Wednesday, May 19, 2010

A Mechanism for Amplifying Planetary Tidal Forces in the Sun's Outer Convective Zone

The image above is a cross-section of the Sun showing the rotational periods of a section of it's interior.
The rotation rates range from about 34.0 days near the poles to about 25.2 days in the Sun's equatorial convective zone. The dotted line that is located ~ 0.7 solar radii out from the centre of the Sun marks the positions the Solar Tachocline. This represents the boundary between the core of the Sun, were the main form of energy transport is by radiation, and the outer convective layer of the Sun, where the main form of energy transport is by convection.

The diagram shows that mean rotation period at a point just below the equatorial Tachocline is ~ 26.3 days, while the mean rotation period in the equatorial mid-convective layer is ~ 25.2 days.

Amazingly, if the rotation period of the point just below the equatorial Tachocline was in fact 26.3365 days, you would get an amplified resonance between the tides of the two dominant tidal forcing Terrestrial planets, Venus and Earth.

Consider the case where the Earth and Venus are aligned in their orbits about the Sun, roughly above the Equator of the Sun (note: these planets can be located up to +/- 7 degrees from the Sun's equator). Take a
point (A) just below the Tachocline boundary that is right on the Sun's equator, and a point (B) that is dierctly above it, at the mid (radial) point in the equatorial convective layer of the Sun. In this configuration, the tidal bulges produced by the combined gravitational forces of Venus and Earth upon the convective layer of the Sun would be superimposed upon one another.

Interestingly, however, you would find that it took 28.38305 days for point A to rotate once around the Sun and then catch up to advacing line connecting the centre of the Sun to the Earth, and 28.38315 days for point B to rotate once around the Sun and then catch up to the advancing line connecting the centre of the Sun to Venus. The net effect being, that rougly every 28.38310 days, the initial tidal bulges produced by the alignment of Venus and Earth would be reinforced by the Earth at the equatorial Tachocline boundary (i.e. point A) and by Venus at the mid-point in the Sun's equatorial convective layer (i.e. point B). More importantly, this reinforcement would repeat 103 times every 28.38310 days, until Venus and Earth again realigned themselves in roughly the same part of the sky roughly 8.0 sidereal years later, where the whole cycle would start all over again. This happens because:

102.9504 x 28.38310 days = 2922.05150 days = 8.0000016 sidereal years
110.9504 x 26.3365 days = 2922.04521 days = 7.9999844 sidereal years
115.9544 x 25.2 days = 2922.05088 days = 7.9999999 sidereal years

Note that Venus and Earth Align rougly once every 1.599 sidereal years and that five these alignments is:

5 x 1.599 sidereal years = 7.9950 sidereal years (difference from 8.0000 sidereal years =1.8256 days !)
Bottom line? This resonance may represent a way for the small tidal forces of Venus and Earth
acting on the convective layers of the Sun to be significantly amplified, so that they become influential in the dynamic process in the outer layers of the Sun.
It is interesting to note that:
4 x SVE = 6.3946 years SVE = synodic period of Venus and Earth
3 x SEM = 6.4059 years SEM = synodic period of Earth and Mars
7 x SVM = 6.3995 years SVM = synodic period of Venus and Mars
28 × SVE = 7 x (6.3946 yrs) = 44.763 yrs
69 × SVJ = 44.770 yrs = synodic period of Venus & Jupiter
41 × SEJ = 44.774 yrs = synodic period of Earth & Jupiter
20 × SMJ = 44.704 yrs = synodic period of Mars & Jupiter
4 x 1.599 yrs = 6.396 yrs
(Repetition time for the alignment of Venus, Earth and Mars)
5 x 1.599 yrs = 7.995 yrs
(Repetition time for the amplification mechanism discussed above)
7 x 1.599 yrs = 11.193 yrs
(Solar Sunspot Schwabe cycle)
14 x 1.599 yrs = 22.386 yrs
(Solar Hale cycle)
28 x 1.599 yrs = 44.772 yrs
(Alignment synodic periods Jupiter with Venus, Earth & Mars)
56 x 1.599 yrs = 89.544 yr
(Solar Gleissberg cycle)
112 x 1.559 yrs = 179.088 yrs
(Jose cycle - overall repetotion cycle for Jovian planets)


Which means that:

345 x Synodic period Venus/Jupiiter = 223.85 yrs
205 x Synodic period Earth/Jupiter = 223.87 yrs
100 x Synodic period Mars/Jupiter = 223.52 yrs


and that for the rotation periods of point A and B in the Sun's outer convective layers:

2883 x 28.38310 days = 81828.4773 days = 224.03026 (sidereal) years
3107 x 26.3365 days = 81827.5055 days = 224.02759 (sidereal) years
3247 x 25.2 days = 81824.400 days = 224.01901 (sidereal) years

with realignment errors of 1 to 3 days.

This is absolutely amazing!

Friday, March 26, 2010

Why Do the Long-Term Periodicities in the ENSO Appear in the Flux Optical Depth Anomalies for Water Vapor in the Earth's Atmosphere?

Figure added at end of post 15/11/2019

Shown above, is the flux optical depth anomalie for the Earth's atmosphere between 1948 and 2007. It turns out that this is a rough measure the total column density of water vapor in the Earth's atmosphere from year to year over this time period.

Shown below, is a comparison between the polar Fast Fourier Transform (FFT) of the flux optical depth anomalie between 1964 and 2001, and a periodogram of the ENSO/SOI over the same time period.

[N. Sidorenkov, Astronomy Reports, Vol. 44, No. 6, 2000, pp 414 - 419, translated from Astronomischeskii Zhurnal, Vol. 77, No. 6, 2000, pp 474 - 480]

Remarkably, the 6.2 (& 6.0), 4.8, 3.6, 2.4, and 2.1-year periodicities in the ENSO/SOI periodogram of Siderenkov (2000), are also clearly evident in the FFT of the flux optical depth anomalies data.

Four of these six long-term periodicities (i.e. 2.4, 3.6, 4.8, and 6.0 years) are sub-harmonics of the 1.2 year period of the Earth's free nutation i.e. the Chandler Wobble. In addition, all six of the long-term periodicities are very close to the super-harmonics of the 18.6 year period of the Earth's forced nutation (i.e. 6.2, 4.7, 3.7, 2.3, and 2.1 years) ie. the periodic precession of the line-of-nodes of the Lunar orbit.

This data tells us that the ENSO must play a major role in setting the overall column density of water vapor in the Earth's atmosphere. In addition, it indicates that the ENSO must also be an important factor in setting the World's means temperature, since water vapor is the dominant greenhouse gas in the Earth's atmosphere.

What is even more remarkelable, is the fact that common frequencies seen in the two data sets are simply those that would be expected if ENSO phenomenon was the resonant response of the Earth's (atmospheric/oceanic) climate system brought about by a coupling between the Earth's forced (18.6 year Nodical Lunar Cycle) and unforced (1.2 year Chandler Wobble) nutations.

Wednesday, March 17, 2010

Monday, March 15, 2010

The synchronization between the Solar Inertial Motion and the Lunar Orbit

Figure 6. The main curve shows the distance of the centre-of-mass of the Solar system from the sub-Jupiter point between 1220 and 2020 A.D. The sub-Jupiter point1 is located just above the solar surface on a line joining the centre of the Sun to Jupiter. Marked above this curve are years in which the Earth experienced exceptionally strong tidal forces over the last 800 years.

Figure 6 shows that the times when Solar/Lunar tides had their greatest impact upon the Earth are closely synchronized with the times of greatest asymmetry in the Solar Inertial Motion (SIM). Over the last 800 years, the Earth has experience exceptionally strong tidal forces in the years 1247, 1433, 1610, 1787 and 1974 (Keeling and Whorf, 1997). A close inspection of Figure 6 shows that these exceptionally strong tidal forces closely correspond in time to the first peak in the asymmetry of the SIM that occurs just after a period low asymmetry. These first peaks in asymmetry in the SIM occur in the years 1251, 1432, 1611, 1791, and 1971, closely correspond the years of peak tidal force.

Thus, there appear to be periodic alignments between the lunar apsides, syzygies and lunar nodes that occur at almost exactly the same times that the SIM becomes most asymmetric for the first time after a period of low asymmetry in the SIM. It means that precession and stretching of the Lunar orbit (i.e. the factors that control the long-term variation of the lunar tides that are experienced here on Earth) are almost perfectly synchronized with the SIM.
We know that the strongest planetary tidal forces acting on the lunar orbit come from the planets Venus, Mars and Jupiter. In addition, we known that, over the last 4.6 billion years, the Moon has slowly receded from the Earth. During the course of this lunar recession, there have been times when the orbital periods of Venus, Mars and Jupiter have been in resonance(s) with the precession rate for the line-of-nodes the lunar orbit. When these resonances have occurred, they would have greatly amplified the effects of the planetary tidal forces upon the lunar orbit. Hence, the observed synchronization between the precession rate of the line-of-nodes of the lunar orbit and the orbital periods of Venus, Earth, Mars and Jupiter, could simply be a cumulative fossil record left behind by these historical resonances.
Of course, the orbital periods of Jupiter and the other Jovian planets are responsible for the
periodicities observed in the motion of the Sun about the Solar Sytem barycentre. Hence, the apparent link between the Sun's barycentric motion and the orbit ofthe Moon may just be an artifact of the fact that both are heavily influenced by the periodicities in the motion of the Jovian planets.