMPUTERS’ Numerical models ‘Computational oceanography’ ‘SUPERCOMPUTERS’ Numerical models ‘Computational oceanography’ ‘SUPERCOMPUTERS’ Numerical models ‘Computational oceanography’ ‘SUPERCOMPUTERS’ Numerical models ‘Computational oceanography’ ‘SUPERCOMPUTERS’ Numerical models ‘Computational oceanography’ ‘SUPERCOMPUTERS’ Numerical models ‘Computational oceanography’ ‘SUPERCOMPUTERS’ Numerical models ‘Computational oceanography’ NCOM Global ocean model NCOM Iberia Peninsula FVCOM Coastal models Physical Modeling Laboratory models Harbours break-waters Scaling ‘DIMENSIONAL ANALYSIS’ Physical Modeling Laboratory models Harbours break-waters Scaling ‘DIMENSIONAL ANALYSIS’ Physical Modeling Laboratory models Harbours break-waters Scaling ‘DIMENSIONAL ANALYSIS’ Physical Modeling Laboratory models Harbours break-waters Scaling ‘DIMENSIONAL ANALYSIS’ Physical Modeling Laboratory models Harbours break-waters Scaling ‘DIMENSIONAL ANALYSIS’ DELFT HYDRAULICS, NERTHERLANDS CORIOLIS PLATFORM, FRANCE Scheldt wave flume 56 x 1 x 1.2 m LABORATORY MODELING WAVES + CIRCULATION+SEDIMENTS... rotating platform 13 x 1.5 m DELFT HYDRAULICS, NERTHERLANDS CORIOLIS PLATFORM, FRANCE Scheldt wave flume 56 x 1 x 1.2 m LABORATORY MODELING WAVES + CIRCULATION+SEDIMENTS... rotating platform 13 x 1.5 m DELFT HYDRAULICS, NERTHERLANDS CORIOLIS PLATFORM, FRANCE Scheldt wave flume 56 x 1 x 1.2 m LABORATORY MODELING WAVES + CIRCULATION+SEDIMENTS... rotating platform 13 x 1.5 m issues to consider: Simplification (of some aspects) Validation => compare w/ reality Trial / error => LOTS! Observations Isolate Important factors Phenomena Research available models Parameterize MODELING MARINE PROCESSES Run Model + Analyze solution AFTER: PHILIP DYKE, (1996). MODELLING MARINE PROCESSES. PRENTICE HALL. LONDON Interpret marine terms Validate compare observations Study dynamics + predict Yes Satisfactory ? No NUMERICAL SOLUTION PROCEDURE Physical system i.e. reality Physical laws + models Mathematical model GFD => PDEs Discretization Algebraic equations Matrix solver Numerical solution NEWTON’S LAWS OF MOTION First law There exists a set of inertial reference frames relative to which all particles with no net force acting on them will move without change in their velocity. This law is often simplified as "A body persists its state of rest or of uniform motion unless acted upon by an external unbalanced force." Newton's first law is often referred to as the law of inertia. Second law Observed from an inertial reference frame, the net force on a particle is proportional to the time rate of change of its linear momentum: F = d(mv)/dt. This law is often stated as "Force equals mass times acceleration (F = ma)": the net force on an object is equal to the mass of the object multiplied by its acceleration. Third law Whenever a particle A exerts a force on another particle B, B simultaneously exerts a force on A with the same magnitude in the opposite direction. The strong form of the law further postulates that these two forces act along the same line. This law is often simplified into the sentence, "To every action there is an equal and opposite reaction." NEWTON’S SECOND LAW OF MOTION ‘ADIMENSIONAL APPROACH’ CONSIDERING: L-LENGTH M -MASS T-TIME SPEED = LENGTH / TIME => LT −1 DENSITY = MASS / LENGTH *LENGTH*LENGTH => pressure = Pascal (N/m^2) N=Kg m / s Mass / Length * Time^2 => −3 ML M L−1 T −2 F=ma <=> Fm=a force per unit mass=acceleration L.H.S. = R.H.S. IN THE OCEAN THIS MEANS: PRESSURE+GRAVITY+TURBULENCE = ACCELERATIONS CORIOLIS + ADVECTIVE + POINT Ω×u ΩU (u∇)u 2 −1 U L ∂u ∂t −1 UT NABLA - SPATIAL GRADIENT ∂u ∂v ∂w (u· ∇) = + + ∂x ∂y ∂z ∂u ∂u ∂u (u· ∇)u = u +v +w ∂x ∂y ∂z HOW TO EVALUATE THE BALANCE BETWEEN CORIOLIS / ADVECTIVE ACCELERATION ? 2 −1 U L ΩU U = fL ‘Rossby number’ (Ro) ADVECTIVE VS POINT ACCELERATION DUE TO CHANGE IN RELATIVE POSITIONS OF FLUID PARTICLES RATE OF CHANGE WITH RESPECT TO TIME A A to t1 B t2 B TURBULENCE <=> MOLECULAR VISCOSITY + FRICTIONAL FORCES Fh Fv ∂2u ∂2u VH 2 + 2 ∂x ∂y ∂2u Vv 2 ∂z −2 νU D νU L CORIOLIS / TURBULENCE −2 νU L ΩU = νΩ −1 −2 L Ekman number (Ek) −2 −2 νU D ΩU = νΩ −1 D −2 MASS CONSERVATION ‘matter is neither created or destroyed’ W D U.D U L W.L CONTINUITY: U.D=W.L => W=UD/L ∂u ∂v ∂w ∇·u= + + =0 ∂x ∂y ∂z NEWTON’S SECOND LAW FOR THE OCEAN PUTTING IT ALL TOGETHER POINT_AC+ADVECT_AC+CORIOLIS=PRESSURE+FRICTION (FH,FV) 1 ∂p ∂u ∂u ∂u ∂u ∂2u ∂2u ∂2u +u +v +w − fν = − +VH ( 2 + 2 ) +Vv ρ ∂x ∂t ∂x ∂y ∂z ∂x ∂y ∂z 2 ∂2v 1 ∂p ∂v ∂v ∂v ∂v ∂2v ∂2v +u +v +w +f u = − +VH 2 + 2 +Vv 2 ∂t ∂x ∂y ∂z ρ ∂y ∂x ∂y ∂z ∂w ∂w ∂w ∂w 1 ∂p ∂2w ∂2w ∂2w +u +v +w =− +V −g + VH 2 + v 2 ∂z 2 ∂t ∂x ∂y ∂x ∂y ∂z ρ ∂z ∂u ∂v ∂w + + =0 ∂x ∂y ∂z Gulf-Stream L ~100 km ~100 000m Ux~1; Uy~0.1 m/s f~10^(-4) s^(-1) Gulf-Stream L ~100 km ~100 000m Ux~1; Uy~0.1 m/s f~10^(-4) s^(-1)
