An additional current caused by this added mass on the surf zone is the undertow. Rip currents form at an alongshore irregularity of the coast and may extend offshore past the breaking zone. Part of this added mass also causes rip currents, which are currents directed offshore for approximately one hundred meters. This current is caused by the added mass of water that breaking waves bring to the surf zone (analogous to the Stokes drift). Furthermore, when these waves arrive forming an angle with the coast they drive a current, a longshore current, between the breaking zone and the shore, i.e., at the surf zone. There is a net onshore transport produced by Stokes drift, markedly by long (shallow water) waves. Stokes drift becomes important as wave grows and breaks. In reality, wave shapes are not perfectly sinusoidal nor are their orbits perfectly closed. There is an alternative way of representing the phase speed or celerity, in terms of the wave frequency ω: The range of depths at which these waves may exist increases with wavelength. Intermediate waves are those that fall between long and short waves. This is an important relationship because it says that long waves such as tides propagating over coastal areas will have phase speeds that are proportional to the square root of the water depth. For shallow water waves, the phase speed, C = (gh) 0.5, depends on the local water depth but not on the wavelength. A deep water wave also called a short wave is found where the wavelength is shorter than twice the water column depth, i.e., λ 20h. The wave celerity or speed depends only on the wavelength λ and on the water depth h. In real cases, the steepness of small amplitude waves is 1/50. Small amplitude means that the wave steepness, which is ratio of wave height H to wavelength λ, is smaller than one twentieth, in idealized situations. The study of wind waves is simplified by treating them as "small amplitude" waves. Thus, long waves travel faster than short waves. The wavelength λ is a function of T, and the celerity C is a function of λ. It should be noted that waves do not change their period T. The units of frequency are time -1, and the units of wave number are distance -1. ( ω is the Greek letter omega, and κ is the Greek letter kappa.) The frequency and the wave number are spatial and temporal analogs of each other: frequency is the measurement of the number of repeating units of a propagating wave per unit of time, and wave number is the measurement of the number of repeating units of a propagating wave per unit of space. The period and wavelength can be expressed in terms of their reciprocals, the wave frequency ω = 2(pi)/T, and the wave number κ = 2(pi)/λ. As you probably have seen in the ocean or a lake, the stronger the wind, the higher the waves. The wave height depends on the energy transferred to the surface by the wind it does not depend on C, λ, or T. The speed C (C stands for celerity) of the wave is the quotient of the wavelength over period. The period T is the time it takes one wavelength or two consecutive troughs (or crests or any other wave reference point) to pass by a fixed position. The wavelength λ (the Greek letter lambda) is the distance between two crests (or two troughs or two inflection points with the same curvature above and below the points). The wave amplitude A equals one half the wave height H, which is the distance between the crest and the trough. The wave crest is the point of maximum elevation, and the wave trough is the point of minimum elevation. We define the properties of waves from these ideal waves (Figure 1). To study wind waves, we should use ideal waves with sinusoidal shape. Ripples are the smallest and most irregular undulations produced by wind on the sea surface. Wind can also generate waves that travel from a remote location in the open ocean, called swell, which travel in one direction and are more regular than sea waves. Wind can generate waves locally, called sea, which travel in different directions and at different speeds. The first class of waves that we will cover is that produced by the wind blowing on the ocean’s surface. The typical periods, wavelengths, and forcing mechanisms of the waves in the ocean that we discuss are presented in the following table. Tectonic forces such as earthquakes that cause vertical displacements of the ocean floor, submarine volcanic eruptions, landslides and meteorite impacts on the ocean all cause tsunamis. Gravitational forces (mostly from the moon and sun) plus centrifugal forces in the solar system produce tides. When the wind blows on the surface of the ocean it produces ripples, waves, and swell. In this document we will discuss three types of waves: wind-driven waves, tides and tsunamis.
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