Equations of Motion - PHYS OCE - Lecture 9

what is the equation for conserved properties derived from continuity equation

∂C/∂t + u(∂C/∂x) +v(∂C/∂y) +w(∂C/∂z) =0

what is the equation for nonconserved properties derived from continuity equation

∂C/∂t + u(∂C/∂x) +v(∂C/∂y) +w(∂C/∂z) =Ah(∂²C/∂x + ∂²C/∂y) + Az(∂²C/∂z) + Qin - Qout

what is local change

∂C/∂t

what is advection

u(∂C/∂x) +v(∂C/∂y) +w(∂C/∂z)

what are heat fluxes

Qin - Qout

what are horizontal diffusion terms

Ah(∂²C/∂x + ∂²C/∂y)

what are vertical diffusion terms

Az(∂²C/∂z)

what is molecular diffusion

fluids contain gradients and mix over time due to molecular motions

what is the molecular diffusion coefficient of sea water

ks = 1.5 × 10^-9 m²/s

is salt or heat diffused faster

heat

why do molecules diffuse faster in the ocean

turbulent mixing

what is turbulence

irregular fluid flow w

what is turbulence caused by

wind stirring, breaking waves, eddies, unstable currents, frction with topography

what are the ways eddy diffusion does not behave like molecular diffusion

eddy coefficients are larger, horizontal larger than vertical, and turbulence affects salt and temp similarly while molecular diffusion of heat > salt

what is the number range of Az

10^-4 to 10^-3

what is the number range of Ah

10^-1 to 10³

what do the equations of motion tell us

ocea motionm=, including currents, circulation, waves, and tides

what are the equations of motion derived from

conservation of momentum

what is the formula for momentum

mass x velocity

what is newtons second law

force = mass x acceleration

what are the equations of motion

du/dt = 1/density EFx, dv/dt = 1/density EFy, dw/dt = 1/density EFz

what are the main forces in the equation of motion

gravity, pressure gradient, friction, and coriolis

which equation of motion does gravity affect

dw/dt = 1/density EFz because it only acts in z direction

what is the gravity term in the equation of motion

Dw/Dt = -g + other forces

how does pressure gradient affect equation of motion

pressure is in the opposite direction to pressure gradient

what is force amplitude

the pressure gradient divided by density

what is barotropic

independent of depth

what is baroclinic

function of depth

what is velocity shear

change of velocity with distance v(z)

what are the two types of viscosity

molecular and eddy

what are the molecular friction terms for constant viscosity

friction(x) = v(∂²u/∂x²) + v(∂²u/∂y²) + v(∂²u/∂z²)

friction(y) = v(∂²v/∂x²) + v(∂²v/∂y²) + v(∂²v/∂z²)

friction(z) = v(∂²w/∂x²) + v(∂²w/∂y²) + v(∂²w/∂z²)

why does molecular viscosity not explain most phenomena in ocean

the ocean is tubulent and mixing

what is the reynolds number

ratio between non-linear terms and molecular friction

what is defined by turbulent floq

large scale stron velocity

what is described by laminar flow

small scale weak velocity

what if Re is large or small

below 1000 is laminar above is tubulent

what is the formula for reynolds number

Re = UL/v

what is the coriolis force

artificial force to account for earth’s rotation

when is coriolis effect maximum

poles and zero at equator