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.

VF oc

2

Vo

2 0

V

kSinjCoso

daysideral __1/2

Rotation-induced Coriolis force:

Coriolis force is always perpendicular to fluidmotion at any moment, the work done to fluids is

Where,

Similar force exists in magnetic field, but the bioelectricity inside our bodies should never be bothered by magnetic field.

Force from a magnetic field ( ) exerted on a

charged particle (q) with instantaneous velocity

( ) and force’s work anytime are

B

Ve

VF)BV(qF emem

0dt)BV(qVdtFVWorkm eeme

1-2.Rotation velocity does not change sensibly, and Earth does not shake terribly, even though bothered by abnormal mass

distribution on the surface.

With the possible maximum unevenness of mass distribution, e.g.,with 1 km of increased ice sheetcovering 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 nomore 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 correspondingweather and climate.

This is done through geostrophic motion and Ekman transport. Coriolis force balances most of gradient force to produce geostrophic motion moving along iso-bars, 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 andquickly 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

,

, , fT

irm

21

||2

cos2

uR

T em

||

cos3

uR

T em

||4

vR

T em

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]

kr

tguj

r

ui

r

vr

The curvature force ( , ) and friction

are small ( is other external forces). Coriolis force and pressure gradient force are two major terms in kinetic balance, which dwarf the nonlinear term . Without Coriolis force, pressure gradient force would be very small, nonlinear term would stands up, making geophysical motions much more unpredicable. Fortunately, the equatorial 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.

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oro

1

)2(

Vr

Fo

VV

5. Earth rotation can muffle Sun-Moon gravitation-induced flow and keep the geophysical fluids from heaping onto afixed 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 andmakes 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 andlow 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, partiallypredictable, 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 climatecomponents: ----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), guidingMonsoon, 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 boundarycurrents, 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 afixed 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: .Earth rotation angular speed relative to Sun:

ST str1510292.7/2

kTkT strs 1099.110292.7/2/2 75 (1/s)k=-1 for current Earth rotation; k=1 for opposite Earth rotation.

Length of 1 solar day: )/1(/2 1TTkTT strstrssun

=24hr for current Earth rotation, 23.87 hr for opposite Earth rotation.

Number of solar days within 1 year: 25.366/ kTTN sunsun =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 oceaniccirculation 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 tobe 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.