A quasi-periodic ~2400-year climate cycle – or not?

We’ll look here at examples of where a 2400 year period has been identified by researchers in radiocarbon data.
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Part of the abstract below is highlighted for analysis. The original Talkshop post on the paper in question:
S. S. Vasiliev and V. A. Dergachev: 2400-year cycle in atmospheric radiocarbon concentration

Abstract. We have carried out power spectrum, time-spectrum and bispectrum analyses of the long-term series of the radiocarbon concentrations deduced from measurements of the radiocarbon content in tree rings for the last 8000 years. Classical harmonic analysis of this time series shows a number of periods: 2400, 940, 710, 570, 500, 420, 360, 230, 210 and 190 years. A principle feature of the time series is the long period of ~ 2400 years, which is well known. The lines with periods of 710, 420 and 210 years are found to be the primary secular components of power spectrum. The complicated structure of the observed power spectrum is the result of ~ 2400-year modulation of primary secular components. The modulation induces the appearance of two side lines for every primary one, namely lines with periods of 940 and 570 years, of 500 and 360 years, and 230 and 190 years. The bi-spectral analysis shows that the parameters of carbon exchange system varied with the ~ 2400-year period during the last 8000 years. Variations of these parameters appear to be a climate effect on the rate of transfer of 14C between the atmosphere and the the ocean.

Looking at the ‘primary’ numbers:
‘The lines with periods of 710, 420 and 210 years are found to be the primary secular components of power spectrum. The complicated structure of the observed power spectrum is the result of ~ 2400-year modulation of primary secular components.’
[See Figure 3 and Table 1 in the paper]
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Analysing this:
2400-year modulation = Mod-2400
210-year = de Vries cycle
420-year = de Vries pair (21 Jupiter-Saturn conjunctions)

With these periods we can derive as an approximation:
Square root of 2400*210 = 709.93 years
Therefore, the geometric mean of Mod-2400 and de Vries pair = ~710-year

The periods quoted in the abstract are rounded by the authors to the nearest ten years, but the pattern is there.

Substituting more accurate numbers for the de Vries pair:
21 Jupiter-Saturn = 417.16575 years
(via NASA JPL data: https://ssd.jpl.nasa.gov/?planet_phys_par)

Using the formula from this post:
24 * 2503y = 25 * 2402.88y
(24:25 = 2.4:2.5)

Then:
2402.88 * 417.16575 = (1001.1988y)² [geometric mean of the two periods]
2402.88 / 2.4 = 1001.2
417.16575 * 2.4 = 1001.1978

1001.2 * 2.5 = 2503
(2.4 = 12/5)

By the same method for the single de Vries period:
2402.88 * 208.58287 = (707.9545)² [geometric mean of the two periods]
This corresponds to the 710 year period referred to in the paper as a ‘primary secular component’ of the power spectrum.

Cross-check: 707.9545 * √2 = 1001.1988
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Vasiliev and Dergachev cite a NASA-sponsored paper by Hood and Jirikowic:
A Probable Approx. 2400 Year Solar Quasi-cycle in Atmospheric Delta C-14
[Alternative link: https://core.ac.uk/reader/10427436%5D

They say:
The residual record can be modeled to first order as an amplitude modulation of a century-scale periodic forcing function by a approx. 2400 year periodic forcing function.

The caption to their Figure 4 says:
Figure 4. Simple model of amplitude modulation of a 200 year sinusoid (a) by a 2400 year sinusoid (b). The product is shown in (c) and has characteristics that are qualitatively similar to those of the residual 14-C record.

They also refer to:
the empirical evidence discussed here for a dominantly solar origin of both the century-scale and longer-term (~ 2400 year) residual variations in the Conference 14-C record.

Figure 4 is worth a look to get a better idea of what they mean.
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A series of three articles under the title ‘Nature Unbound IV – The 2400-year Bray cycle’ can be found here:
https://judithcurry.com/?s=bray

Finally, Ivanka Charvatova finds a ~2402 year solar inertial motion period in this paper:
Responses of the basic cycles of 178.7 and 2402 yr in solar–terrestrial phenomena during the Holocene