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Exploring Physical Oceanography: Mass, Density, Momentum, and Velocity in Frobisher Bay, CANADA

Join Mary O'Brian and David Huntley as they measure density, velocity, and momentum in Frobisher Bay using hydrocast, CTD, radars, and sonars. Learn about the laws of motion, calculus, and the time rate of change in natural systems. Dive into equations of motion and study key concepts in physical oceanography.

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Exploring Physical Oceanography: Mass, Density, Momentum, and Velocity in Frobisher Bay, CANADA

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

  5. Law of Motion (Physics): F = m * a Force = Mass * Acceleration Sum of all forces = time-rate of change of (mass*velocity) � if velocities small relative to speed of light � if measured in an appropriate frame of reference (one that does NOT rotate) Forces and velocities have magnitude and direction that vary in time and space.

  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 Or per unit volume: ∑  = *dv/dt 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 c = dv/dt c * dt = dv Model: [F=m*a] Integration-1: [computer] c*∫ 1 dt = ∫ 1 dv c*(t-0) = v(t)-v(t=0) Initial condition: [data] v(t=0) = v0 Solution-1: [prediction] v(t) = v0+c*t

  9. v(t) = v0 + c*t Solution-1: Recall: v = dx/dt v*dt = dx Integration-2: [computer] ∫ v(t) dt = ∫ 1 dx ∫ (v0 + c*t) dt = ∫ 1 dx v0*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

  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.

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