Physical Oceanography:

• Mass is conserved– density measurements (mass/volume)

• Momentum* is conserved– velocity measurements

(*) momentum=mass*velocity

Mass: Hydrocast and CTD

Frobisher Bay, CANADA

Mary O’Brian, chemistry, lab technician

David Huntley with “sonar”

Velocity:Radars + Sonars

Radars send and receiveelectromagnetic waves (radio, police)

Sonars send and receives acoustic waves (sound, whales)

Same physics.

Force = Mass * Acceleration

Sum of all forces = time-rate of change of (mass*velocity)

F = m * a

Law of Motion (Physics):

Forces and velocities have magnitude and direction that vary in time and space.

� if velocities small relative to speed of light � if measured in an appropriate frame of reference (one that does NOT rotate)

Time Rate of Change (Mathematics):

A most fundamental property of all natural systemsat all scales from universe to sub-nuclear particles

Calculus:

Formalizing “time rate of change” to answer the question

How do we calculate the difference of a property at time t and a little time dt later as dt approaches zero?

Sum of all forces = time-rate of change of (mass*velocity)

∑ F = m*dv/dt

∑ = *dv/dt

Or per unit volume:

where

=force/volume=mass/volume=density

Example: F is a constant wind force is a constant ocean densityc=F/=const.Find v(t) of a water parcel

Model:[F=m*a]

c = dv/dtc * dt = dv

Integration-1:[computer]

c*∫ 1 dt = ∫ 1 dvc*(t-0) = v(t)-v(t=0)

Initial condition:[data]

v(t=0) = v0

Solution-1:[prediction]

v(t) = v0+c*t

Solution-1: v(t) = v0 + c*t

Recall: v = dx/dt

Integration-2:[computer]

v*dt = dx

∫ v(t) dt = ∫ 1 dx

∫ (v0 + c*t) dt = ∫ 1 dxv0*t + c*t2/2 = x(t)-x(t=0)

Initial condition:[Data]

x(t=0) = x0

Solution-2:[Prediction]

x(t) = x0 + v0*t + c*t2/2

Homework: Please read Knauss (1997), chapter-5:

p. 81-85 (acceleration and pressure gradient)p. 87-89 (Coriolis force)p. 96-99 (friction, eddy viscosity, wind stress)p. 101-102 (Reynolds stressp. 104 (Equations of motion)

Study guide questions will be posted 9/16 noon atClass web-site.