PHYS OCE - intro to equations of motion- continuity- Lecture 8

what is the conservation of mass equation

continuity equation, how velocity components relate to each other

what is an example of continuity equation

upwelling/downwelling

what is conservation of heat equation

temperature equation that predicts how temp changes

what is an example of conservation of heat

daily and seasonal cycle changesw

what is the conservation of salt equation

salinity equation that predicts how salinities change

what is conservation of momentum

equations of motion (u, v, w)

what is an example of conservation of momentum

ocean currents where momentum = mass x velocity

why do we use partial derivative instead of d

because properties are a function of multiple variables - not just one

what do differential equations tell us

changes in variables

what do differential equations not tell us

the exact variables at a specific time and place

what is a derivative

slope at point X of function f(X)

what does the first derivative tell us

slope, how big small

what does the second derivative tell us

the curvature of the line, positive U, negative opposite

what are partial derivatives in phys oceano

function of more than one variable

what is the formula for velocity vector

V = ui + vj = wk

what is a conserved property

without sinks or sources, the change is zero

formula for mass flux

mass flux = density x velocity x area

what is the formula for the continuity equation of an incompressible fluid

∂u/∂x + ∂v/∂y ∂w/∂z = 0

what is the equation for boussinesq approximation

D(density)/Dt = 0

what is the boussinesq approximation

since ocean densities are small and water compressibility is small, seawater is assumed to be incompressible

why can we not use boussinesq approximation for atmosphere

density of air changes alot due to temp, P, and humidity

what are applications of continuity equation

measure horizontal velocities and vertical velocities

what are examples of horizontal velocities measured by continuity equation

CODAR current meters and satellite altimetry

what are examples of vertical velocities measured by continuity equation

upwelling increased by biological productivity

when are currents divergent

u + v > 0

when are currents convergent

u + v< 0

are converging currents downwelling or upwelling

downwelling

are diverging currents upwelling or downwelling

upwelling

where is upwelling and downwelling more prevalent

near coast, topographic features

why is upwelling important for biological productivity

wind blows along shore, and coriolis blows it away from coast so it causes upwelling of nutrients from deep ocean