Waves Waves result from interplay between disturbing forces & restoring forces In the oceans, disturbances originate –At the surface, winds, ships, etc. perturb still water –At the bottom, earthquakes, volcanic explosions, submarine landslides, etc. perturb the still water Primary restoring force for water waves is gravity Waves transport effects of local disturbance to other parts of the disturbed substance –Effect of disturbance moves through a substance with little (if any) movement of the substance itself

Waves All wave phenomena result from interplay between disturbing forces & restoring forces All wave phenomena transport the effects of a local disturbance to other portions of the disturbed substance –Effect of disturbance travels through a substance, but there is little (if any) transport of the substance itself In the oceans, disturbances originate –At the surface, where winds, ships, etc. perturb the flat surface of the water –At the bottom, where earthquakes, volcanic explosions, submarine landslides, etc. perturb the still water Primary restoring force for water waves is gravity These perturbations generate waves that travel along the surface of the ocean (along interface between air and water) –or waves that travel along interfaces between water masses with different properties - internal waves

Some terminology for waves

Ideal waves Have sinusoidal form Have regularly-spaced crests or troughs Vertical distance from crest to trough = wave height (H) Horizontal distance between adjacent crests (or troughs or inflection points) = wave length (L )

Progressive waves Effect of disturbance, either a lone wave crest, a lone wave trough or a sequence of several crests & troughs, travels through water (think of effect of a pebble tossed in a pond) –We call these water waves progressive waves In some cases that we will examine, a wave’s inflection point may appear to be stationary while the wave crests become troughs & the wave troughs become crests –We call these water waves standing waves Standing waves are really the sum of two or more progressive waves (more about this later)

Progressive waves As progressive wave moves through water, different water parcels occupy crest at different times Frequency (F) of wave is the number of crests or troughs that pass a point per unit time –Measure frequency in cycles per second Period (T) of wave is the time interval between the passage of successive crests or troughs Wave speed (C) = wavelength divided by period (C= L/T) Wave speed (C) wavelength times frequency (C = LF)

Progressive wave movement As ideal progressive waves move through water, they cause individual parcels of water to oscillate The oscillation of water parcels in water waves does not match movement in longitudinal or transverse waves Water waves are orbital waves; parcels trace out circular (or elliptical) orbits Radius of orbital circle decreases with depth At water depth D = L/9 = 0.11L, radius of path is about half that at surface No water movement due to wave passage at depth greater than D = L/2

Sea surface rarely resembles shape of ideal waves Sea surface has irregular form that is the sum of many different waves traveling through water simultaneously - waves interfere constructively or destructively

Constructive interference

Destructive interference

Shapes of water waves If L>1.73 cm or T>0.1 sec, gravity is the primary restoring force for water waves Gravity causes the shapes of water waves to vary with relative sizes of wave height H & wavelength L When H/L is small, wave form resembles a sine curve When H/L is large, wave crests become more pointed & wave takes a shape called a trochoid H/L ratio, called the wave steepness, correlates with wave stability –When H/L 120°, wave is stable –When H/L = 1/7 and crest angle = 120°, wave is unstable & breaks

Deep water vs. shallow water waves Water waves are orbital waves; parcels trace out circular or elliptical orbits Observe different orbits as wave travels from deep to shallow water Deep water vs. shallow water - all relative to wavelength Where water depth (D) exceeds one half the wavelength (D>L/2), get deep water wave Where water depth (D) is less than one half the wavelength (D<L/2), get shallow water wave

Deep water waves Water depth D>L/2 Wave forms are sinusoidal or rounded Individual water parcels trace out circular orbits –At surface paths have relatively large diameter & do not quite close –Diameters of paths decrease with depth –Effect of passing wave not felt below L/2 Wave speed is a function of only wavelength or only wave period C = g T/ 2  or C = (g L) 1/2

Shallow water waves Water depth D<L/2 Wave usually have trochoidal shapes Individual water parcels trace out elliptical orbits –Passage of wave affects water particles to depth of D = ~L/2, but that is entire water column –As waves feel the bottom, the interaction alters the orbital shape from circular to elliptical –Elliptical shape is flatter nearer the bottom –At bottom, water particles simply sway back & forth Wave speed is a function of only water depth C = (g D) 1/2

Wave generation Most waves generated by frictional drag of wind Small fraction of wind energy transferred into drift currents; most energy goes into buckling the surface Wind then generates different pressure on windward & leeward sides of buckles, causing buckles to grow into waves & then causing waves to move Energy transferred into water as waves depends on –Wind speed –Consistency of wind direction –Duration - how long consistent wind blows –Fetch - maximum length of open water over which constant wind blows

Waves at their point of origin Directly under wind (i.e. under a storm), usually find sea, which is an irregular, choppy water surface Irregular surface that we call sea is the net result, literally the sum, of many different waves traveling through water simultaneously Waves interfere constructively & destructively to create rough water surface

Waves far from their point of origin As waves move away from where they were generated, they tend to disperse –Dispersion = separation of waves on the basis of their period or wavelength –Dispersion occurs because deep water waves move at speed proportional to wave period or wavelength –Longer wavelength waves move away faster Dispersion leads to swell - smoother water surface with long-crested waves of nearly constant wavelength (or period) May see wave train or group behavior (another effect of wave interference)

Wave refraction Where water depth D>L/2, get deep water wave Where water depth D<L/2, get shallow water wave As wave travels from deep to shallow water, speed changes from function of wavelength (C = [gL] 1/2 ) to function of depth (C = [gD] 1/2 ) –When D = L/2, deep & shallow water wave speed equations predict same speed –When D<L/2, waves eventually slow & may refract

As waves travel to shore Waves might slow by reducing wavelength (L) or increasing period (T); observe that waves reduce L but keep T constant –Wave height & kinetic energy remain constant (in fact waves that follow may add energy to waves already slowed) –Crest heights of waves often increase –Waves steepen, & often take on trochoidal form –Energy of water particles in different parts of wave remains nearly constant –Particles in upper parts of wave less affected by bottom, so keep circular path

In response to the slowing, steepening, etc, waves eventually break, usually when wave height H = 0.8D

Breaking waves Shallow water waves feel the bottom, and, because their speed depends on the water depth, slow down Orbits of water particles near sediment water interface first become elliptical then devolve to a back-and-forth movement as waves travel to shallower water Waves could slow by reducing wavelength (L) or increasing period (T); observe that waves reduce L but keep T constant –Wave height is unchanged but wavelength is shorter, so waves steepen, and often take on trochoidal form –As waves slow, their total kinetic energy remains about the same; later waves add energy to waves already slowed, so crest heights of waves may actually increase –Energy of particles of water at different positions in wave remains as nearly constant as possible; particles in upper parts of wave less affected by bottom, so keep circular path In response to the slowing, steepening, etc, waves eventually break, usually when wave height H = 0.8D

Types of breaking waves Spilling breakers - wave crests spill forward, creating foam and turbulent water, as wave fronts travel across a gently- sloped beach Plunging breakers - wave crests form spectacular open curl; crests fall forward with considerable force, dissipating energy in a well-defined area on a moderately-sloped beach Collapsing breakers - wave fronts form steep faces that collapse as waves move forward across a moderately-sloped beach under moderate winds Surging breakers - long, relatively low waves whose front faces and crests remain relatively unbroken as waves slide up and down a steeply-sloped beach