9.4: Making Waves
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Once they are created, waves must have a restoring force to sustain the wave motion, but waves must be formed initially by a displacing force. Small waves can be created by small displacing forces acting over short periods of time. Large waves can be created only by large displacing forces or lesser displacing forces exerted continuously for extended periods of time.
Most ocean waves are caused by the interaction of winds with the water surface, but waves are also created by impacts on ocean water, by rapid displacement of ocean water, by gravitational attraction between the Earth, moon, and sun, and by the passage of vessels or marine animals through the ocean surface. The ocean waves created by these various processes vary from waves with a period of less than one-tenth of a second to waves with a period of more than a day (Fig. 9-5).
Impact and Displacement Waves
Waves can also be created by impact or displacement. For example waves can be created by earthquakes or volcanic explosions that cause the seafloor to move abruptly, and by meteorite impacts on the ocean surface. Rapid displacements of ocean water can be caused by seafloor slumps (landslides) and turbidity currents, and by collapses of coastal cliffs. Such impacts can create waves with very long periods (typically 10 to 30 min) called tsunamis (or sometimes “seismic sea waves”). Tsunamis are occasional events and contribute only a fraction of the total wave energy of the oceans (Fig. 9-5), but they can be extremely destructive.
Impact and displacement waves can also be generated by comparatively minor events, such as whales and dolphins jumping out of the water and ships moving through the water leaving wakes. Waves created by these minor impacts are insignificant in number and intensity, in comparison with wind-generated waves. However, in sheltered harbors ship wakes may be the principal source of wave energy and erosion of the shoreline.
The gravitational attraction between the Earth, moon, and sun is the force that creates waves that we know as tides (Chap. 10). Tide waves have periods of predominantly about 12 or 24 h and contribute a significant amount of the total wave energy of the oceans (Fig. 9-5).
Wind Waves
As we know from experience, winds are highly variable, or gusty, and may change speed and direction from second to second. Air moving over a land or ocean surface becomes turbulent when more than a gentle breeze blows. Small variations of wind speed and pressure that occur as the wind blows across a smooth ocean surface are believed to lead to the creation of capillary waves, which then grow larger if the wind continues to blow. Capillary waves have a maximum wavelength of 1.73 cm, rounded crests, and V-shaped troughs.
Winds generate waves on lakes and other fresh water bodies as well as in the oceans. While ocean waves are considered here, the principles of wind wave generation discussed in this section apply equally to all water bodies, including bodies such as lakes, estuaries, and rivers.
The mechanism by which wind generates capillary waves is not fully understood, but two factors seem to be important. First, because of turbulence in the atmosphere, atmospheric pressure is slightly increased at some locations at the sea surface compared to locations a few millimeters or centimeters away. In these areas with slightly higher air pressure, the sea surface tends to be slightly depressed in relation to the adjacent ocean surface, where the pressure is lower. Thus, when winds blow across a perfectly flat sea surface, tiny areas of elevated or depressed sea surface are formed. Second, when winds blow over the ocean surface, a shear stress (friction) develops between the air and water because of the velocity difference across the air-sea interface.
The formation of capillary waves increases the roughness of the surface, which in turn increases the shear stress between wind and ocean surface and this enhances the ability of the wind to build larger waves. Capillary waves also alter the sea surface, so that some areas are tilted slightly up toward the wind (windward side) and others (leeward side) are tilted slightly away from the wind. The wind pushes harder on the back of the wave than on the front, further accelerating and building the wave (Fig. 9-6).
Wind-wave interaction actually is more complicated than this simple description suggests. For example, a wave generates turbulence as the wind flows across the water’s surface just as an aircraft wing alters the airflow to provide the lift necessary for a plane to fly. Once a wave is formed, the wind tends to build the wave height, primarily by uplifting the leeward side of the wave. In addition, differences in wave speeds cause small capillary waves to combine into the longer-period, higher waves called gravity waves. In this way, as the wind continues to blow across the sea surface, wind energy accumulates, and longer-period waves form. These longer period waves comprise most of the ocean’s wind wave energy (Fig. 9-5).

