6.1: Introduction
- Page ID
- 4183
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)
The first thing that comes to your mind when I mention water waves are probably the waves that appear on the water surface when the wind blows. These range in size from tiny ripples to giants up to a few tens of meters high and up to a few thousands of meters long. But many other kinds of waves make their appearance on water surfaces in nature. Here are the important kinds:
- Flood waves in rivers: Very long and very low, these waves propagate downstream at a speed that is different from the speed of the flowing water itself. It is important to try to predict both the speed and the maximum height of the flood wave.
- Seiches in lakes and estuaries: These are standing waves that are set up in an elongated basin by a sudden change in water-surface elevation in part of the basin, for example by a sudden drop in atmospheric pressure or by transport of surface water by a sudden strong wind. They may have just one node or more than one node.
- Tidal bores in estuaries: These are waves of translation, in which the water moves along with the wave. They have steep turbulent fronts, which can be hazardous to small boats.
- Tsunamis (seismic sea waves) in the ocean: These are extremely long and low-amplitude waves with high propagation speeds that are generated by sudden large-scale movements of the sea floor, usually by movement on faults but also by volcanic eruptions or submarine landslides. Their extreme destructiveness comes about because their amplitude increases spectacularly, sometimes to several tens of meters, when they shoal.
- Internal waves in the atmosphere and the ocean: When a fluid is stratified by density, waves can develop within the layer through which the density varies. This is easiest to appreciate when the density change is compressed to a jump discontinuity at a well-defined surface, but internal waves can exist also in layers with only gradual change in density. Internal waves care common in many settings in the ocean, and water velocities associated with the waves are in some cases strong enough to move bottom sediment. They are also common in the atmosphere.
Water waves of these kinds are called gravity waves, because, as you will see in a minute, gravity is the important force involved. But another important kind of waves, pressure waves, are present also in fluids, both air and water.