Evidence is presented showing that lunar tides do have a significant influence on the strength and position of the polar Jet Stream. The Jet Stream drives northern latitude weather patterns especially during winter months.

I was intrigued by a proposal made by an Italian meteorologist Roberto Madrigali that varying tidal forces during the lunar cycle change the position of meanders (Rosby waves) in the polar Jet Stream. He has also written a book on the subject. This winter saw stormy but mild weather in the UK with exceptionally cold weather over North America. Both were likely caused by large distortions in the Jet Stream. Does the moon’s ever-changing tidal force affect Rosby gravity waves in the polar Jet Stream? The hypothesis, put simply, is that atmospheric tides acting just below the stratosphere affect the flow of Jet Streams. Increased tidal forces pull the Jet Stream to lower latitudes thereby inducing the mixing of polar air with tropical air. The result of such forcing is an increase in waves and oscillations in the Jet Stream and lower pressure differences.

One indicator of how contorted the Jet Stream becomes is the measurement of the difference in pressure between the Icelandic Low and the Azores High. There are two indices used to do this–one called the Arctic Oscillation (AO), which treats the flow over the entire Northern Hemisphere, and another called the North Atlantic Oscillation (NAO), which covers just the North Atlantic. The two are closely related. When these indices are strongly negative, the pressure difference between the Icelandic Low and the Azores High is low. This results in a weaker Jet Stream with large, meandering loops, allowing cold air to spill far from the Arctic into the mid-latitudes.

Severe UK winters such as those in 2009/2010 and 2010/2011 coincided with strong negative values of AO/NAO , whereas the mild but stormy winter of 2013/14 coincided with strong positive values of AO/NAO. The Jet Stream influence on Europe is stronger during the winter. This is also the time when solar heating of the atmosphere is diminished over the Arctic, so any possible lunar tidal effect will be enhanced.

To investigate further the hypothesis of a lunar influence on the Jet Stream I downloaded the data from NOAA and calculated the net tides for each day from 2000 until 2014 using the JPL ephemeris. I am basing these calculations on the formulae derived in Understanding Tides. Figure 1 shows the AO and NOA during the interval plotted together with the net solar/lunar tidal acceleration.

It is seen that in general the AO and NAO agree with each other so we simply now concentrate on the AO data. The period of oscillation of both is indeed similar to the monthly change in lunar tides, but no obvious cause and effect stands out at this level. We now look in more detail at two years of data: 2003-2004.

Intriguingly the oscillation period of the Jet Stream is also around one month. However there is only a small 3% anti-correlation between net tidal forces and AO. This gives just a hint of a tendency that when tidal forces are large the AO tends to go negative. The largest apparent “atmospheric tides” are those due to solar diurnal expansion. These are not gravitational tides. During northern winters such “solar heating” is diminished over the Arctic. Winters are the period when lunar gravitational tides could be expected to play more of a role in the positioning and strength of the Jet Stream, if such an effect exists at all.

I therefore decided to look more closely into the latitude dependence of the lunar tidal forces and in particular at the horizontal component of the tide or traction. It is this component which can move water and air long distances during the tidal cycle. Its strength varies during the lunar month and during the 18.6 year precession cycle. I calculated the tractional force/unit mass or acceleration for 60N and 30N which covers the range in latitudes typical of the Jet Stream.

What is particularly interesting here is the dependence of the tidal force on the 18.6 year precession cycle of the lunar orbit. The maximum standstill of the moon was around 2006-2007 when the declination angle reached a maximum of 28.6°. Since then it has been declining and is currently around its minimum value of 19.5°. A high declination angle actually reduces the tractional force most evident in the 30°N value shown in green above. There have been several papers reporting a link between the 18.6 year cycle and droughts across the US and central Asia. If the moon really is affecting the Jet Stream then this could be the explanation.

**Winters 2010 and 2014**

Now we look in detail at two winter periods. Firstly the harsh winter for the UK in 2009/2010 which corresponded to low values of AO. Is there any evidence for a lunar tidal effect on the Jet Stream in winter ?

I find this result remarkable. It shows clear evidence of a relationship between the strength of the lunar tidal force and the positioning and strength of the Jet Stream. There is an underlying anti-correlation showing a reduction in AO with tractional force at 60N even matching some details. There must also be a stochastic component so the agreement cannot be expected to be exact. Finally we look at last winter 2013/14 which saw the Jet Stream meander further south bringing storms to the UK. Since the meanders of the Jet Stream reached down to lower latitudes, I calculated the tractional forces for 45N. The results are shown below.

Again there is clear evidence that high latitude lunar tides modulated the Jet Stream. The severe storms in the UK caused coastal flooding because they coincided with high spring tides. Now I suspect that probably those high spring tides may have also have been a major cause of these very storms by also perturbing the Jet Stream!

Did I read that right? R = -0.03?

If you take every day from 1950 to 2014 to compare global tides with AO and then run it through the IDL procedure ‘correlate’ the answer is just -0.03, but – it is still statistically non zero. However it is just the winter months that show clear correlation with the horizontal component of lunar tides at jet stream latitudes. I am currently driving through France so my reply is a bit cryptic I am afraid.

There definitely is an effect. It’s importance needs to be evaluated

I realise now that the correlation I quoted is wrong. The two time series need to be normalised first. I will re-do the calculation and see what the result is.

What is “PNA”?

What is “NAP”?

How are PNA and NAP related to the NAO? Typos?

Sorry Clive, I do not see a correlation between AO and your tide data.

PNA is real and stands for Pacific/NorthAmerican pattern. see http://www.cpc.ncep.noaa.gov/products/precip/CWlink/pna/pna.shtml

NAP is a typo and should of course be NAO.

I met Roberto Madrigali while I was in Italy and he is convinced that changes in atmospheric tides tweak the Jet Stream causing it to meander and mix cold and warm air. Now I am back I intend to look at this in more detail. For over 20 years there have been reports of 18.6 year lunar cycles in droughts from China to the US. The tractional forces of spring tides changes significantly with latitude during the 18.6 year precession cycle.

Clearly it is not a simple cause and effect type phenomena if it exists at all. There is clearly also a chaotic component which may be dominant.

Isn’t it true that arctic air mass, being dense, would be subject to lunar gravitational pull in the winter when the Moon is closest to Earth? If so, then the shifting of that air mass would also shift the jet stream for a short period of time.

pier Corbyn has much to say and datta to sow and use on such

Could be relevant?

https://twitter.com/bbcweather/status/1164806010214596609

It sure is. Thanks for the link!

All these indices (NAO, AO, PNA, SAM, ENSO, etc) are related via the nonlinear solution to Laplace’s Tidal Equations.

https://geoenergymath.com/2019/08/12/ao-pna-and-sam-models/

The denialist sites such as oldbrew’s Tallbloke won’t like this because it’s not numerology and instead builds from the conventional fluid dynamics approach

On the contrary, we do like it. Looking at this:

1/(365.242/(27.321582)-13) = 2.72 years

and this:

1/(365.242/(27.2122)-13) = 2.37 years,

we propose that the difference between the number of each in one lunar nodal cycle, if the calculations are done more exactly, is 1.

In addition we find the number of occurrences of each has an interesting relationship to phi², but maybe that’s ‘numerology’.

has any one done Fourier analysis on the data to reveal known cycles?

This is just published

“Switch Between El Nino and La Nina is Caused by Subsurface Ocean Waves Likely Driven by Lunar Tidal Forcing”

https://www.nature.com/articles/s41598-019-49678-w

They reference the connection between ENSO and the Length-of-Day anomaly, which is predominately due to tidal forcing

All the cycles show up in the ENSO spectrum

Since Fourier transforms produce such beautiful spikes where they are supposed to be, the tidal effects are waves. My specific interest is the fact that these fluctuations are moving very fast! The order of 1000 miles an hour, depending on latitude. Energy waves dragged at supersonic speeds is the issue I am concerned with. In a 2-D model, it is like the “V” shaped wake from a speeding boat causing waves faster than the regular wind-driven surface waves. My interest is that there are “energy waves” which can at times travel faster than sound. They are displacement waves. Yanking on a long bar will cause a displacement that could be faster than sound waves traveling down the bar. Displacement or energy waves have the same units of circulation and torque which would account for all the wisps, twists, billowing and other atmospheric disturbances at any scale! I believe that is the main mechanism which causes “LIFT” for moving foils and other lifting bodies. The displacement wave causes an asymmetrical pressure distribution around the foil which gives a net pressure acting on the foil. Therefore I am interested in “displacement waves” or “energy waves” in an elastic medium such as air. Any comments?

Jim, Tidal effects are known to be solutions to a wave equation, which has been known since 1776 when Laplace developed the tidal equations. These later were shown to be shallow water or stratified approximations to the full Navier-Stokes equations of fluid dynamics/ Are you willing to work out the math of Laplace tidal equations or are you just providing a qualitative take based on some intuition you have?

Doing the math and showing excellent quantitative agreement with the observational data is the only way a model will get accepted. The agreement to data will need to be as good as conventional tidal analysis, which can predict sea level gauge readings very accurately once calibrated to historical data.

I am only interested in the qualitative discussion. I was interested in the velocity of the waves which would be faster than sound, therefore they are special waves more related to displacement waves caused by aerodynamic surfaces to provide lift. The displacement waves travel with the foil regardless of the speed of sound limitations. I believe the lift force is the vertical component of the asymmetric pressure distribution around the foil. If my qualitative theory is correct, I have an application which needs quantitative analysis, which is beyond my abilities. I want to estimate the lift produced by rolling cylinders in contact at near sonic surface velocities – assuming no seepage and no longitudinal flow. I assumed a linear pressure distribution from zero above the contact line and twice the ambient under the contact line. The result works out to a total of twice the ambient pressure applied to lift. This is considerably more than the drag which means a change of momentum and mass flow rate are not the only lift force mechanisms. Wave creation would seem to be a possible explanation. The rolling cylinders in contact produce a wave directly. Foils do the same thing but foils sit on only part of the wave. Also, the upper portion of the foil makes a similar wave. The difference between the waves produces lift. After the foil passes the effect is lost in the wake. Rolling cylinders in contact makes a wave with one half above and the other half below.

Now then – considering an inverted pair of rollers in contact near the ground. There would be a low-pressure wave forming below near the ground. Above the rolling cylinders in contact – there would be the high-pressure wave half formation. Therefore we have a stationary wave extending upward. This is a wave which could extend thousands of feet upwards depending on the scale. We could form an artificial mountain in the path of the prevailing winds. This could be turned on or off depending on humidity or other factors. Causing wind to rise – changing the wave of air as it passes by – could cause rain when conditions are right. Strategically locating such equipment could deflect tornadoes or hurricanes.

So what I need is something tangible to prove that adding a wave to existing waves can adjust local weather. Analysis of rolling cylinders in contact came from utilizing the Magnus effect to make an aircraft that can take off vertically. I first considered approaching air from two sides of counter-rotating cylinders which led to putting spinning the rollers in contact. Thanks for your reply.

Jim, There are a million qualitative arguments, just like there are a million Kipling “just-so” stories possible. But without supporting evidence for your ideas, no one will fund the construction of deflecting equipment to test this out. What you need to do is provide a mathematical formulation for what you are proposing,

You started by suggesting tidal forces will create the gravity waves. So start with the most fundamental behaviors that we can measure, say the quasi-biennial oscillations (QBO) in the equatorial stratospheric winds. Align these with the swings in long-period lunar and semi-annual solar forcings, and it all mathematically aligns.

Yet even with this clear evidence, it will take much more to make any kind of dent in convincing others that lunar forces are more important than we are lead to believe.

You have misunderstood what I am saying. Tides are the result of gravity and the results of gravity produce tidal waves. Gravity waves are a different phenomena. Since waves are the result of gravitational forces – those waves may be moderated by other waves of the correct frequency, power, and wavelength. I have surmised that they are “energy waves” or “displacement waves” that have been combined to force the weather and climate systems we see.

I surmised this from my study of rolling cylinders in contact which is the only interest to me. That study leads me to suggest that one could “modify” the tidal weather waves by adding another wave.

What is needed is a “quantitative study” to see the pressure distribution acting on a pair of rollers in contact with no slipping. I believe that study will show that more force and pressure is available than moving foils at high speed through the air as in conventional aircraft. That high force you will get will show that a stationary wave is produced. Since rolling cylinders in contact will produce a stationary wave – a wave in still air – would produce a pressure field around the system. That pressure field will alter the winds passing by the neighborhood.

My calculations showed twice the ambient pressure across the diameter of a rolling cylinder. I assumed no seepage with no longitudinal flow or heat transfer. I simply assumed linear pressure change from the top side of the contact line to the bottom. At sonic surface velocity, a vacuum will form above the contact line. Using similar logic, twice the ambient pressure will accumulate below the contact line. The air can’t come to the contact line on top since the roller surfaces are separating at “near sonic” speed. In the same way, the roller surfaces approach each other at the underside of the contact line means pinched air will accumulate. The air cannot seep through the contact line, therefor the accumulated air will cause the pressure to increase. From the conservation of matter, I have assumed that twice the ambient pressure is on the underside of the contact line since what is removed from above the contact line has to go someplace. Since the pressure below the contact line started at ambient, the additional air would be added and sum to be twice the ambient. Therefore, the pressure would change linearly from above the contact line where it is zero to below the contact line where the pressure is twice the ambient. Integrating around one cylinder gives an average pressure in the upward direction. (I am concentrating on producing a lift force for aircraft.)

The asymmetrical pressure distribution around a pair of rolling cylinders is a wave wrapped toward itself from the contact line to contact line in both directions. The “high” pressure half of the wave will form below the cylinders while the “low” pressure half of the wave will form above the contact line. No experimental apparatus is required to know that a pressure differential will occur. All I want to do at this point is to prove quantitatively what is the strength of the asymmetrical pressure wave produced by rolling cylinders in contact. The analytical proof will justify further empirical study and applications – including modifying weather.

The “theory of flight” includes balancing the mass flow rate downward with the lift force upward. The drag force caused by rolling the cylinders at sonic speed is equal to the mass flow rate from above – to below the rolling cylinders. The mass flow rate is small relative to the pressure calculation described above. That is what motivated further study and consideration that in fact some kind of waves is produced. Torque is observed as circulation which has the same units as energy so energy waves bend and curl as they dissipate showing circulation as something displaces the air at high speed.

Conventional foil produced lift force also produces “asymmetrical pressure waves” but only uses half of the wave! Foils produce two waves – one above the foil and the other below the foil. The difference between these two waves produces lift. What I am proposing with two rollers in contact is also two waves but these waves separate on top while they collide under the contact line. A foil has to have velocity through still air to make a lift force, while rollers in contact do not need to move through the air. The pair of rollers in contact have approaching and departing surface velocities that are not dependent on moving through the air. This concept will produce lift for vertical take-off vehicles.

Proving this concept analytically will allow proposals for weather modifying equipment as alluded to previously. Artificial “energy waves” or “displacement waves” will lift an aircraft or effect the prevailing winds on larger scale apparatus.

The question is – how much aerodynamic force would be produced from the asymmetrical airflow field surrounding rolling cylinders in contact at sonic surface velocity?

I suggest that twice the average pressure will be applied to the lift force. This would be of the order of twice the ambient pressure per roller. This assumes adiabatic, no seepage and longitudinal flow.

Helicopters have limited horizontal velocity because the foil wingtip velocity is added to its airspeed on one side while subtracted on the other. Therefore, lift on one side of the helicopter is reduced while increased on the other as it moves horizontally. Orienting the rolling cylinders parallel with the direction of travel will allow axial or longitudinal flow of air over the rolling surfaces. With appropriate “angle of attack” and increasing roller axial speed – higher horizontal flight and lift will be achieved.

Jim, This is a tidal-forced model of ENSO

The top is the model comparison to data, and the bottom is the spectral representation of the forcing function, which is approximated by the arcsin() of the data. Note the spectral peaks are all physically aliased against the well-known long-period tidal cycles via an annual impulse. Easy to calculate these by hand.

Math versus Prose, take your pick. I will go with the former.