The vorticity vector u is the curl

The vorticity vector u is the curl of the
velocity vector v:
u ¼ V
v ¼ iðvv=vz  vw=vyÞ
þ jðvw=vx  vu=vzÞ þ kðvv=vx  vu=vyÞ
(7.32)
Vorticity, therefore, has units of inverse time,
(sec)
1.
Fluids (and all objects) have vorticity
simply because of Earth’s rotation. This is
called planetary vorticity. The vector planetary
vorticity points upward, parallel to the rotation
axis of Earth, which has an angular rotation
rate of U:
uplanetary
¼ 2U (7.33)
where U ¼ 2p/day ¼ 2p/86160 sec ¼ 7.293

10
5 sec
1, so uplanetary ¼ 1.4586
10
4 sec
1.
The vorticity of the fluid motion relative to
Earth’s surface (Eq. 7.32) is called the relative
vorticity. The total or absolute vorticity of a piece
of fluid is the sum of the relative vorticity and
planetary vorticity.
For large-scale oceanography, only the local
vertical component of the total vorticity is
used because the fluid layers are thin compared
with Earth’s radius, so flows are nearly horizontal.
The local vertical component of the
planetary vorticity is exactly equal to the
Coriolis parameter f (Eq. 7.8c) and is therefore
maximum and positive at the North Pole (4 ¼
90

N), maximum and negative at the South
Pole (4 ¼ 90

S), and 0 at the equator.
The local vertical component of the relative
vorticity from Eq. (7.32) is
2 ¼ ðvv=vx  vu=vyÞ ¼ curlzv (7.34)
where v is the horizontal velocity vector. The
local vertical component of the absolute
vorticity is therefore (z þ f). The geostrophic
velocities calculated from Eq. (7.23) (Section 7.6)
are often used to calculate relative vorticity.
7.7.2. Potential Vorticity
Potential vorticity is a dynamically important
quantity related to relative and planetary
vorticity. Conservation of potential vorticity is
one of the most important concepts in geophysical
fluid dynamics, just as conservation of
angular momentum is a central concept in solid
body mechanics. Potential vorticity takes into
account the height of a water column as well
as its local spin (vorticity). If a column is shortened
and flattened (preserving mass), then it
must spin more slowly. On the other hand, if
a column is stretched and thinned (preserving)

Hasil (Bahasa Indonesia) 1:

Vorticity vektor u adalah curlkecepatan vektor v:u ¼ V v ¼ iðvv = vz vw = vyÞþ jðvw = vx vu = vzÞ þ kðvv = vx vu = vyÞ(7,32)Vorticity, oleh karena itu, memiliki unit invers waktu,(sec)1.Cairan (dan semua objek) telah vorticityhanya karena rotasi bumi. Ini adalahdisebut vorticity planet. Vektor planetpoin vorticity ke atas, paralel untuk rotasisumbu bumi, yang memiliki sudut rotasitingkat U:uplanetary¼ 2U (7.33)mana U ¼ 2p/hari ¼ 2p/86160 sec ¼ 7.293105 detik1, uplanetary begitu ¼ 1.4586 104 sec1.Vorticity gerakan fluida relatifPermukaan bumi (EQ 7,32) disebut relatifvorticity. Vorticity total atau mutlak sepotongcairan adalah jumlah dari vorticity relatif danplanet vorticity.Oseanografi skala besar, hanya lokalkomponen vertikal total vorticity adalahdigunakan karena cairan lapisan tipis dibandingkandengan jari-jari bumi, sehingga aliran hampir horisontal.Komponen vertikal lokalplanet vorticity persis sama denganCoriolis parameter f (EQ 7,8 c) dan karena itumaksimum dan positif di Kutub Utara (4 ¼90N), maksimum dan negatif di SelatanTiang (4 ¼ 90S), dan 0 di khatulistiwa.Komponen vertikal lokal relatifvorticity dari EQ (7,32) adalah2 ¼ ðvv = vx vu = vyÞ ¼ curlzv (7,34)di mana v adalah kecepatan horisontal vektor. Thelokal vertikal komponen mutlakvorticity adalah (z þ f). Geostrophickecepatan dihitung dari EQ (7,23) (Bagian 7.6)sering digunakan untuk menghitung vorticity relatif.7.7.2. potensi VorticityVorticity potensi penting secara dinamiskuantitas relatif dan planetvorticity. Konservasi potensi vorticity adalahsalah satu konsep yang paling penting dalam GeofisikaDinamika fluida, seperti konservasimomentum sudut adalah konsep pusat dalam padatmekanika tubuh. Potensi vorticity memperhitungkanrekening tinggi kolom air sertaspin lokal (vorticity). Jika kolom disingkatdan rata (melestarikan massa), makaharus berputar lebih lambat. Di sisi lain, jikakolom membentang dan menipis (melestarikan)