**3. Distribution of vortex structures in the Venus wake**

Different from those properties it is necessary to examine changes of the vortex structures in their position along the nearly 8 years of observations conducted with the VEX spacecraft (between 2006 and 2013). A quantitative analysis of their location was made when VEX entered and exited those structures that was derived from the energy spectra of the planetary ions in the 20 VEX orbits listed in **Table 1**. A comparative view of the distribution of the vortex structures on the XZ plane of the solar wind velocity direction is presented in **Figure 3** to show the position of the VEX entry and exit crossings in orbits that probed near the midnight plane. Two sets with 4 orbits corresponding to measurements made in 2006 and in 2009 indicate a different displacement of the vortex structures in the Z-direction. There is a general preference of those features to occur closer to Venus in the 2009 measurements since their passage across the Z = 0 axis is by X = −1.7 RV in that set while it reaches X = −2.2 RV in the 2006 measurements.


**67**

wake varies during that cycle.

*4 orbits in 2006 and 2009 [10].*

*Solar Cycle Variations in the Position of Vortex Structures in the Venus Wake*

**Date UT X Y Z n v (**ρ**v2**

*VEX coordinates (in RV) at the time of its crossing (in UT) during an entry and exit (third to fifth columns) through a plasma structure within the Venus wake. Values for the density (cm−3) and speed v (km/s) of* 

*columns, and the last column has the time width of the vortex structure measured between the inbound and the outbound crossings (the segment between x =* −*2.30 RV and x =* −*1.95 RV is the same for both the sept 21–2009* 

*2*

 *(10−10 ergs/cm−3) are given in the sixth to eight* 

May 29-2013 04:38 -1.28 -0.02 0.40 3 20 3 10 May 30-2013 04:20 -2.00 0.07 -0.73 2 15 1 10 May 30-2013 04:30 -1.68 -0.04 -0.12 1 10 <1 10

**) ΔT**

This difference implies that the vortex structures are located closer to Venus during solar cycle minimum conditions by 2009 and that their position along the

*Position of the VEX spacecraft projected on the XZ plane during its entry (inbound) and exit (outbound) through a corkscrew plasma structure in orbits traced by the midnight plane. The two traces correspond to* 

A more extended description of the position and geometry of the vortex structures implied by the data of the orbits listed in **Table 1** is depicted in **Figure 4** to show changes in their location and extent during 8 years of VEX operation. In particular, they describe variations in their width as follows: For each orbit there is a segment bounded by the entry and exit of the spacecraft with a number that marks the two last digits of the year when measurements were made (they include the 4 orbits for 2006 and 4 for 2009 that were discussed in **Figure 3**). Most notable is that the segments identify 2 different regions; one corresponding to orbits before the minimum solar cycle conditions (between 2006 and 2009) and the other to orbits that occurred during and after those conditions (between 2009 and 2013). Two big circles select schematically different set of orbits that are located either far away from Venus between 2006 and 2009 (left circle) and

*DOI: http://dx.doi.org/10.5772/intechopen.96710*

*planetary O+ ions together with their kinetic energy density* ρ*v*

**Table 1.**

**Figure 3.**

*and the sept 26–2009 orbits).*

*Solar Cycle Variations in the Position of Vortex Structures in the Venus Wake DOI: http://dx.doi.org/10.5772/intechopen.96710*


**Table 1.**

*Solar System Planets and Exoplanets*

**Date UT X Y Z n v (**ρ**v2**

Aug 22-2006 01:45 -2.87 -0.15 -1.12 10 20 10 9 Aug 22-2006 01:54 -2.55 -0.15 -0.40 10 20 10 9 Aug 23-2006 01:59 -2.64 -0.07 -1.30 10 15 **6** 6 Aug 23-2006 02:05 -2.40 -0.07 -0.44 10 15 **6 6** Aug 24-2006 02.10 -2.48 0.01 -0.83 10 30 23 10 Aug 24-2006 02:20 -2.04 0.01 0.20 10 30 23 10 Aug 28-2006 02:22 -2.40 0.28 -0.38 20 20 20 6 Aug 28-2006 02:28 -2.18 0.07 0.91 20 20 20 6 Nov 13-2007 00:56 -2.60 -0.22 -0.70 10 20 10 7 Nov 13-2007 01:03 -2.38 -0.21 -0.38 10 20 10 7 Nov 15-2007 00:57 -2.60 -0.08 -0.65 10 20 10 6 Nov 15-2007 01:03 -2.40 -0.08 -0.38 10 20 10 6 June 27-2008 03:26 -2.60 0.03 -0.14 5 15 **3** 10 June 27-2008 03:36 -2.30 0.04 -0.20 5 15 **3** 10 June 28-2008 03:33 -2.52 0.04 -0.14 5 15 **3** 12 June 28-2008 03:45 -1.96 0.01 -0.20 5 15 **3** 12 Sept 19-2009 01:54 -2.42 -0.04 -1.04 10 15 6 9 Sept 19-2009 02:03 -2.11 -0.05 -0.55 10 15 6 9 Sept 21-2009 02:02 -2.30 0.08 -0.65 10 15 **6** 10 Sept 21-2009 02:12 -1.95 0.06 -0.12 10 15 **6** 10 Sept 25-2009 02:14 -2.15 0.33 -0.45 10 20 10 13 Sept 25-2009 02:27 -1.60 0.23 0.21 10 20 10 13 Sept 26-2009 02:12 -2.30 0.42 -0.70 10 20 10 10 Sept 26-2009 02:22 -1.95 0.34 -0.20 10 20 10 10 Aug 22-2010 08:24 -1.80 0.01 0.25 6 25 10 7 Aug 22-2010 08:31 -2.08 0.01 0.04 1 18 8 7 Aug 23-2010 08:16 -1.25 0.05 0.68 10 15 6 13 Aug 23-2010 08:29 -2.02 0.05 0.02 8 7 10 13 July 23-2011 02:53 -2:53 -0.14 -0.90 2 18 16 13 July 23-2011 03:06 -1.93 -0.13 -0.40 2 12 7 13 July 29-2011 03:07 -2.25 -2.25 -1.00 10 20 10 16 July 29-2011 03:23 -1.70 0.17 -0.10 7 15 4 16 Mar 05-2012 06:23 -2.07 -0.04 -0.60 30 25 48 12 Mar 05-2012 06:35 -1.50 -0.05 0.15 30 20 31 12 Oct 16-2012 01:26 -2.00 -0.02 -0.85 2 28 4 13 Oct 16-2012 01:39 -1.70 -0.03 0.10 6 13 26 13 May 29-2013 04:28 -1.70 -0.01 -0.14 8 20 8 10

**) ΔT**

**66**

*VEX coordinates (in RV) at the time of its crossing (in UT) during an entry and exit (third to fifth columns) through a plasma structure within the Venus wake. Values for the density (cm−3) and speed v (km/s) of planetary O+ ions together with their kinetic energy density* ρ*v 2 (10−10 ergs/cm−3) are given in the sixth to eight columns, and the last column has the time width of the vortex structure measured between the inbound and the outbound crossings (the segment between x =* −*2.30 RV and x =* −*1.95 RV is the same for both the sept 21–2009 and the sept 26–2009 orbits).*

**Figure 3.**

*Position of the VEX spacecraft projected on the XZ plane during its entry (inbound) and exit (outbound) through a corkscrew plasma structure in orbits traced by the midnight plane. The two traces correspond to 4 orbits in 2006 and 2009 [10].*

This difference implies that the vortex structures are located closer to Venus during solar cycle minimum conditions by 2009 and that their position along the wake varies during that cycle.

A more extended description of the position and geometry of the vortex structures implied by the data of the orbits listed in **Table 1** is depicted in **Figure 4** to show changes in their location and extent during 8 years of VEX operation. In particular, they describe variations in their width as follows: For each orbit there is a segment bounded by the entry and exit of the spacecraft with a number that marks the two last digits of the year when measurements were made (they include the 4 orbits for 2006 and 4 for 2009 that were discussed in **Figure 3**). Most notable is that the segments identify 2 different regions; one corresponding to orbits before the minimum solar cycle conditions (between 2006 and 2009) and the other to orbits that occurred during and after those conditions (between 2009 and 2013). Two big circles select schematically different set of orbits that are located either far away from Venus between 2006 and 2009 (left circle) and

#### **Figure 4.**

*Time-width (in minutes) measured between the VEX inbound and outbound crossings of a vortex structure as a function of the X-distance (RV) downstream from Venus in 20 orbits. The numbers at the side of each segment represent the two last digits of the year when measurements were made in different orbits between 2006 and 2013 (four orbits were examined during 2006 and 2009). The two circles confine orbits between 2006 and 2009 (left circle) prior to a solar cycle minimum and those between 2009 and 2013 (right circle) during that period.*

those that are placed closer to Venus between 2009 and 2013 (right circle) during solar cycle minimum conditions. The implication here is that as in **Figure 3** vortex structures occur closer to Venus during minimum solar cycle conditions.

Equally notable is that the time width ΔT (segment length) in the 2006–2009 orbit range is clearly smaller (placed at lower values along the vertical coordinate within the left circle) than that in the 2009–2013 orbit range (larger values in the right circle). As a result the thickness of the vortex structures located far away from Venus (left circle) becomes smaller with increasing distance along the wake thus implying that like in a corkscrew flow they thin out with distance downstream from Venus.

A schematic view of a corkscrew vortex flow structure in fluid dynamics is illustrated in **Figure 5** to represent the equivalent geometry of a similar structure in the Venus wake and that is formed by the distribution of planetary O+ ions eroded by the solar wind from the Venus ionosphere. The shape of the vortex structure in **Figure 5** shows how it becomes thinner with increasing distance from an object that is immersed in a streaming fluid. Such representation is consistent with the wider width of the vortex structures measured closer to Venus in the 2009–2013 orbit set (right circle in **Figure 4**) during solar minimum conditions instead of their thinner width measured in the 2006–2009 orbit set measured before the minimum solar cycle conditions (left circle), and that are located farther away along the Venus wake. As a result the thickness of the vortex structure gradually decreases with distance downstream from Venus and that eventually fade away and diffuse with the solar wind plasma. Further studies of more extended data are required to examine the evolution of the vortex structures far downstream along the Venus tail. It should also be noticed that in addition to changes associated to a solar cycle

**69**

*Solar Cycle Variations in the Position of Vortex Structures in the Venus Wake*

there is evidence that the solar energy output and thus that of the solar wind during the last cycle have decreased with respect to values measured in the previous cycle and thus there is a tendency for the input solar wind pressure to now reach smaller

*View of a corkscrew vortex flow in fluid dynamics. Its geometry is equivalent to that of a vortex flow in the Venus wake with its width and position varying during the solar cycle. Near minimum solar cycle conditions the vortex is located closer to Venus (right side) and there are indications that its width becomes smaller with increasing distance downstream from the planet. Such is the case for orbits within the left circle of Figure 4 and that were conducted before the solar cycle minimum at 2009–2010 thus implying that it becomes thinner when it* 

The main output of these concepts is that the position of the vortex structures along the Venus wake and their width measured along the VEX trajectory vary along the solar cycle thus implying a continuous displacement of the region where they apply. Similar conditions should also be applicable along the plasma wake of other planets and satellites within the solar system and may as well reach those

Throughout the solar system the most likely candidates are Venus and Mars which do not have a strong intrinsic magnetic field that deflects the solar wind before it reaches their upper atmosphere/ionosphere. While plasma vortices have been inferred from measurements made along the flanks of the earth's magnetosphere [11–13] changes in their position are not expected to produce local variations as notable as those measured in the Venus wake. On the other hand observations of vortex oscillations have been reported from measurements conducted with the MAVEN spacecraft by the solar wind Mars ionosphere boundary [14] and it is possible that they produce vortex structures similar to those detected in the Venus wake. Comparable conditions may also occur around the Titan ionosphere when it is subject to the solar wind flow and/or to plasma motion within Saturn's magnetosphere when it moves across it. The dynamic pressure of the plasma pressure that reaches Titan is very different in both cases and thus

*DOI: http://dx.doi.org/10.5772/intechopen.96710*

values under solar minimum conditions.

*is detected further downstream along the wake.*

**Figure 5.**

**4. Conditions applicable to other planets**

suitable to exo-planets impacted by stellar winds.

*Solar Cycle Variations in the Position of Vortex Structures in the Venus Wake DOI: http://dx.doi.org/10.5772/intechopen.96710*

#### **Figure 5.**

*Solar System Planets and Exoplanets*

those that are placed closer to Venus between 2009 and 2013 (right circle) during solar cycle minimum conditions. The implication here is that as in **Figure 3** vortex

*Time-width (in minutes) measured between the VEX inbound and outbound crossings of a vortex structure as a function of the X-distance (RV) downstream from Venus in 20 orbits. The numbers at the side of each segment represent the two last digits of the year when measurements were made in different orbits between 2006 and 2013 (four orbits were examined during 2006 and 2009). The two circles confine orbits between 2006 and 2009 (left circle) prior to a solar cycle minimum and those between 2009 and 2013 (right circle)* 

Equally notable is that the time width ΔT (segment length) in the 2006–2009 orbit range is clearly smaller (placed at lower values along the vertical coordinate within the left circle) than that in the 2009–2013 orbit range (larger values in the right circle). As a result the thickness of the vortex structures located far away from Venus (left circle) becomes smaller with increasing distance along the wake thus implying that like in a corkscrew flow they thin out with distance downstream

A schematic view of a corkscrew vortex flow structure in fluid dynamics is illustrated in **Figure 5** to represent the equivalent geometry of a similar structure in the Venus wake and that is formed by the distribution of planetary O+ ions eroded by the solar wind from the Venus ionosphere. The shape of the vortex structure in **Figure 5** shows how it becomes thinner with increasing distance from an object that is immersed in a streaming fluid. Such representation is consistent with the wider width of the vortex structures measured closer to Venus in the 2009–2013 orbit set (right circle in **Figure 4**) during solar minimum conditions instead of their thinner width measured in the 2006–2009 orbit set measured before the minimum solar cycle conditions (left circle), and that are located farther away along the Venus wake. As a result the thickness of the vortex structure gradually decreases with distance downstream from Venus and that eventually fade away and diffuse with the solar wind plasma. Further studies of more extended data are required to examine the evolution of the vortex structures far downstream along the Venus tail. It should also be noticed that in addition to changes associated to a solar cycle

structures occur closer to Venus during minimum solar cycle conditions.

**68**

from Venus.

**Figure 4.**

*during that period.*

*View of a corkscrew vortex flow in fluid dynamics. Its geometry is equivalent to that of a vortex flow in the Venus wake with its width and position varying during the solar cycle. Near minimum solar cycle conditions the vortex is located closer to Venus (right side) and there are indications that its width becomes smaller with increasing distance downstream from the planet. Such is the case for orbits within the left circle of Figure 4 and that were conducted before the solar cycle minimum at 2009–2010 thus implying that it becomes thinner when it is detected further downstream along the wake.*

there is evidence that the solar energy output and thus that of the solar wind during the last cycle have decreased with respect to values measured in the previous cycle and thus there is a tendency for the input solar wind pressure to now reach smaller values under solar minimum conditions.
