Phys 629: Selected Topics in Physics I (Spring 2020) — Fluid Mechanics & Acoustics in the Ocean

Instructor: Dr. Zheguang Zou (zou@olemiss.edu)
Lectures: Monday, Wednesday, Friday 9:00-9:50am @ Google Meet (http://meet.google.com/rej-rjte-ejp)
Office Hours: Online, by appointment
Website: https://zou.olemiss.edu/phys629

Syllabus | Lectures | Homework

Fluid Mechanics

Lecture 01 - Introduction & Fluid Properties (1/22)

• What is a fluid?
  • DEF. — deforms contineously when acted on by a shearing stress of any magnitue.
  • sheering stress
  • tangential force
• "Heaviness"
  • density
  • specific volume
  • specific weight
  • specific gravity

Lecture 02 - Fluid Properties (cont.) (1/24)

• Compressibility
  • bluk modulus
  • compressible vs. incompressible fluids
  • isothermal vs. isentropic processes
  • sound speed
• "Stickiness"
  • viscosity
  • no-slip condition
  • shear stress
  • rate of shearing strain
  • Newtonian vs. Non-Newtonian
  • shear thinning vs. shear thickening

Related Videos:

• Test the Viscosity of a Liquid
• Shear Thickening vs. Shear Thinning
• Shear Thickening Fluids
• Fun with Non-Newtonian Fluid (shear thicking)
• Why is ketchup so hard to pour?

Lecture 03 - Fluid Properties (cont.) (1/27)

• Surface Tension
  • \sigma = F/L
  • mechanism: due to imbalance of molecular force
  • Why droplets are spherical? — To minimize the surface area
  • contact line
  • contact angle
  • high/low wetting = small/large contact angle
  • capillary rise (wetting) vs. capillary fall (non-wetting)
  • cohesive force (liquid) vs. adhesive force (solid-liquid)

Related Videos:

• Floating Razor Blade
• Water strider - Walking on water
• What is Surface Tension?
• Soil Basics: Capillary Rise

Lecture 04 - Fluid Statics (1/29)

• Pressure at a Point
  • Pascal's law: the pressure at a point in a fluid at rest, or in motion, is independent of direction as long as there are no shearing stresses present.
• Basic Equation for Pressure Fields
  • surface force; body force
  • gradient operator
  • pressure gradient
  • general equation of motion
• Pressure Variation at Rest
  • depends on depth only (shape or size doesn't matter)
  • pressure head

Related Videos:

• The Science of Water Pressure
• The effects of underwater pressure on the body

Lecture 05 - Fluid Statics (cont.) (1/31)

• Hydraulics
  • hydraulic lift, hydraulic press
  • requirements: imcompressible fluid; no air
• Pressure Measurement
  • absolute pressure
  • gauge pressure
  • standard atmosphere pressure: 101.325 kPa (or 14.7 psi)
  • underwater pressure: ~ 1 atmophere pressure every 10 m
  • piezometer, U-tube, etc.
• Buoyancy
  • Archemedes' Priciple
  • stability of floating objects

Related Videos:

• Basic Principles of Hydraulics Explained
• How taking a bath led to Archimedes' principle

Lecture 06 - Fluid Statics (cont.) (2/7)

• Pressure Variation in Linear Motion
  • linear acceleration
  • curvature: line
  • example: a bottle of Coke in an accelerating car
• Pressure Variation in Rotation
  • angular acceleration
  • gradient in cylindrical coordinates
  • curvature: parabolic shape

Related Videos:

• Rotating Water Tank
• Spinning Water: The Experiment

Lecture 07 - Elementary Fluid Dynamics & Bernoulli Equation (2/10)

• Fluid Particle
• Velocity Vector
• Streamlines
  • DEF. = lines that are tangent to velocity vector
  • two acceleration components
    • a_s: along a streamline
    • a_n: normal to a streamline
• Ideal Flows
  • inviscid (no viscosity)
  • steady (no change over time)
  • imcompressible (density doesn't change)
• Bernoulli Equation (along a streamline)

Related Videos:

• Fluid Flow and Vector Fields
• Physics: Fluids in Motion: Streamlines, Continuity

Lecture 08 - Bernoulli Equation (cont.) (2/12)

• Bernoulli Equation (normal to a streamline)
• Static, Dynamic, Hydrostatic Pressures
• Stagnation
  • stagnation point
  • stagnation streamline
• Conservation of Mass (continuity equation)
• Pitot-Static Tube: to measure flow velocity
• Free Jet

Related Videos:

• Stagnation Point in a Flow
• Illustration of Stagnation Point
• Pitot-Static Tube
• Pitot-Static Systems in a Airplane

Lecture 09 - Bernoulli Equation (cont.) & Fluid Kinematics (2/14)

• Cavitation
  • pressure and boiling point
• Flow Descriptions
  • Eulerian: one fixed position
  • Lagrangian: one particle
• Pathline (vs. Streamline)
• Velocity Components (u, v, w)
• Material Derivative (D/Dt)
  • as "seen" by a material point
  • local term
  • convective term
• System, Control Volume, Control Surface

Related Videos:

• Cavitation
• Eulerian and Lagrangian Descriptions in Fluid Mechanics

Lecture 10 - Fluid Kinematics (cont.) (2/17)

• Flow Rate
  • volume flow rate
  • mass flow rate
  • in vector form: the area vector is always pointing outwards from the volume
• Extensive vs. Intensive Property
  • B = mb
  • unit of b = [unit of B]/kg
• Reynolds Transport Theorem
  • link between system & control volume
  • net outflow = outflow - inflow

Related Videos:

• Reynolds Transport Theorem (hahaha~)

Lecture 11 - Fluid Kinematics (cont.) & Finite Control Volume Analysis (2/19)

• Reynolds Transport Theorem and Material Derivative
  • a collection of fluid particles vs. a fluid particle
  • in fact, dB/dt = DB/Dt
• Conservation Laws (applying Reynolds Transport Theorem)
  • Conservation of Mass
  • Conservation of Momentum (Newton's Second Law of Motion)
  • Conservation of Energy (First Law of Thermodynamics)
• Absolute Velocity and Relative Velocity
  • V (abs velocity) = W (relative) + V_cv (velocity of control volume)

Related Videos:

• The Law of Conservation
• Relative Vecolity - How Fast Are You Moving?

Lecture 12 - Differential Analysis (2/26)

• Linear Deformation
  • imcompressible condition
• Angular Deformation
  • irrotational condition
  • vorticity
• Conservation of Mass (differential form)

Related Videos:

• Rotational & irrotational flows

Lecture 13 - Differential Analysis (cont.) (2/28)

• Stress
  • normal stress
  • shearing stress
• Eulers Equation of Motion (without viscosity)
  • assupmtion: imcompressible, no viscosity
• Navier-Strokes Equation (with viscosity)
  • assumption: imcompressible, constant viscosity

Related Videos:

• Navier-Strokes Equation and $1 Million Problem

Lecture 14 - Differential Analysis (cont.) & Dimensionless (3/2)

• Navier Strokes Equation
• Reynolds Number
  • inertial force vs. viscous force
  • Laminar flows (Re < 2000)
  • Turbulent flows (Re > 4100)
• Mach Number
  • inertial force vs. compressible force
  • imcompressible (Ma < 0.3)
• Bond Number
  • gravitational force vs. surface tension

Related Videos:

• water looks frozen but isnt - laminar flow illusion
• Laminar Flow is AWESOME

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Ocean Dynamics

Lecture 15 - Introduction & Physical Settings (3/4)

• Physical Settings of the Earth
  • Earth Radius: Re = 6378 km, Rp = 6357 km
  • Latitude: 1 deg = 111 km
  • Longitude: 1 deg = 111 cos(Latitude) km
  • Nautical Mile (nm): 1 nm = 1.852 km
• Continental Margin
  • continental shelf, slope, rise
• Ocean Basin
  • abyssal plains, hills, seamounts, trenches
• Mid-Ocean Ridges
• Aspect Ratio: ~1:1000
  • the ocean is shallow if compared to its width

Lecture 16 - The World Ocean (3/6)

• Oceans
  • Pacific Ocean: largest, 1/3 of earth surface, oldest ocean
  • Atlantic Ocean: 2nd largest, 1/5 of earth surface, youngest ocean
  • Indian Ocean: 3rd largest, currents change direction twice a year due to monsoon
  • Artic Ocean: smallest, shallowest, 50% being continental shelf
  • Southern Ocean: not existed before 2000, defined by antartica circumpolar currents
• Scales
  • time scale: 0.1 s to 10^4 years
  • sptial scale: 1 mm to 10^4 km
• Some Ocean Phenomona
  • capillary-gravity waves
  • surface wind waves
  • internal waves
  • eddies

Related Videos:

• Learn 5 Oceans of the Earth
• Modeling Dynamic Surface Ocean Currents

Lecture 17- Physical Properties of Seawater

• Pressure
  • hydrostatic balance
  • 1 bar = 10^5 Pa = 1 atmosphere pressure
  • 1 dbar = 0.1 bar = pressure caused by water of 1 m depth
• Temperature
  • absolute temperature (Kelvin)
  • adiabatic process
  • potential temperature
    • take out the temperature raise due to compression
• Salinity
  • the measure of how many grams of salt in 1 kg seawater (
    • unit: parts per thousand (ppt)
  • morden measurement: based on conductivity
    • unit: psu (practical salinity unit)
  • CTD (conductivity, temperature, depth) profiler

Related Videos:

• Oceanographic Sampling

Lecture 18- Physical Properties of Seawater (Cont.)

• Density
  • seawater density: often write out last two digits
  • depends on temperature, salinity and pressure
  • potential density
    • density calculated from the potential temperature
• Temperature-Salinity (T-S) Diagram
  • water parcel remains its temperature and sanlity characterists once sink from the surface
• Thermohaline Circulation

Related Videos:

• Global Convey Belt

Lecture 19 - Ocean Circulations (4/1)

• Two Types of Ocean Circulations
• Thermohaline Circulation
  • deep ocean
  • density-driven
  • low-latitude vs. high-latitude profiles
  • pycnocline, thermocline
• Wind-Driven Circulation
  • atmospheric circulation
  • Coriolis effect
    • deflection of moving fluids
    • northern hemisphere
  • ocean gyres

Related Videos:

• Global Convey Belt
• Atmospheric Circulation
• Coriolis Effect

Lecture 20 - Ocean Circulations (Cont.) (4/3)

• Ekman Theory
  • Ekman spiral
  • Ekman transport: net water transport due to surface wind
  • directions of wind, surface current, and net water transport
• Upwelling and Downwelling
  • coastal regions
  • equator upwelling
  • biological production
• Geostrophic Balance
  • horizontal pressure gradient force
  • coriolis force
  • geostrophic flow along isobars
• Sea Surface Height
  • invert geostrophic currents
  • satellite altimetry
• eddies
  • warm core rings and cold core rings

Related Videos:

• Ekman Theory: Wind, Surface Currents, Upwelling and Downwelling
• Sea Surface Height from Satellite Altimetry
• How do ocean currents work?

Lecture 21 - Tides (4/6)

• Tidal Force
• Two Water Bulges
  • gravitational force and centrifugal force
  • high tide and low tide
• Tidal Patterns
  • semidiurnal tides
  • diurnal tides
  • mixed tides
• Spring and Neap Tides
  • the alignment of sun and moon
  • spring tide: full moon or new moon
  • neap tide: first-quarter moon or third quater moon
• Lunar Day
  • period: 24 hr 50 mins
• Tidal Prediction

Related Videos:

• Spring Tides in Halls Harbour, Bay of Fundy
• Tides in The Hopewell Rocks

Lecture 22 - Tides (Cont.) (4/8)

• Tides in a Narrow Basin
  • deflected to the right (left) in the northern (southern) hemisphere due to Coriolis Effect
  • tidal time and range
• Tides in an Open Basin
  • slossing water
  • amphidromic system
    • tidal spider
    • amphidromic point (AP)
• Tidal Bores
  • A large wave caused by the constriction of the spring tide as it enters a long, narrow, shallow inlet
  • the biggest tidal bore in the world: Qiantang River, China
• Tidal Currents
  • flood: seawater moves landward
  • ebb: seawater moves seaward
  • slack: tidal current is about to reverse direction
• Estuaries
  • interaction between freshwater and seawater
  • stratification patterns

Related Videos:

• Tidal Bores in Qiantang River | National Geographic

Lecture 23 - Waves (4/13)

• Wave Parameters
  • wavelength, wavenumber
  • wave period, angular frequency
  • wave speed
  • dispersion
• Water Motion
• Deep Water Waves
  • water depth > 1/2 wavelength
  • Waves can feel the bottom
  • circular motion
• Shallow Water Waves
  • water depth < 1/20 wavelength
  • Waves cannot feel the bottom
  • elliptical motion
• Wind-Driven Ocean Waves
  • generation: wind speed, fetch, duration
  • sea: "confused", irregular state, strong wave interefence
  • swell: regular state, dispersion
  • surf: get to coastal area
    • wave breaking
    • wave refraction

Related Videos:

• Confused Sea
• How do waves break?

Lecture 24 - Waves (Cont.) (4/15)

• Tsunami
  • Japanese: "harbor waves"
  • caused by an earthquake, submarine landslide, or other disturbance
  • big wave, high energy
  • shallow water wave (wavelength >> water depth)
  • speed: extremely fast
• Internal Waves
  • stratification in the ocean
  • waves inside the ocean interior
  • surface signature
  • stability
  • Buoyancy Frequency

Related Video:

• How Tsunami Work?
• Internal Waves

Lecture 25 - Waves (Cont.) 4/20

• Internal Waves
  • buoyancy frequency, N
  • internal interfacial waves
  • Internal waves in continuously stratified ocean
    • inertial currents
    • Coriolis frequency
  • generation
• Kelvin Waves
  • Coriolis effect
  • at the equator
• Rossby Waves
  • planetary, relative and total vorticity
  • conservation of total vorticity
• Wave Type, Restoring Force, and Dispersion Relation

Related Videos:

• Buoyancy Frequency
• Kelvin Waves
• Rossby Waves

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Ocean Acoustics

Lecture 26 - Basics of Sound Propagation (4/22)

• Sound Speed
  • lower compressibility, higher sound speed
  • increase with temperature, salinity and pressure
• Refraction
  • Snell's Law
  • "lazy": bending to smaller sound speed
• Sound Speed Profiles
  • positive: down-refracting
  • netactive: up-refracting
• Multipath Effect
  • direct path, surface reflection, bottom reflection
• Transmission Loss
  • sphereical spreading ~ R^2
  • cylindrical spreading ~ R (shallow-water)

Lecture 27 - Basics of Sound Propagation & Time-Varying Environment (4/24)

• Attenuation
  • absorption
  • scattering
• Rayleigh Parameters
  • P < 1, coherent reflection
  • P > 1, incoherent scattering
• Doppler Effect
• Ambient Noise
• Variability
  • daily: tidal dynamics
  • seasonal: seasonal temperature, global dynamics
• Ocean dynamics
  • Internal Waves
  • Biological Effect

Lecture 28 - Sound Propagation in the Ocean (4/27)

• Acoustic Modeling
  • ray-tracing model
  • parablic equation (PE) model
• Acoustic Channel
  • multipath effect
  • direct path
  • surface reflections

Lecture 29 - Environmental Variability on Acoustics (4/29)

• Ocean Stratification
  • temperature, salinity and density
• Estuariane Stratification
  • ebbing vs. flooding

Lecture 30 - Environmental Variability on Acoustics (5/1)

• Direct-path Fading Phenomenon
• Richardson Number
• Case Study: HFA97