(2011 ), based on tidal constants derived from the TPXO7-ATLAS ( ). A world map showing ocean regions with asymmetric tides was published by Song et al. (2003) and several other studies since (Nidzieko, 2010 Zhang, 2018 ). Although this was known for a long time (Doodson, 1921), it has received renewed attention more recently due to the observations and analyses of Hoitink et al. However, it must be noted before that linear ocean tides are not fully symmetric, due to the superposition of certain tidal components with mutually related frequencies (for example, the sum of the frequencies of the K1 and O1 tides is equal to the frequency of the M2 tide). In the following we shortly review the major nonlinear processes involved in initiating shallow-water tidal distortion. Nonlinear hydrodynamic processes that are insignificant in the deep ocean become important when the tidal range is larger than a small fraction of the mean water depth. We will use the term positive duration asymmetry for tides with a longer fall and shorter rise and negative duration asymmetry for tides with a shorter fall and longer rise. Here the term tidal wave distortion is to be understood as a systematic (long-term averaged) difference between the periods of rising and falling tide, also called tidal asymmetry. Ocean tidal waves are distorted when they propagate into shallow coastal waters. The semidiurnal lunar tide (M2) is usually the dominant component, in which case the ocean tide can be described fairly accurately with a single sine function. Tidal motion in the oceans can be described by a limited number of sinusoidal components, because earth's rotation and the relative movements of earth, sun and moon have a cyclical character, see the article Ocean and shelf tides. Tides result from the response of the ocean water bodies to the attractive gravitational forces by sun and moon. 6 Morphology of estuaries with tidal rivers.5 Tidal wave deformation in a converging channel.4 Morphology of shallow tidal basins with small river inflow.3 Tidal wave deformation in the presence of friction and intertidal areas.2 Tidal wave deformation in the absence of friction.1 Tidal wave deformation in shallow water.
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