The Beautiful Roles
of the Earth Rotation
Climate presents abundant, beautiful, and colorful
rhythms. Theoretically, its periods can be from zero
to indefinitely long. Climate in a sense is so visible
that every body can predict the coming mornings,
months and seasons if one needs to know them for
getting ready for them, which makes us feel safe.
On the other hand, the weather and climate are
such rhythm-abundant that no body can predict it
exactly, and no body can go through the exactly
same weather conditions in two days in ones life.
This gives invisible charm to climate lest making us
feel bored.
The rotation of Earth plays basic roles in the climate
rhythms by remembering forcing on multiple periods,
maintaining orderly and stable motion of
geophysical fluids, etc..
---- Capriccio from Physical Oceanography
Zhiren (Joseph) Wang
1. Sustaining Earth rotation
1-1.Rotation associated Coriolis force does
not do the work on the objects (fluids) at
any time; therefore, the rotating Earth
does not consume its energy and can
keep its original angular momentum to
rotate on and on.
Rotation-induced Coriolis force:

Fc


 2 o  V
Coriolis force is always perpendicular to fluid
motion at any moment, the work done to fluids is



 2 o  V  V  0
Where,



o    Cos j    Sin k
  2 / 1 _ sideral _ day
Similar force exists in magnetic field, but the
bioelectricity inside our bodies should never be
bothered by magnetic field.

Force from a magnetic field ( B ) exerted on a

charged particle (q) with instantaneous velocity ( Ve)
and force’s work anytime are



Fm  q  ( Ve  B )




Fm  Ve



Workm   Ve  Fm  dt   Ve  q( Ve  B )  dt  0
1-2.Rotation velocity does not change sensibly,
and Earth does not shake terribly, even
though bother ed by abnor mal mass
distribution on the surface.
With the possible maximum unevenness of mass
distribution, e.g.,with 1 km of increased ice sheet
covering the whole hemisphere, I established a
simple model to compute obliquity and rotation velocity:
Schematic for basic parameters and relationships
Obliquity changes no more than 3%
Obliquity vs ice sheet thickness-extent.
Iso-lines indicate inertia momentum
Rotation velocity of Earth changes no
more than 0.03 %
Rotation angular speed vs ice sheet thickness and extent.
Iso-lines indicate inertia momentum
2. Rotation associated Coriolis force
maintains a relatively orderly and steady
geophysical motion and corresponding
weather and climate.
This is done through geostrophic motion and Ekman
transport. Coriolis force balances most of gradient
force to produce geostrophic motion moving along isobars, keeping most fluids from moving from high to low
pressure, only small geostrophic departure moves from
high to low pressure through Coriolis force associated
Ekman transport to form weathers. If Earth did not
rotate, there would be no geostrophic motion, fluids
would move from high to low pressure directly and
quickly to erase the pressure unevenness.
Schematic diagram for the jobs of Earth rotation-induced
geostrophic motion and departure
3. The rotation of Earth plays the key role
for memory of forcings.
With the rotation of Earth, geophysical fluids can memory
forcings to have multi-period oscillations. All the periods
depend on the Earth-rotation. Without the rotation, the
memory for both the basic and comprehensive periods
would totally lost [Wang et al.,B]. The basic memorial
periods for geophysical fluids to memory forcings are
T m1 

 Re cos 
 Re
 Re cos 



T m4
T
2 f ir , T m 2
2 | u | , m3
|v|
|u|
,
4. Rotation associated geostrophic motion
increases the predictability of geophysical fluids as
it causes geotrophic motion and waves (Kelvin,
Rossiby, etc.). [Wang et al., A,C]







V 
1
 V   V  ( 2 o   r )  V   p  g k  F o
t

 

v
u
u  tg 
The curvature
force ( r V ,    r i  r j  r k ) and friction

are small (F o is other external forces). Coriolis force and
pressure gradient force are two major terms
in kinetic


balance, which dwarf the nonlinear term V   V . Without
Coriolis force, pressure gradient force would be very small,
nonlinear term would stands up, making geophysical
motions much more unpredicable. Fortunately, the equatorial
r
region, where Coriolis force is zero or very small, provides an open
effective channel to external forces from Sun and Moon and makes climate
from chaos, together with rotation.
5. Earth rotation can muffle Sun-Moon
gravitation-induced flow and keep the
geophysical fluids from heaping onto a
fixed direction.
For fluids of small viscidity the vertical speed of which
can increase by ~29 (for Moon) to ~365 (for Sun) times
if without rotation [Wang et al., B]. This maybe is one of the
reasons why there is no fluids on Moon’s surface. For
solids or fluids of very big viscidity, rotation does not that
matter. Obviously, rotation avoids the solar heating from
being fixed at one Earth side for too long and
makes heating distribution even.
Schematic for cumulated motion induced by the Sun-Moon attraction
6. Further discussions
The sustaining Earth rotation together with obliquity and revolution are
maintained to basically define the visible semi-diurnal, diurnal, seasonal,
and annual rhythm in weather, climate, and the related astronomical
phenomena. Without consuming angular momentum of Earth, Earth rotation
*maintains the geophysical fluids with desirably stable and even high and
low systems,
*remembers the external drives with multi-periods;
*makes weather and climate charmy and elegant of both linear and
nonlinear, quasi-geostrophic, quasi- and multi-periodical, partially
predictable, etc.;
*produces multi-waves and motions in abundant ways, including Kelvin,
Rossby, Ekman, initio, inito-gravity, geostrophic, quasi-geostrophic, cyclonic,
anti-cyclonic, etc..;
*directly and indirectly forms and changes various weather and climate
components:
----in atmosphere, makes the poleward motion turn to east and equator-ward
motion turn to west, forming multi-meridional and zonal circulation cells
(Hadley, Ferrel, polar, Walker, ect.,), issuing various belts for wind, rain,
temperature, and pressure (trade winds, midlatitue westerlies, polar
systems, inter-tropical convective zone, subtropical highs, jets), guiding
Monsoon, etc.;
----in ocean, even the wind-driven current and thermohaline are very
abundant: Moonson-driven Indian currents, equatorial currents systems,
intensified narrow western boundary currents, broad weak eastern boundary
currents, polar currents, etc.;
*avoids the solar heating from being fixed at one Earth side for too long and
makes heating distribution even, keeps Earth fluids from being attracted at a
fixed direction for too long and from escaping;
* and son on.
If Earth did not rotate, or rotating rate were too fast or too slow, or Earth
rotated in the opposite direction, the current beneficial weather and climate
would be changed, the fluids would either exist on Earth in an odd (more
chaotic) way or escape from Earth. Both ways make the non-rotational Moon
have no fluids on its surface, from the view of the intelligent design or reality.
For instance, Earth rotated in the opposite direction with
the same self-rotation angular speed and revolution period,
then:
•Solar day length would reduce from 24 hr to , there would
be 367.25 days within one year (2 days more than current
year). The periods for semidiurnal and diurnal signals and
for the heating and tidal-forcing time on a fixed point would
be shorter, caUse the changes in tidal, climate, biology,
geology, and human activities.
Basic parameters: Earth revolution period: T=365.25days, number of
sidereal days within 1 year: Nstr=366.25 days, length of 1 sidereal day:
Tstr=24*3600*365.25/366.25=86164 secs, Earth rotation angular speed:
  2 / T str  7.292  10 5 S 1 .Earth rotation angular speed relative to Sun:
s  2 / T str  2k / T  7.292  105 1.99107 k
(1/s)
k=-1 for current Earth rotation; k=1 for opposite Earth rotation.
Length of 1 solar day:
1
T sun  2 / s  T str (1 k T str / T )
=24hr for current Earth rotation, 23.87 hr for opposite Earth rotation.
Number of solar days within 1 year:
N sun  T / T sun  k  366.25
=365.25 days for current Earth rotation, 367.25 days for opposite Earth rotation
Schematic diagram for solar and sidereal day-lengths with Earth rotating (a)
antilockwise and (b) clockwise (with Earth-orbital velocity unchanged,not plotted to scale).
*All the motions and waves that are controlled under Earth rotation
would change their directions oppositely in both northern and southern
hemispheres, including geostrophic flow, inertio-motion, gradient
(cyclonic and anti-cyclonic) flows, Ekman and other similar transports,
Kelvin wave, Rossby wave, inertio-wave, inerto-gravity waves, tidal
wave, etc.. The concerned circulations would also change their
directions oppositely in both northern and southern hemispheres,
including trade winds, Monsoon, jets (e.g., upper troposphere jets,
Somali jet stream), wind belts (original westerlies/eastlies would be
easterlies/westerlies), Walker cells; oceanic current systems:
equatorial, polar, west-boundary, east-boundary, Indian; etc..
*Together with the given topography, land-sea distribution, and
astronomical conditions (e.g., Moon’s motion), further weather and
climate changes would occur with the changes in periods and
directions listed above. The inter-tropical convective zone (ITCZ),
Monsoon, and Walker cells would change. The original warm pool
would change into “cold pool” and the warmer sea surface would shift
to the east tropical Pacific and west tropical Indian due to the change
of trade winds. Compared with the original warm pool located in joint
Indian-Pacific, the two new warm pools would get weaker, Walker cells
would get weaker. Thermocline would weaken as it would reverse its
direction. The original strong, warm, and narrow western-boundary
poleward currents (e.g., Kuroshio and Gulf stream) would change into
weak, cold, and broad currents toward equator; the weak, cold, and
broad east boundary equatorward current would be strong, warm,
narrow poleward current. Indian-Himalaya Monsoon driving
mechanism would change and even shift to the east Pacific region with
weakened intensity due to the new atmospheric and oceanic
circulation patterns.
*The temperature and precipitation patterns would correspondingly
change. E.g., east coasts would get drier and colder; west coasts
would get warmer and moist. And the global climate variations tend to
be smaller with the weakened ENSO and Monsoon. * Ect..
7. References
Wang, Zhiren, et al., A: The basic wave characteristics
and climatological meanings of Sun’s-Moon’s
gravitation and solar radiation (to be contributed).
Wang, Zhiren, et al., B: The nonlinear response and
multi-temporal scales of cumulative momentum
memory for geophysical fluids to Sun-Moon gravitation
(to be contributed).
Wang Zhiren,D.X. Wu , D. Chen, H.D.Wu, X.J.Song
and Z.H.Zhang, C: Critical Time Span and Nonlinear
Action Structure Of Climatic Atmosphere and Ocean.
ADVANCES IN ATMOSPHERIC SCIENCES,
Vol.19,pp741-756,2002.