Revisiting Alfven Waves

 Alfven waves are the most important waves propagating in the solar atmosphere, as well as the Earth’s magnetosphere (underpinning the coupling between it and the ionosphere). They are important in that they efficiently carry energy and momentum along the magnetic field.

     One way to get a handle (of sorts) on Alfven waves is to look at the analogy with mechanical waves – say propagating along in a single direction x  for a string put under tension T.

     Consider the reference frame or coordinate system for a transverse wave on a string:

Where we have in terms of the string tension T:

 T _u  = T sin q

As usual per these approaches, assume q is very small, in which limit, sin q  » tan q

Then:

T sin q = T tan q =  T  (¶  u/ ¶x)

 Taking  the force difference:  

[T _u ] _{x + dx} -   [T _u ] _x  =  ¶  / ¶x (T  (¶  u/ ¶x) dx

    To ensure no net horizontal forces due to tension,  we limit the situation to small slopes. Also, neglect the possibility of a vertical force per unit length, so:

 r dx (¶ ² u/ ¶ t²) = ¶  / ¶x (T  (¶  u/ ¶x) dx

Which simplifies to:

 r  (¶ ² u/ ¶ t²) = T  (¶  ² u/ ¶x² )

Now, transform to the standard wave equation in 1-dimension:

 ¶² u/ ¶x²  -  1/ c² (¶ ² u/ ¶ t²) = 0

 From this we can solve for the velocity  c:

c = (T/ r ) ^½

Say x marks the direction of propagation in the above coordinate system, and y is the direction of transverse (wave) displacement. Then the vertical force component is:

F_y = - T(¶ y/ ¶ x)

where T is the tension. Thus, just as the restoring force for a mechanical wave is the string tension T, the restoring force for an Alfven wave is the magnetic tension. This magnetic version of “tension” accelerates the plasma and is opposed by the inertia of the ions (mainly from proton masses m _p)

Now, the wave speed on a string is related to u (mass per unit length), and T such that:

v = (T/ u) ^1/2

And as we can see, increasing the string tension T _u increases the wave speed in an analogous way to what magnetic tension does for the Alfven wave. The magnetic tension analog can be expressed (as we shall see) as:

T _M = B² / m _o

where B is the magnetic induction and m_o  is the magnetic permeability for free space ( 4π x 10 ^-7 H/m)

In what follows we assume a uniform plasma in equilibrium, which will then be subjected to velocity disturbance or perturbation that affects all other key quantities. The treatment is kept as simple as possible (considering the complexity of the subject matter!) , and we don’t veer out of the linear domain. Nevertheless it should be stated at the outset that some details are omitted, or left as work for yourself with hints provided. In this way you will better understand and appreciate the genesis of Alfven waves.

Examining the origin of these waves always starts with setting out the basic equations for what we call “ideal MHD”:

1) ¶ r / ¶ t  = - DIV (r v)

2) ¶ (r v)/ ¶ t  =

- DIV (r vv) – grad p + 1/ m _o [(Curl B) X B]

3) ¶ B / ¶t = Curl (v X B)

4) ¶p/ ¶ t = - v. grad p –  g p DIV v

      Where v is the fluid velocity, p the pressure, B the magnetic induction, and g = - d ln p/ d ln V where V denotes volume.   Next we  introduce small perturbed quantities (e.g. imagine introducing a small perturbation into the plasma velocity such that v_o < < v _l , which will also subject the mass density, fluid pressure and magnetic field to perturbation), such that:

r  = r_o  +   r _l

v = v _l    ,   B = B _o + B _l   ,   p = p _o + p _l

Now,  substitute these back into the original ideal MHD equations to obtain:

5) ¶ r _l / ¶ t = -  r _o  DIV v _l

6) r_o  (¶v _l/ ¶ t) = - grad p _l + 1/ m _o  [(Curl B _l) X B _o ]

7) ¶ B  _l  / ¶t  = Curl (v _l  X B _o )

8)  ¶ p  _l  / ¶t = - g p _o DIV v _l

Now, divide through the 2nd equation above by  the mass density r:

¶v _l / ¶t  = -(c _s²) grad p  _l  / r  - 1/ m _o  r  [B _o x Curl B₁]

where ‘c _s’ is the sound speed. Using this result and the last two equations of the perturbed set, we apply Fourier transforms to obtain:

w²  v _l –  c _s  ²  (kv _x )k* + 

B _o / m _o  r _o [k X k* X ( v _l  X B _o)]  =   0

Where w  denotes the plasma frequency, k is the wave number vector (k* the wave vector orientation) and the other quantities are as before.

It is of interest here to obtain the x, y-components of velocity associated with the wave, by use of Fourier transforms.  The procedure is straightforward and I show it in what follows.

The x-component is:

w²  v _x   –  c _s  ²    k ²    v _x  + B  _z k ²  /  m _o  r _o  [v _z   B  _x  –  v _x  B  _z] = 0

The y-component is decoupled from the others (e.g. x, z) and can be written:

 w²  v _y   -  B  _x ²   k ²  v _y / m _o   r _o = 0

Or simply:

w²   = [B  _x ²   / m _o  r _o] k ²

where the quantity in brackets is the Alfven velocity or alternatively written:

v  _A  = [ w/ k] =  B _x  / [m _o  r _o]  ^{1/ 2}

Or :

v  _A   = B_o  / [m _o  r _o]  ^{1/ 2}

(Since B_o    is in the x –direction)

For completeness, we should be able to show the z-component equation is:

w²  v _z  -  B _x  k ²  / m _o  r _o  [v _z  B _x  -  v _x  B  _z] = 0

I  refer  again to the basic wave equation one can obtain by getting the second derivative of:

¶v _l / ¶t  = - (c _s ² ) grad p _l / r  - 1/ m _o  r  [B _o X Curl B ₁]

One can then find the solution in terms of plane waves by assuming: 

v  ₁ = v  ₁ [exp ikx – iwt]

For which taking the second derivative, of  v  ₁ with respect to t yields the original equation in w  found earlier. 

For completeness, I note what happens when you solve the preceding (simultaneous) equations in x, and z.

w ⁴ +  w² [- c _s  ²  k  ²  - B _x ²  k  ²  / m _o  r _o ] + 

c _s  ²  k  ⁴    [B _x ²  / m _o  r _o ] = 0

Or:

w ⁴ -   w²  (c _s ²   + v  _A ² )k ²  +  c _s  ² v  _A ²  cos  ² (Θ) k ⁴  = 0

And finally,

w²   = ½[( c _s ² v  _A ²  k ²  +  

 [(c _s ² v _A ²  k ⁴  –  4 c _s ² v _A ²    cos ² (Θ) k⁴ ]^1/2 

Careful variation of Θ  for the above equations leads to special conditions which can also identify the “fast” and “slow” megnetosonic waves

The conditions and associated results are expressed in summary form:

For  Θ   =  0,   w²   =  {  v _A ² k ²  

                                          { c _s ²   k ²  

For  Θ   =  90,   w²   = {(c _s ²   + v  _A ² )k ²  

                                       =  {0

It is convenient to distinguish these waves  of differing velocity using the diagram shown below:

Note in particular the orientation of the wave number vector (k) as well as the lobes for the sound speed  c _s  and the Alfven velocity  v _A - both in relation to (c _s  ²  + v  _A ² ) and the  equilibrium magnetic field intensity,  B _o.  Note (c _s  ²   + v  _A ²)  is called the “fast mode” magneotsonic wave velocity, while  c _s  denotes the “slow mode” velocity.  If one plots the preceding using (c _s  ²   + v  _A ² ) for the vertical axis and B _o (e.g. x)  for the horizontal,  one will also get what is called “Friedrich’s diagram”  shown below:

   The Friedrich diagram  consists of :

1)A smaller “dumb bell” or figure-8 shaped graph centered at the origin. This will be for what we call “slow mode” waves

2)A double lobe enveloped by a larger circle and itself enveloping a smaller double lobe. This will be for Alfven waves proper.

3) A circle shaped graph surrounding both 1, 2 above. This will be for what we call the “fast MHD” mode.

 The critical aspect to note here is that the fast mode is the only MHD wave able to carry energy perpendicular to the magnetic field. This has important ramifications for solar flares, as well as magnetospheric effects (such as the aurora). Meanwhile, the phase velocity (w/k) of the slow mode wave perpendicular to the magnetic field is always zero. In the limit where the sound speed:

 c _s  ²  > > v  _A ², and the Alfven speed:

 v  _A ²  < < c _s  ²,

The slow wave disappears. (Which one can easily validate and confirm for the equation in w² )

Other properties, points to note:

-The velocity perturbation v ₁ is orthogonal to B _o

-The wave is incompressible since DIV v ₁ = ik.v ₁ = 0

-The magnetic field perturbation (B ₁) is aligned with the velocity perturbation. Since both are perpendicular to k and B _o

-The current density perturbation (J ₁) exists as a current perturbation perpendicular to k and B _o  e.g.

J ₁ = k X  B _o

- When c _s  ²  >>  v  _A ² the fast mode wave becomes a compressional Alfven wave. This has a group velocity equal to its phase velocity w /k

For fast mode waves with k ⊥  B _o   we can present the diagrams below showing the relations between the distinct field directions and applicable velocity as well as wave number vector in relation to B-field perturbations.

Suggested Problems:

1) For the mechanical wave diagram for transverse wave on a string  sketch the x, y-components of the string tension T. Show how the components and differences between them lead to the result:

[T _u ] _{x + dx} -   [T _u ] _x  =  ¶  / ¶x (T  (¶  u/ ¶x) dx

2) (a) A student sketches the  diagram below to show the different modes of plasma waves  which he argues exist in the Sun.

Redraw the diagram to improve its clarity and then explain the reasons for any changes made.  Would the parameters shown really make sense for such waves propagating in the Sun? Why or why not?  Give a quantitative explanation if possible.

(b)Compute the Alfven velocity in a layer of the Sun for which:

  r _o =   0. 2 g/ cm  ³  and B = 0.1 T.

The Stock Markets' Carnage Is Only Getting Started - And The Roles Of Defensive And Cyclical Stocks

 

                              "I gonna prove stocks will soar as me tariffs go up!"

                                            Finance data showing 'defensives' vs  'cyclicals'

                                            (James Mackintosh, WSJ, Apr. 5-6, p. B4 )

“I do think that at this point we might have passed the event horizon, meaning that even if Trump backs off from the tariffs, there’s been enough damage done to the U.S. economy, to the global economy, to investor confidence, consumer confidence, that we’re probably going to see a recession regardless of what happens,”- Peter Berezin, global strategist BCA Research, 'Why Did So Many Delude Themselves  About Trump?' NY Times

"Tariffs on Switzerland, a country that has, in effect, no import duties? Singapore? What are we doing punishing Korea and Japan with duties based on a calculation that isn’t based on tariffs or other barriers to trade? Add to that the duties on those hapless penguins of the Australian territory of Heard Island and McDonald Islands, and we look not only mean but stupid". - Gerard Baker, WSJ, 'Trump is Trashing America's Reputation'

“A trillion comments have been wasted accusing the wrong people of Trump derangement syndrome. The real TDS afflicts those who keep seeing a rational actor, or an economic chess game, where none exists. The whole market arguably suffers from this syndrome. Shortly after plummeting on Monday morning, a fake news release surfaced that said Trump would announce a pause on his tariffs this week. The markets more than erased their opening losses. All those gains, in turn, were wiped out when the White House issued a denial. The merest rumor he might be sane can trigger a buying frenzy.” – Edward Luce, Financial Times, ‘Trump Has No Idea What He’s Unleashed’

Stocks are facing another week of “elevated uncertainty about tariffs, their duration, and the potential for more retaliation,” said Carol Schleif, chief market strategist at BMO Private Wealth in Minneapolis, noting that investors are puzzling through what makes sense under new tariff regimes. But let's be clear, not even the market meltdown instigator of the greatest unforced economic  error in history knows.

In a July, 2017 WSJ column ('Now May Be Time To Sell Stocks'), Mackintosh observes:

"Explanation is not the same as justification. The fact that everything has been awesome recently is little guide to the future of the economy or inflation - and the rise of stocks makes it less likely the general awesomeness will continue."

So, in a sense, investors' belief that things will continue in the "awesome"  mode is because they have been awesome the past year-   is a twist on the classical logical fallacy known as Post hoc ergo propter hoc .   But when we have a psychotic and semi-senile president who spouts nonsense at will and can't tell a tariff from a tattoo, then no degree of forecast or confidence is possible.  Because every financial datum has been tossed into a giant mixer allowing no certainty by which to make one's money placements or investments. Hence, in his most recent column (April 5-6, p. B4) Mackintosh argues the current market carnage could just be a start.  Indeed, yesterday's onset of a meltdown was only halted - turning into an up-swing then diving again and more volatility - after a nitwit tweeted Trump planned a "90 day halt on tariffs."  None of which was true.

But even before this fiasco, Mackintosh wrote (ibid.):   

"The market carnage may be just the beginning.  If the tariffs- in effect the biggest tax increase since at least the 1950s  - cause the economy to shrink, stocks and Treasury yields still have a long way to go down." 

 He then points to two opposing forces in the markets, also displayed in the top graphic: "defensive stocks" and "cyclical stocks". As he describes the relationships:

"As recessions take hold, stocks are hit both by lower earnings and lower valuations. Defensive stocks - such as sellers of food and other staples, better able to maintain sales -beat those selling optional purchases, known as 'cyclicals'.  Since the S&P 500 peaked in February, investors have moved fast to dump cyclicals and switch to defensives.

My measure of cyclical sectors which equally weights stocks within each sector, has lagged behind defensives by the most (over such a short period) since the March, 2020 Covid lockdown. The lowest rated junk bonds - most likely to default on tough times - have also been hit hard.  Their extra yield above Treasurys has risen by more than 2 percentage points."

Recall here, that when bond yields rise, their prices fall. Mackintosh's point is that the market is currently playing 'catch up' in trying to price in a higher chance of recession. After all, "the S&P 500 is only down 12% from its all time high and back to where it stood in August."

Generally in a recession stocks "fall at least 20 percent and give up more than 7 months gains".  This means that if the chances of recession are as high as some - like Jamie Dimon - estimate, there is a way to go before it manifests. But that also implies a much bigger drop (i.e. "carnage") is on the way. As Mackintosh puts it:  

"Investors who think the return to tariffs is higher than the Smoot Hawley rates will hammer the economy into recession should expect much bigger falls in stocks and bond yields as 2025 goes on."

I am definitely in this camp-  and following CBS finance expert Jill Schlesinger's advice yesterday-  have advised all in the extended family ready to retire in 1-2 years to pull money from whatever stocks (especially tech) and put it into safe havens (i.e. cash, money markets).  You won't become a millionaire, but then you also won't end up living in a box eating cat food and kibbles in your 'golden years'.

Mackintosh concludes with a heads up for the financial Pollyannas:

"Those who think the rest of the world won't seriously retaliate and that Trump will quickly negotiate the rates away will be happier with the higher prices. But even they ought to worry about the damaging effects of prolonged uncertainty on the economy."

Which is solid advice given no one, no sane person in his or her right mind - and who has any investments anywhere - should be betting on Dotard's logic, or capacity for any rational thinking to make sound decisions.  The man is incapable of them, and is invested only in his own ego, and narcissism -fueled power trips, not the nation's welfare.   So no wonder so many former pro-Trump billionaires are now calling the orange imp's moves "stupid", i.e.

Wall Street Bursts With Anger Over Tariff ‘Stupidity’ - The New York Times

Given no consistency of logic or reasoning exists in our "commander-in- chief" there can be no certainty on which businesses, citizens - or any other countries - can depend to make their own sound decisions.  It is a giant Trump casino from day to day.  Just ask the people in the Caribbean - including Barbados - who were informed (by Marco Rubio) - that U.S. aid may be cut if they continue to allow Cuban doctors in to give medical aid.  Like Barbados did during the Covid pandemic, e.g.

Brane Space: Bravo To Cuban Doctors Now Helping Barbados In Its New, Critical Battle Vs. COVID

Let us say that Barbados PM Mia Mottley has not been pleased with the veiled threat.  Nor will Bim take kindly to any tariffs exacted by the orange fungus impersonating a president.

 See Also:

Donald Trump

The Real Reason We’re in a National Emergency

by Robert Reich | April 7, 2025 - 5:38am | permalink

— from Robert Reich's Substack

It’s hard to remember that only 10 weeks ago, the American economy was quite good, our foreign relations were on the whole positive, we were on the way to dealing with climate change with subsidies for wind and solar energy, and we still lived in a democracy.

Today, all that is disappearing. The economy is in acute danger, our relationships with traditional allies are collapsing, we’re subsidizing fossil fuel polluters, and we’re turning into a dictatorship.

This has happened in part because of Trump’s continuing creation of fake national emergencies.

He has declared foreign trade a national emergency and used the International Emergency Economic Powers Act of 1977 to raise tariffs to levels not seen since the disastrous Smoot-Hawley tariff of 1930.

» article continues...

And:

Trump’s Crazy Trade War

by Mel Gurtov | April 7, 2025 - 5:00am | permalink

A Scatter Gun Approach

The Trump tariff shock is going to take a bit of time to sink in, though stock markets worldwide have already sunk. Altogether, 60 countries have been slapped with at least 10 percent tariffs; those with large trade surpluses with the US will pay a much higher rate. Trump’s public argument was two-fold: force US trade partners with the highest surpluses to lower their tariffs on US imports, and encourage US and other multinational firms to move their manufacturing to the US.

Interestingly, the tariff announcement did not apply to Russia, North Korea, Cuba, and Belarus, supposedly because they don’t run a trade surplus with the US. Except that Russia does.

On the other hand, Japan, South Korea, Taiwan, Israel, Ukraine, and just about every other country, whether friend or foe, was not spared, with tariff rates ranging from 24 to 40 percent. Even Britain, whose prime minister had thought the invitation to Trump from the king for a visit would help put off a tariff increase, was not spared. Nor for that matter were several islands that are not countries and have no humans. Everyone must pay.

» article continues...

And:

Trade

‘Violates the Law As Written’: Trump-Loving Billionaires Sue To Stop Tariffs

by Carl Gibson | April 8, 2025 - 5:34am | permalink

— from Alternet

President Donald Trump's tariff announcement last week has not only rattled financial markets, but even a group of far-right billionaires who have a history of supporting Republican causes.

The Guardian reported that both a far-right group funded by both multibillionaire Charles Koch and the Federalist Society's Leonard Leo is now suing to stop Trump's new trade duties on China from taking effect. The New Civil Liberties Alliance argued that Trump's invocation of the International Emergency Economic Powers Act (IEEPA) to justify his unilateral imposition of new tariffs is illegal, and that the courts should intervene based on precedent that requires Congress weigh in on certain policy-related matters.

“This statute authorizes specific emergency actions like imposing sanctions or freezing assets to protect the United States from foreign threats,” the organization stated. “It does not authorize the president to impose tariffs. In its nearly 50-year history, no other president – including President Trump in his first term – has ever tried to use the IEEPA to impose tariffs.”

» article continues...

And:

China | Trade

What America Misunderstands About China’s Trade Resolve

by Jianlu Bi | April 9, 2025 - 4:57am | permalink

— from Foreign Policy In Focus

Following the U.S. implementation of new reciprocal tariffs on Chinese goods, China’s swift and decisive imposition of a 34 percent tariff on American imports, coupled with tightened export controls on rare earths and the blacklisting of U.S. companies, underscores Beijing’s resolve to defend its economic interests against what it perceives as unilateral bullying. The timing and scale of China’s response, just days after the United States unveiled its own reciprocal tariffs, sends a clear message: Beijing is prepared to play hardball.

The notion that China would meekly acquiesce to Washington’s demands, even with the dangling carrot of a TikTok deal, has been soundly rejected. Instead, China’s actions signal a new era of economic confrontation, where reciprocal measures and targeted sanctions are the weapons of choice. The 34 percent tariff, effective April 10, represents a substantial blow to American exporters, particularly those in the agricultural and industrial sectors, and the suspension of sorghum and poultry product exports demonstrates China’s willingness to leverage its market power.

» article continues...

How The Milankovitch Hypothesis To Explain The Ice Ages Has Been Proven Wrong.

 The grandiose name “Milankovitch theory” purports to account for the recurrence of the ice ages. In fact, it is more correct to call it the “Milankovitch hypothesis” or better, conjecture - especially as few astronomers that I know accept it. On that note, we can examine how it's basically been disproven as a valid theory. That is to say, an entity that is capable of making verifiable predictions based on a self-consistent hypothesis.

Milankovitch proponents claimed decades ago that a geological proxy climate record revealed the same temporal cycles manifested in the three orbital parameters: eccentricity, obliquity, and precession.  All this was intended to substantiate the so-called Milankovitch theory which asserts these three distinct cycles are applicable to Earth's orbital motion.

To fix ideas the eccentricity (a) describes the shape of Earth's orbit around the Sun,  said by the Milankovitch proponents to vary from near circular (as it is now) to more elliptical, with a period of 96,000 years.  The obliquity (b) is the tilt of the Earth's axis of rotation with respect to the orbital plane, and oscillates with a period of 41,000 years -  according to Milankovitch proponents The precession (c) combines the spin of Earth's orbital axis and its orbital path over time, producing a 21,000 year cycle, again according to Milankovitch proponents.

To my knowledge no proponent has actually made predictions that have verified the 3 cycles' connection to the geological proxy record.  Technically, one would also expect such predictions to come out of a dynamic model from celestial mechanics - not one dependent on sea floor topography or geology.  These are two distinct sciences after all. (Paleo-climatology, i.e. based  on marine micro-fossils,  is also distinct from celestial mechanics.) What we have then is not a theory but a conjecture.

Missing such theoretical connections it's relatively easy to disprove this conjecture, focusing on just one cycle. We can then examine the putative change in the eccentricity e, which is currently at 0.0167 but which Milankovitch adherents claim can reach e = 0.07. (Elongating the orbit so as to influence climatic factors, e.g. see this video demonstration:

But what would it take to change the shape of the Earth's current orbit, to the one proposed by Milankovitch supporters?  How much energy would be required?  We can use the equation for the total energy of the orbit, in terms of the eccentricity, e, and the dimension of orbit known as the semilatus rectum,: r o   (=   b ² /a)  and the other familiar parameters for Newtonian orbit computations, e.g.

The objective is to find the change in energy E, i.e. when the eccentricity is altered from 0.0167 to 0.07.  This turns out to be approximately:

D E   »  1.9  x 10   ⁴² J


This is an enormous amount of energy input.  WHERE does it come from? HOW is it produced?  What is the time evolution - in energy increments- leading to the final more eccentric orbit?  The Milankovitch adherents who adopt the work of a Serbian civil engineer, provide us no answers.  How can they when they are working from reconstructed sea floor geology  findings and not celestial mechanics per se?

Given the preceding we should acknowledge that  there are significant problems with that Serbian civil engineer's hypothesis that bid us to exercise much more caution, i.e. before adopting it without qualification.  Especially given its reversed engineered construction from geological data, to arrive at a celestial mechanics format requiring new orbital elements.   Or conferring the benediction of an origin in celestial mechanics, as opposed to geology. One major issue was raised in a paper by Daniel B. Karner and Richard A. Muller ² which pointed out a number of serious problems, inconsistencies associated with the Milankovitch hypothesis. 

Specifically the authors – after  assessing the  data from numerous sources (e.g. U-Th dating from the Devil’s Hole cave in Nevada) found that the Devil’s Hole data indicated a shift in d ¹⁸ O  to interglacial values and was “essentially complete by 135 ka but the Northern Hemisphere summer insolation hadn’t yet warmed to the point when it would have triggered anything extraordinary, let alone a glacial termination”  Adding: “We call this discrepancy the causality problem”:

-       The authors conclude (op. cit.):

“The standard Milankovitch insolation theory does not account for the termination of the Ice Ages.”

Adding that:

“We can conclude that models that attribute the terminations to large insolation peaks (or equivalently to peaks in the precession parameter)…are incompatible with the observations.”

Equally significant, perhaps, Richard A. Muller  has pointed out in a separate paper ³ that “the spectral shapes predicted by the Milankovitch theory do not match those in the spectrum and bispectrum of the data..”

In addition, Muller notes that the net forcing associated with clouds, i.e. about 30 W/m ²  is substantially greater than the rms variations in insolation.   This leads him to conclude: 

 “The changes in cloud cover could be more important than the changes in Milankovitch parameters.” 

Finally, Puetz et al⁴,  employed a “universal cycle model” – using a Universal Wave Series (UWS) with cycles in the kyr range -  to show that  orbital tuning limits independent and objective testing of an empirical hypothesis like that of Milankovitch. In effect, while Milankovitch offers a “seductively elegant solution to the problem of age-stratum mapping”, its template remains a trap for selection effects (and data bias) to enter. This results in a condition, as it pertains to the Milankovitch hypothesis,  whereby:

 ”Reporting bias occurs when articles mention favorable results from orbitally tuned records, which are supportive of the Milankovitch theory, while failing to mention unfavorable results from un-tuned versions of the same records.”

The reason is clear given that (ibid.): “Statistically significant positive results that support a desired outcome are more likely to be published in high impact journals.”

Thus, while one can certainly appreciate Prof. Maslin’s article, it is also worthwhile to be aware of the problems to do with the underlying hypothesis, most of which I suspect were engendered by the origins in sea floor geologic data.. 

My contention then is if there is no independent confirmation of the Milankovitch hypothesis from celestial mechanics proper, the whole conjecture falls apart. (Or if you prefer, the "theory
 is disproven.)  I cn here the Milankovitch proponents screaming already: "But what do you expect us to do then?"

Easy. Provide us with the model, or even just a numerical simulation, showing how the three orbital parameters evolve over time t to yield  the temporal cycles suggested by the  marine microfossil studies?  

 In effect, leaving out the geological data, show us how Earth's orbit changes its parameters to yield the temporal cycles claimed by Maslin, as well as Hays et al, and oh yes, Milankovitch.

References:

1. J.D. Hays, J. Imbrie, N.J. Shackleton, Science 194, 1121 (1976)

2.Daniel B. Karner, Richard A. Muller, A Causality Problem for Milankovitch, Science, 288, 2143 (2000)

3. Richard A. Muller, Limitations and Failures of the Milankovitch Theory, poster paper, American Geophysical Union Fall Meeting (2001)

4. Stephen J. Puetz, Andreas Prokoph, Glenn Borchardt, Evaluating Alternatives To The Milankovitch Theory, Journal of Statistical Planning and Inference, 170,  158 (2016)