Pengguna:NFarras/Proyek 3

Selancar di atas gelombang pecah yang mengalami pendangkalan.

Kecepatan fase c_p (biru) dan kecepatan grup c_g (rmerah) sebagai fungsi kedalaman air h pada gelombang air dengan frekuensi konstan, menurut Teori gelombang Airy.

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. Panjang gelombang yang mengalami pendangkalan akan berkurang, sementara 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. 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 $H$ pada lokasi tertentu dapat dinyatakan dengan rumus:

$H=K_{S}\;H_{0},$

dengan $K_{S}$ adalah koefisien pendangkalan dan $H_{0}$ adalah tinggi gelombang di perairan dalam. Koefisien pendangkalan $K_{S}$ bergantung pada kedalaman air lokal $h$ dan frekuensi gelombang $f$ (dapat dicari menggunakan rumus $f=1/T$). Perairan dalam merupakan kondisi ketika dasar perairan tidak terlalu mempengaruhi gelombang. Kondisi ini terjadi ketika kedalaman $h$ lebih besar daripada sekitar setengah panjang gelombang di laut dalam $L_{0}=gT^{2}/(2\pi ).$

Physics

Convergence of wave rays (reduction of width $b$) at Mavericks, California, producing high surfing waves. The red lines are the wave rays; the blue lines are the wavefronts. 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.

Shoaling coefficient $K_{S}$ as a function of relative water depth $h/L_{0},$ 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 $H$ at a certain mean water depth $h$ is equal to $H=K_{S}\;H_{0},$ with $H_{0}$ the wave height in deep water (i.e. when the water depth is greater than about half the wavelength). The shoaling coefficient $K_{S}$ depends on $h/L_{0},$ where $L_{0}$ is the wavelength in deep water: $L_{0}=gT^{2}/(2\pi ),$ with $T$ the wave period and $g$ 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 $L=T\,{\sqrt {gh}}.$

For non-breaking waves, the energy flux associated with the wave motion, which is the product of the wave energy density with the group velocity, between two wave rays is a 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. For waves affected by refraction and shoaling (i.e. within the geometric optics approximation), the rate of change of the wave energy transport is:

${\frac {d}{ds}}(bc_{g}E)=0,$

For shallow water, when the wavelength is much larger than the water depth – in case of a constant ray distance $b$ (i.e. perpendicular wave incidence on a coast with parallel depth contours) – wave shoaling satisfies Green's law:

$H\,{\sqrt[{4}]{h}}={\text{constant}},$

with $h$ the mean water depth, $H$ the wave height and ${\sqrt[{4}]{h}}$ the fourth root of $h.$

Water wave refraction

Following Phillips (1977) and Mei (1989), denote the phase of a wave ray as

$S=S(\mathbf {x} ,t),\qquad 0\leq S<2\pi$.

The local wave number vector is the gradient of the phase function,

$\mathbf {k} =\nabla S$,

and the angular frequency is proportional to its local rate of change,

$\omega =-\partial S/\partial t$.

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;

${\frac {\partial k}{\partial t}}+{\frac {\partial \omega }{\partial x}}=0$.

Assuming stationary conditions ($\partial /\partial t=0$), this implies that wave crests are conserved and the frequency must remain constant along a wave ray as $\partial \omega /\partial x=0$. As waves enter shallower waters, the decrease in group velocity caused by the reduction in water depth leads to a reduction in wave length $\lambda =2\pi /k$ because the nondispersive shallow water limit of the dispersion relation for the wave phase speed,

$\omega /k\equiv c={\sqrt {gh}}$

dictates that

$k=\omega /{\sqrt {gh}}$,

i.e., a steady increase in k (decrease in $\lambda$) as the phase speed decreases under constant $\omega$.

Lihat pula

• Airy wave theory
• Breaking wave
• Dispersion (water waves)
• Ocean surface waves
• Shallow water equations
• Shoal
• Waves and shallow water
• Wave height
• Ursell number

Pranala luar

• Transformasi gelombang di Coastal Wiki