Lecture 18 - Waves in the Ocean

3 different wave classifications

1. longitudinal waves: move left right

2. transverse waves: move up and down

3. orbital waves: circular motion

what classification are ocean waves

orbital waves

progressive waves

profile of a wave moves relative to the medium

standing wave

profile of wave does not move just oscillates in place

what properties of ocean waves do we want to find

wave height, wavelength, wave period, propagation speed, wave spectrum

wave spectrum

wave energy vs wave frequency

what factors affect wave characteristics

gravity, density, wind, ocean depth

how can we study ocean waves

observations, dynamic theory, computer models

what can the basic characteristics of any wave be described by

dispersion relation

dispersion relation

relation between wavelength and period

oldest way to observe waves

from ships and shores

how do you measure waves from observations

estimate wave height relative to a stick and count the wave crests per minute

how do you measure larger waves by observation

estimate length/height of wave relative to ship’s size

types of direct measurements to measure waves

pressure gauge on sea floor, DART, accelerometer in a moored floating buoy

when do you use a pressure gauge on the sea floor to measure waves

for long waves, sealevel change, tsunami detection

example of pressure gauge on sea floor

DART deep ocean assessment and reporting of tsunamis

assumptions for using pressure gauge on sea floor

hydrostatic constant density

when would you use accelerometer in a moored floating buoy

for short waves, nondirectional or direction (there are vertical and horizontal accelerometers)

indirect measurement of waves

satellite remote sensing

what is satellite remote sensing based on for wave measurement

reflective properties of waves using visable light , electromagnetic, and radar

what do you need to know for satellite remote sensing when measuring waves

wave physics like wave steepness, propagation, whitecaps, sea roughness because they all affect reflective properties

what other properties can you derive from waves

wind and surface currents

example of measuring waves from satelltes

scatterometer

what does a scatterometer do when measuring waves

provides data on waves since wave height and steepness depend on wind, wind can be calculated

highest global wind height from satellites

highest waves in southern ocean due to lots of wind

longest type of wave and caused by what

tides and caused by sun and moon

smallest wave type and cause

capillary waves or ripples caused by light

highest wave and cause

swell caused by strong winds

shortest to longest wave period

capillary < chop or seas < swell < seiche < tsunami < tide

seiche waves

those in lakes

what can linear surface waves be described as

sinusoidal form (sine or cosine)

linear surface wave equation

ɳ (x,t) = Asin(kx- ωt)

k in linear surface wave eq

wave number

k wave number eq

2pi/λ

ω from linear surface wave eq

wave frequency 2pi/T

T

wave period

wave period

time it takes 2 successive wave crests to pass a fixed point

λ

wavelength

wavelength

the distance between 2 successive wave crests at a fixed time

A in linear surface wave eq

wave amplitude

wave amplitude

½ wave height H

difference between sine or cosine waves

90 degree phase shift

phase speed equation

c = λ /T

phase speed

propagation of the wave

what challenge does waves rarely being sinusoidal bring

poses a challenges on how to describe them mathematically

significant wave height

average height of the one third highest waves

what does significant wave height tell us

nothing actually significant but is close to what an experienced observer will estimate the height of waves as

example equation of significant wave height Hs

Hs = (h1 + h2 + h3)/3

how do we study different types of ocean waves

measurements and analysis and theoretical studies

what encompasses studying different types of ocean waves theoretically

developing equations, solving them, and studying the waves from the solutions of the equations

assumptions of surface gravity waves

neglect coriolis, constant density, no friction, two dimensional flow from x and z plane, cannot use hydrostatic approx because u~w, constant h, waves small,

what can surface gravity waves solve for

simple waves

3 equations for surface gravity waves

1. continuity equation: ∂u/∂x + ∂w/∂z =0

2. momentum equation for x: ∂u/∂x + u∂u/∂x + w∂u/∂z = -1/ρ∂p/∂x

3. momentum equation for z: ∂w/∂t + u∂w/∂x + w∂w/∂z = -1/ρ∂p/∂z -g

dispersion relation

relation between wave frequency and wave number

what can we learn from dispersion relation

wave speed, impact of water depth, impact of gravity

symbols represented by dispersion relation

ω and k or T and λ

dispersion relation of surface gravity waves

ω² = g k tanh(kh)

tanh(kh) ~kh

shallow water small h and long waves (small k)

tanh(kh)~ 1

deep water (larger h) and short waves (large k)

what does the behavior of the wave depend on

ratio between water depth (h) and wavelength (λ)

kh = ?

kh = 2π(h/λ)

C =?

wave phase speed

C equation

C =g(T/2π)

what makes a wave move faster

longer waves and waves with longer period

dispersive waves

waves of different wavelength move at different speeds

example of dispersive waves

deep water waves (DWW)

non-dispersive waves

wave speed does not depend on the wave properties (all waves move at same speed)

example of non-dispersive waves

shallow water waves (SWW)

equation for dispersive waves

C = sqrt(f(λ/2π))

equation for non-dispersive waves

C = sqrt(gh)

particle motion under waves in deep water

in deep water they will move in a circular motion with decreasing diameter with depth

particle motion under waves in shallow water

elliptical motion with decreasing minor axis with depth

phase speed

propogation of phase, crest location of one wave

group speed

propogation of energy or packet of waves

phase velocity

speed a particular phase of a single wave is moving in space

group velocity

speed a packet of waves is moving in space, the speed in which the energy is moving in space

shallow water waves controller

controlled by depth only

deep water waves controller

controlled by wave length and period

height = ?

2A (amplitude)

phase speed c=?

c =L/T (L= lambda)

wave number =?

k = 2π/λ