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{{short description|The effect by which surface waves entering shallower water change in wave height}}
[[Berkas:Surfer 2.jpg|upright=1.3|thumb|[[Selancar]] di atas [[gelombang pecah]] yang mengalami pendangkalan.]]
[[Berkas:Phase and group velocity as a function of depth.svg|upright=1.3|thumb|Kecepatan fase ''c''<sub>p</sub> (biru) dan kecepatan grup ''c''<sub>g</sub> (rmerah) sebagai fungsi kedalaman air ''h'' pada gelombang air dengan frekuensi konstan, menurut [[Teori gelombang Airy]].<ref>{{cite book |title=Oceanographical Engineering |last=Wiegel |first=R.L. |publisher=Dover Publications |year=2013 |isbn=978-0-486-16019-1 |page=17, Figure 2.4 }}</ref>]]
 
Dalam [[dinamika fluida]], '''pendangkalan gelombang''' merupakan efek perubahan tinggi gelombang air ketika [[ombak]] merambat pada perairan yang lebih dangkal. Dalam kondisi stasioner, penurunan kelajuan transpor harus disertai dengan kenaikan kerapatan energi supaya fluks energi tetap konstan.<ref name=lon64>{{cite journal | last1=Longuet-Higgins |first1=M.S. |last2=Stewart |first2=R.W. | title = Radiation stresses in water waves; a physical discussion, with applications | journal = Deep-Sea Research and Oceanographic Abstracts | volume = 11 | number = 4 | pages = 529–562 | year = 1964 | url = http://chinacat.coastal.udel.edu/cieg682/protect/longuet-higgins-stewart-dsr64.pdf |doi=10.1016/0011-7471(64)90001-4 |bibcode=1964DSRA...11..529L }}</ref> [[Panjang gelombang]] yang mengalami pendangkalan akan berkurang, sementara [[Frekuensi|frekuensinya]] akan tetap konstan.
 
Pada perairan yang dangkal dan memiliki kontur paralel, gelombang yang tidak pecah akan meningkat tingginya ketika memasuki perairan yang lebih dangkal.<ref name=wmo98>{{cite book | last=WMO | year=1998 | title=Guide to Wave Analysis and Forecasting | volume=702 | publisher=World Meteorological Organization | edition=2 | isbn=92-63-12702-6 |
url=http://www.wmo.int/pages/prog/amp/mmop/documents/WMO%20No%20702/WMO702.pdf}}</ref> Hal ini terjadi pada gelombang [[tsunami]] yang mengalami peningkatan tinggi gelombang ketika mendekati [[garis pantai]].
 
==Ikhtisar==
 
Gelombang yang mendekati wilayah pesisir mengalami perubahan tinggi melalui beberapa efek yang berbeda. Beberapa proses penting gelombang antara lain refraksi, difraksi, refleksi, gelombang pecah, interaksi gelombang–arus, gesekan, pertumbuhan gelombang akibat angin, dan pendangkalan gelombang. Pendangkalan gelombang adalah perubahan ketinggian gelombang yang hanya dipengaruhi oleh perubahan kedalaman – tanpa perubahan arah rambat gelombang dan disipasi. Tinggi gelombang <math>H</math> pada lokasi tertentu dapat dinyatakan dengan rumus:<ref name=god00/><ref name=dal91/>
:<math>H = K_S\; H_0,</math>
dengan <math>K_S</math> adalah koefisien pendangkalan dan <math>H_0</math> adalah tinggi gelombang di perairan dalam. Koefisien pendangkalan <math>K_S</math> bergantung pada kedalaman air lokal <math>h</math> dan frekuensi gelombang<ref>{{Cite web|date=2021-05-11|title=Pengertian Tsunami Shoaling · Pencarian.id|url=https://pencarian.id/berita/pengertian-tsunami-shoaling/|website=Pencarian.id|language=id-ID|access-date=2021-05-11}}</ref> <math>f</math> (dapat dicari menggunakan rumus <math>f=1/T</math>). Perairan dalam merupakan kondisi ketika dasar perairan tidak terlalu mempengaruhi gelombang. Kondisi ini terjadi ketika kedalaman <math>h</math> lebih besar daripada sekitar setengah [[panjang gelombang]] di laut dalam <math>L_0=gT^2/(2\pi).</math>
 
==Physics==
[[File:Mavericks wave diagram.gif|thumb|right|Convergence of wave rays (reduction of width <math>b</math>) at [[Mavericks, California]], producing high [[surfing]] waves. The red lines are the wave rays; the blue lines are the [[wavefront]]s. The distances between neighboring wave rays vary towards the coast because of [[refraction]] by [[bathymetry]] (depth variations). The distance between wavefronts (i.e. the wavelength) reduces towards the coast because of the decreasing [[phase speed]].]]
[[File:Shoaling coefficient as a function of depth.svg|thumb|right|Shoaling coefficient <math>K_S</math> as a function of relative water depth <math>h/L_0,</math> describing the effect of wave shoaling on the [[wave height]] – based on [[conservation of energy]] and results from [[Airy wave theory]]. The local wave height <math>H</math> at a certain mean water depth <math>h</math> is equal to <math>H=K_S\;H_0,</math> with <math>H_0</math> the wave height in deep water (i.e. when the water depth is greater than about half the [[wavelength]]). The shoaling coefficient <math>K_S</math> depends on <math>h/L_0,</math> where <math>L_0</math> is the wavelength in deep water: <math>L_0=gT^2/(2\pi),</math> with <math>T</math> the [[frequency|wave period]] and <math>g</math> the [[gravity of Earth]]. The blue line is the shoaling coefficient according to [[Green's law]] for waves in shallow water, i.e. valid when the water depth is less than 1/20 times the local wavelength <math>L=T\,\sqrt{gh}.</math><ref name=dal91/>]]
 
For non-[[breaking wave]]s, the [[energy flux]] associated with the wave motion, which is the product of the [[wave energy]] density with the [[group velocity]], between two [[ray tracing (physics)|wave rays]] is a [[conservation of energy|conserved quantity]] (i.e. a constant when following the energy of a [[wave packet]] from one location to another). Under stationary conditions the total energy transport must be constant along the wave ray – as first shown by [[William Burnside]] in 1915.<ref>{{cite journal | title = On the modification of a train of waves as it advances into shallow water | first = W. | last = Burnside |author-link = William Burnside | year = 1915 | journal = Proceedings of the London Mathematical Society | series = Series 2 | volume = 14 | pages = 131–133 | doi = 10.1112/plms/s2_14.1.131 | url = https://zenodo.org/record/1447774 }}</ref>
For waves affected by refraction and shoaling (i.e. within the [[geometric optics]] approximation), the [[rate of change (mathematics)|rate of change]] of the wave energy transport is:<ref name=dal91/>
:<math>\frac{d}{ds}(b c_g E) = 0,</math>
For shallow water, when the [[wavelength]] is much larger than the water depth – in case of a constant ray distance <math>b</math> (i.e. perpendicular wave incidence on a coast with parallel depth contours) – wave shoaling satisfies [[Green's law]]:
:<math>H\, \sqrt[4]{h} = \text{constant},</math>
with <math>h</math> the mean water depth, <math>H</math> the wave height and <math>\sqrt[4]{h}</math> the [[fourth root]] of <math>h.</math>
 
==Water wave refraction{{anchor|Refraction}}==
Following [[Owen Martin Phillips|Phillips]] (1977) and [[Chiang C. Mei|Mei]] (1989),<ref name=phi77>{{cite book | first=Owen M. | last=Phillips | author-link=Owen Martin Phillips |year=1977 | title=The dynamics of the upper ocean (2nd ed.) | isbn=0-521-29801-6 | publisher=Cambridge University Press | url=https://www.google.com/books?id=fYk6AAAAIAAJ&lpg=PP9&ots=htfM77pfaz&dq=phillips%20dynamics%20of%20the%20upper%20ocean&lr=&pg=PA23#v=onepage&q=phillips%20dynamics%20of%20the%20upper%20ocean&f=false}}</ref><ref name=mei89>{{cite book | first=Chiang C. | last=Mei | author-link=Chiang C. Mei | year=1989 | title=The Applied Dynamics of Ocean Surface Waves | publisher=World Scientific | location = Singapore | url=https://www.google.com/books?id=LKCQorj3XZwC&lpg=PA1&ots=qk-kn82-z2&dq=mei%201989&lr=&pg=PA62#v=onepage&q=mei%201989%20page%2063&f=false | isbn=9971-5-0773-0}}</ref> denote the [[Phase (waves)|phase]] of a [[Ray (optics)|wave ray]] as
:<math>S = S(\mathbf{x},t), \qquad 0\leq S<2\pi</math>.
The local [[wave vector|wave number vector]] is the gradient of the phase function,
:<math>\mathbf{k} = \nabla S</math>,
and the [[angular frequency]] is proportional to its local rate of change,
:<math>\omega = -\partial S/\partial t</math>.
Simplifying to one dimension and cross-differentiating it is now easily seen that the above definitions indicate simply that the rate of change of wavenumber is balanced by the convergence of the frequency along a ray;
:<math>\frac{\partial k}{\partial t} + \frac{\partial \omega}{\partial x} = 0</math>.
Assuming stationary conditions (<math>\partial/\partial t = 0</math>), this implies that wave crests are conserved and the [[frequency]] must remain constant along a wave ray as <math>\partial \omega / \partial x = 0</math>.
As waves enter shallower waters, the decrease in [[group velocity]] caused by the reduction in water depth leads to a reduction in [[wave length]] <math>\lambda = 2\pi/k</math> because the nondispersive [[Waves and shallow water|shallow water limit]] of the [[Dispersion (water waves)|dispersion relation]] for the wave [[phase speed]],
:<math>\omega/k \equiv c = \sqrt{gh}</math>
dictates that
:<math>k = \omega/\sqrt{gh}</math>,
i.e., a steady increase in ''k'' (decrease in <math>\lambda</math>) as the [[phase speed]] decreases under constant <math>\omega</math>.
 
==Lihat pula==
{{refbegin|2}}
*{{annotated link|Airy wave theory}}
*{{annotated link|Breaking wave}}
*{{annotated link|Dispersion (water waves)}}
*{{annotated link|Ocean surface waves}}
*{{annotated link|Shallow water equations}}
*{{annotated link|Shoal}}
*{{annotated link|Waves and shallow water}}
*{{annotated link|Wave height}}
*{{annotated link|Ursell number}}
{{refend}}
 
==Catatan==
{{reflist|2}}
 
==Pranala luar==
{{Commons category|Wave shoaling|Pendangkalan gelombang}}
*[http://www.encora.eu/coastalwiki/Wave_transformation#Shoaling Transformasi gelombang di Coastal Wiki]
 
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{{oseanografi fisik}}
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[[Kategori:Geografi pesisir]]
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[[Kategori:Gelombang air]]
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