Physical Oceanography:
description
Transcript of Physical Oceanography:
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.