1. Physical Oceanography: Mass is conserved –density measurements (mass/volume) Momentum* is conserved –velocity measurements (*) momentum=mass*velocity

2. Mass: Hydrocast and CTD Frobisher Bay, CANADA

3. Mary O’Brian, chemistry, lab technician

4. David Huntley with “sonar” Velocity: Radars + Sonars Radars send and receive electromagnetic waves (radio, police) Sonars send and receives acoustic waves (sound, whales) Same physics.

5. 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)

6. Time Rate of Change (Mathematics): A most fundamental property of all natural systems at 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?

7. 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

8. Example:F is a constant wind force  is a constant ocean density c=F/  =const. Find v(t) of a water parcel Model: [F=m*a] c = dv/dt c * dt = dv Integration-1: [computer] c* ∫ 1 dt = ∫ 1 dv c*(t-0) = v(t)-v(t=0) Initial condition: [data] v(t=0) = v 0 Solution-1: [prediction] v(t) = v 0 +c*t

9. Solution-1: v(t) = v 0 + c*t Recall: v = dx/dt Integration-2: [computer] v*dt = dx ∫ v(t) dt = ∫ 1 dx ∫ ( v 0 + c*t) dt = ∫ 1 dx v 0 *t + c*t 2 /2 = x(t)-x(t=0) Initial condition: [Data] x(t=0) = x 0 Solution-2: [Prediction] x(t) = x 0 + v 0 *t + c*t 2 /2

10. 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 stress p. 104 (Equations of motion) Study guide questions will be posted 9/16 noon at Class web-site.