Description of the streak structure

A calibrated image of the night-side of Venus taken by IR2 is shown in Fig. 1. This image captures infrared radiation at 2.26 μm emitted by the hot atmosphere around 30 km altitudes and partly absorbed by dense middle and lower clouds lying at altitudes of around 49–57 km13,14. That is, bright colour in Fig. 1 indicates low-opacity regions and dark colour indicates high-opacity regions. One of the most prominent features in this image is the existence of a planetary-scale streak structure that is composed of many bright streaks located in both hemispheres with a rough equatorial symmetry. The streaks are enhanced and become clearer as shown in Fig. 2a by an edge-emphasis process described in Methods. In the northern hemisphere, for instance, the streaks extend from the northwest to southeast, at least for 7700 km from (lon, lat) ~ (210, 35) to (290, 15), and the width of each streak is hundreds of km. Since downward flow is considered to decrease the cloud opacity, the streak structure in bright colour may indicate the presence of strong downward flow19. A further discussion on the relation between the lower-cloud opacity and downward flow is given in Discussion.

Fig. 1 Calibrated image of the night-side of Venus taken on 25 March 2016 07:33 UT by IR2, the 2-μm camera, on board the Venus Climate Orbiter/Akatsuki. Contrast features in the image are believed to reflect the opacity contrast of dense middle and lower clouds with a particle size of about 3.7 μm (called mode 3) located around 49–57 km height. Note that the sub-spacecraft longitude and latitude are 246.0 deg. and −9.1 deg., respectively Full size image

Fig. 2 Morphology of the observed and the simulated planetary-scale streak structures. a Edge-enhanced image of Venus’ night-side obtained from the image in Fig. 1; see Methods for the edge-emphasis process. b Vertical velocity at an altitude of 60 km simulated in STD after 3 Earth years (about 9.38 Venusian solar days) of time-integration, shown as a satellite view mimicking the panel a. c, d Same as b but for orthographic views from the south pole and the north pole, respectively, at the same altitude. e Same as b but for meridional cross-section at lon = 60 deg.; horizontal dotted lines indicate 50 and 60 km heights, which are the approximate boundaries of the simulated low-stability layer. Note that the planetary-rotation direction in the simulation is opposite to that of Venus, but the panel b is displayed with a 180-deg. rotation to easily be compared with the Venus image shown in the panel a. The colour bar is common for the panels from b to e Full size image

Figure 2b shows a simulated vertical velocity (w) field in the STD run at an altitude of 60 km mapped as a satellite view mimicking the IR2 image shown in Fig. 2a. Note that the planetary rotation direction in our simulation is opposite to that of Venus, so that Fig. 2b is rotated to be reasonably comparable with Fig. 2a. Strong downward flows indicated by bright areas form a streak structure similar to that observed. The simulated structure is composed of several narrow streaks of downward flows and stretches from high-latitudes to low-latitudes of ±30 deg. in both hemispheres. In the lower hemisphere in Fig. 2b, the latitudinal locations of the streaks agree well with those in the southern part of the IR2 image; whereas, in the upper hemisphere, the simulated streaks are located slightly poleward compared with those in the northern part of Fig. 2a. There is a notable qualitative morphological similarity between the simulated and the observed streak structure, although there are quantitative differences between them. As shown later in Fig. 2e, the downward flows composing the narrow streaks at the altitudes of about 60 km penetrate down to the altitudes of about 50 km. However, the streak structure at 50 km height is less clear as a whole. The discrepancy in altitudes between the IR2 image representing the features of around 49–57 km heights and our simulation will be discussed later.

Polar projections of simulated streaks are shown in Fig. 2c and d. In the polar regions (about >75 deg.) of each hemisphere, there is a dipole structure similar to the polar vortex observed by VIRTIS10, as previously reported30. The streaks extend from the edge of the polar region and form huge spirals in each hemisphere; the morphology is similar to the spiral observed in the hemispheric image obtained by VIRTIS3. The simulated spirals and polar dipoles seem to be evolving independently. The simulated spirals in both hemispheres are persistently developed with mostly equatorial symmetry (i.e., they are synchronised with each other), while the simulated polar dipoles are not synchronised (see Supplementary Movies 1 and 2). The rotation period of the simulated dipoles is around 2–4 Earth days, while that of the simulated streak structure is about 6 Earth days. The rotation period of the mean zonal flow at this level is about 4.9 Earth days at the equator and is shorter in higher latitudes, so that the rotation period of the simulated streak structure is longer than that of the mean flow. The streak structures appear permanently in our simulation at least for 1 Earth year (about 3 Venusian solar days).

A snapshot of the meridional cross-section of vertical velocity (Fig. 2e) shows that downward flows of the streaks penetrate to the altitudes of around 50 km, where the mean static stability becomes as high as 1.2 K km−1 as shown in Fig. 3a. Downward flows form slantwise from polar-upper regions to equatorward-lower regions. The polar view of the meridional velocity (v; northward is positive) field is shown in Fig. 4e, which is at the same level and time as in Fig. 2c. Regions of downward flow stronger than −0.05 m s−1 are overlaid by green hatches. A sharp convergence zone of the meridional flow, shown as the boundary between equatorial-sided blue (poleward) regions and polar-sided red (equatorward) region, is formed and its location corresponds to that of the upper, equatorial side edge of the downward flow streaks. The meridional cross-section (Fig. 4i) shows that the sharp convergence zone is also tilted poleward as height increases and corresponds to the starting points of the downward flows. Consequently, at a given height level, several narrow streaks appear side by side as shown in Fig. 2b.

Fig. 3 Vertical profiles of the static stability (Γ − Γ d ). The dashed line shows the static stability of the basic temperature profile for Newtonian cooling and solid line shows that of globally averaged simulated atmosphere in each run of a STD, b ZS0, c ZS2, and d ZS4. Horizontal dotted lines show 50 and 60 km heights Full size image

Fig. 4 Results of the numerical experiments. Settings are shown on the top of the figure. Panels a–d show snapshots of vertical velocity at the altitude of 60 km, and e–h show those of meridional velocity seen from the south pole in the model; i–l are meridional cross-sections of meridional velocity. Green hatching indicates strong downward flow (w < −0.05 m s−1). In i–l, the longitude of the meridional cross-section is shown in each panel Full size image

Importance of the low-stability layer

Sensitivity experiments are performed to explore the importance of the diurnal heating and the low-stability layer simulated in STD. The conducted simulation runs are listed in Table 1 and their details are described in Methods. The planetary-scale streak structure also appears in the ZS0 run that includes the same radiative cooling profile as in STD to represent the low-stability layer but excludes the diurnal variation of the solar heating as shown in Fig. 4b. In addition, the streaks in both hemispheres in ZS0 also rotate synchronously (see Supplementary Movie 3), and polar disturbances rotate faster and independently as in STD. The meridional velocity field in ZS0 is also similar to that in STD as shown in Fig. 4f and j. These results indicate that the diurnal variation of the solar heating does not play an essential role in the formation of the streak structure or its inter-hemispheric synchronisation. This might be surprising because the solar diurnal variation seems to be the largest, equatorially symmetric external forcing (at least in the altitudes of 50–70 km) in the Venus atmosphere. The inter-hemispheric synchronisation of the planetary-scale streak structure in ZS0 suggests that the streak structure exists in the Venus atmosphere irrespective of the local time through the Venusian solar day.

Table 1 Experimental settings of the simulation runs Full size table

In contrast to the solar diurnal heating, the low-stability layer is crucial for the appearance of the streak structure. The static stability to form the low-stability layer given in the basic temperature profile for the Newtonian cooling is increased from 0.1 K km−1 of STD/ZS0 to 2.0 K km−1 in ZS2 and to 4.0 K km−1 in ZS4, respectively as shown by dashed lines in Fig. 3. Note that these given static-stability profiles are used for the basic temperature for the Newtonian cooling, whereas the simulated ones shown by solid lines in Fig. 3 are results of thermal balance among the Newtonian cooling, solar heating, and adiabatic heating/cooling due to atmospheric circulations. In ZS2 and ZS4 the simulated static stability do not reach as low as 1.0 K km−1 around 50–60 km heights. In ZS2, the area of strong downward flow still exists but is no longer concentrated or elongated and cannot be recognised as a streak structure (Fig. 4c); the convergence region of meridional velocity is confined in high-latitudes and does not extend to mid- or low-latitudes (Fig. 4g and k). In ZS4, the highest-stability run, vertical velocity is much weaker than in other runs (Fig. 4d), meridional velocity and its convergence are also weak (Fig. 4h and l), and no feature like the streak structure can be found.

The true nature of the streak structure (i.e., it’s formation mechanism) remains to be identified. The upper panels in Fig. 5 show mean heat transport by eddies \(\left( {\overline {\rho v\prime \theta\prime } ,\overline {\rho w\prime \theta\prime } } \right)\) in each run, where ρ is the density, θ is the potential temperature, prime indicates deviation from the zonal mean, and overline indicates zonal- and time-mean. There is a large amount of poleward and upward heat transport, indicating the presence of baroclinic instability, in the STD and ZS0 runs shown by vectors in Fig. 5a and b, respectively. These heat fluxes can be classified into two groups by their locations. One is in the mid-latitudes (from −30 to −60 deg.) at the altitudes of about 55–70 km; and the other in the high-latitudes (from −60 to −80 deg.) at the altitudes of about 50–65 km. Such two-grouped eddy heat fluxes are also shown in Fig. 3b of Sugimoto et al.21 with diurnal solar heating, though they did not explore them separately. With the increase of the static stability, the vertical component of the eddy heat transport weakens in ZS2 (Fig. 5c), and the entire heat transport by eddies almost disappears in ZS4 (Fig. 5d).

Fig. 5 Zonally and temporally averaged fields of eddy heat transport and potential vorticity (PV). Panels a–d show heat transport due to eddies by vectors and its convergence by colour, and e–h show PV by colour and potential temperature by contour. For the colouring of PV, a linear scale is used for the range between ±10−8 and a logarithmic scale is used for outside of the range to visualise the positive and negative PV-gradients. The time-average period is 30 Earth days (about 5–7 periods of the superrotation at 60 km height) Full size image

Increasing the static stability of the low-stability layer also brings a significant change in the mean (Ertel’s) potential vorticity (PV) field as shown in Fig. 5e–h. In the southern hemispheres in STD and ZS0, the mean PV fields are rather complicated but have common characteristics; slightly negative or even positive PV are widely distributed in the mid-latitudes of about 50–60 km heights and polar region of about 55–60 km. Here, not only the lowness of the stability but also the horizontal component of vorticity contributes to produce positive values of PV in the southern hemisphere. In contrast to the low-stability cases, such local maxima of PV do not exist in the high-stability cases shown in Fig. 5g and h; note that positive PV in the equatorial region would be due to fluctuation across the equator and may disappear by taking much longer time-averaging period. As for the emergence of the baroclinic instability, a mean PV-gradient along isentropes must reverse in the vertical direction36. The isentropic PV-gradient is mostly positive (PV increases with latitude). However, in the mid-latitudes of STD and ZS0, there are regions of negative isentropic PV-gradient on the equator- and lower-side of the PV maxima, which indicates a possibility of baroclinic instability caused by the coupling of disturbances on different levels of isentropes with opposite sign of PV-gradient. Similarly, in the polar regions of STD and ZS0, there appears negative PV-gradient along the isentropes close to the polar PV maxima. In contrast to the low-stability cases, there appear almost no regions of negative isentropic PV-gradient in ZS2 and ZS4; especially in the mid-latitudes, PV increases quite monotonically with latitude. This indicates that the necessary condition for baroclinic instability is not satisfied in those higher-stability cases. These PV trends confirm that the existence of the low-stability layer may cause baroclinic instability as previously reported in simulation studies of Venus atmosphere20,21,37, and suggest that intense baroclinic disturbances are essential for the formation of the streak structure. However, the resulting disturbance structures seem to be more complicated than formerly expected and are left to be investigated in our future work (see Discussion).

Horizontal structure regulating the north-south symmetry

A longitude-time cross-section (as known as Hovmöller diagram) of pressure anomaly from the zonal mean (p′) at 35 deg. south latitude and 65 km height in ZS0 is shown in Fig. 6a. Here, assuming that the streak structures in STD and ZS0 are caused by the same mechanism, we analyse ZS0, which does not have the influence of the diurnal heating, to investigate the reason for the north-south symmetry of the structure. The latitude and the height used for Fig. 6a are where the amplitude of an equatorial Rossby-like wave explained below is large in ZS0. The dominant pressure anomaly has a longitudinal structure of wavenumber one and coherently moves eastward with a rotation period of about 5.8 Earth days (about 62.1 m s−1 at this latitude; remember that the direction of the planetary rotation is eastward in our simulation). It is slower than the mean flow rotating with a period of about 3.3 Earth days (about 109.3 m s−1) at this latitude shown by the yellow solid line. The dominant pressure anomaly at this level propagates westward relative to the mean flow. The strong downward flow shown by green hatches also propagates with the same speed as the pressure anomaly. In Fig. 6b, p′ at the lower altitude (55 km height) is plotted. We can recognise a clear signal in p′, though it is noisy compared to the upper level, which propagates with nearly the same speed as that at 65 km. Now, the rotation period of the mean flow at 55 km height is about 6.8 Earth days (about 53.1 m s−1), which is slower than the disturbance. That is, the dominant pressure anomaly at 55 km propagates eastward relative to the mean flow.

Fig. 6 Longitude-time cross-sections (Hovmöller diagram) of the pressure anomaly (red-blue shading) at the latitude of −35 deg. for ZS0. The altitudes are a 65 km and b 55 km. Green hatching shows regions of downward flow stronger than −0.03 m s−1. The yellow solid line shows the zonal mean zonal velocity at each height Full size image

In order to investigate the disturbance structure, we took composite means of pressure disturbance p′, horizontal wind disturbance (\(u\prime ,v\prime\)) and vertical flow w following the propagation of the dominant pressure signal at 65 km height shown in Fig. 6a. The composite means highlight the coherent structure associated with the dominant signal by averaging the snapshots of the fields shifted zonally according to its propagation. The composited structure of p′ and (\(u\prime ,v\prime\)) on 65 km height in the low- and mid-latitudes (<60 deg.) shown in Fig. 7a resembles that of the equatorial Rossby wave38 with wavenumber one; i.e., two pairs of low- and high-pressure anomalies associated with cyclonic and anti-cyclonic circulations, respectively, are straddling the equator. On the other hand, in the lower altitude at 55 km height, the composited structure in latitude <50 deg. resembles that of the equatorial Kelvin wave38 with wavenumber one (Fig. 7d); i.e., a low- or high-pressure anomaly is located on the equator associated with intense westward or eastward flow anomaly, respectively, while meridional flow is weaker than zonal flow. Note that one of the reasons why the Hovmöller diagram of Fig. 6b is noisy is that the plot is not at the equator but at 35 deg. south latitude where there are influences of other disturbances.

Fig. 7 Composite means of pressure anomaly p′ (red-blue shading) superimposed by horizontal flow anomaly (\(u^\prime ,v^\prime\)). Panels a, d show the composite means on z = 65 km and 55 km, respectively, for ZS0; e shows that on z = 65 km for ZS4. Composite means are taken along the propagation speeds associated with the dominant Rossby-like waves at z = 65 km, the equatorial values of which are 75.6 m s−1 for ZS0 and 96.0 m s−1 for ZS4, respectively. Green hatching indicates strong downward flow (w < −0.03 m s−1). b, f Temporal and zonal mean meridional transports of angular momentum by eddies at 65 km height for ZS0 and ZS4, respectively. The period of time-average is the same as that in Fig. 5. c, g Same as b and f but for angular velocity (shaded solid line, scales written in bottom axis) and zonal wind (thick dashed line, top axis) Full size image

Recall that the propagation speed of p′ is nearly the same at both levels as shown in Fig. 6. This implies an occurrence of vertical shear instability by the combination of the equatorial Rossby-like wave around z = 65 km and the equatorial Kelvin-like wave around z = 55 km39,40. Coincidence in the zonal distribution of u′ in the equatorial region on both levels (eastward in 100–240 deg. and westward in the other longitudes) shows that these waves are coupled with and maintained by each other. The vertical shear instability that contains the structure of the equatorial Kelvin-like wave would result in the north-south symmetry or synchronisation of disturbances in the low- and mid-latitudes in the hemispheres.

Temporal and spatial structures similar to those shown in Fig. 6 and 7 are also obtained in STD where the diurnal solar heating is included (not shown). Though the thermal tide of wavenumber one appears with a noticeable amplitude in the snapshots of the pressure anomaly field, it disappears after taking the composite mean and has no significant effects on the horizontal structure described above.

In Fig. 7, there are strong signals in the polar regions (>75 deg.). However, the north-south symmetry no longer holds there. The polar anomalies in both hemispheres develop independently from the symmetric equatorial waves at least in STD and ZS0. In other words, the polar pressure anomalies could prevent the equatorial waves and the streak structure from reaching the polar regions. We should note that, as mentioned earlier, those polar disturbances propagate faster, and they should eventually vanish in the composite fields if we took the average over a far longer time period. We should also note that the structure of polar anomalies is quite deep ranging over the altitudes from 40 to 70 km roughly along an isentropic surface (shown in Supplementary Fig. 1). Since these polar disturbances seem to have locally uniform structure in the vertical direction, the instability generating them might be interpreted as barotropic instability as previously reported31. However, because of the presence of the meridional eddy heat fluxes shown in Fig. 5, we suggest that the high-latitude baroclinic instability that is separated from the mid-latitude baroclinic instability also contributes to the polar disturbances (see also Discussion and Fig. 8).

Fig. 8 Zonally and temporally averaged distributions of zonal winds (contour) and north-south eddy heat fluxes (colour) in ZS0. White dashed lines indicate locations of large poleward heat fluxes suggesting the emergence of baroclinic instability in mid-latitudes; black dashed lines indicate those in high-latitudes and the axes of high-latitude jets. Red arrows show approximate latitudes of large poleward angular momentum fluxes by eddies at the altitude of 65 km, which is shown in Fig. 7b. The time averaging period is the same as Fig. 5 and contour interval is 15 m s−1 Full size image

Key features for the formation of the steak structure

A characteristic feature corresponding to the streak structure is a meridional tilting of the phase of the equatorial Rossby-like wave (Fig. 7). In ZS0, the polar-side halves (in latitudes from 45 to 65 deg.) of the equatorial Rossby-wave-like structure in the pressure anomalies (p′) and eddy circulations (\(u\prime ,v\prime\)) are tilted eastward with increasing latitude as shown in Fig. 7a. The tilted p′ and (\(u\prime ,v\prime\)) seem to extend poleward and intrude into the polar anomalies appearing in latitudes around 75 deg. Such tilting and extension of the circulations seem to be related with the horizontal-wind convergence that forms the streak structure of the strong downward flow in the low-pressure regions as shown by green hatches. Conversely, in the high-stability case (ZS4), although an equatorial Rossby-like wave with zonal wavenumber one still emerges as seen in Fig. 7e obtained by taking a similar composite average as that of ZS0, the pressure anomalies are not meridionally tilted and the downward flows are weak. The difference in tilting of the eddy circulations between ZS0 and ZS4 is also apparent in angular-momentum transport by eddies shown in Fig. 7b and f. A large amount of poleward transport of angular momentum exists in ZS0, whereas the angular momentum transport is very small in ZS4. Correspondingly, another characteristic feature observed in ZS0 contrasted with ZS4 is the existence of high-latitudinal zonal jets (local maximum in the zonal mean zonal wind) around 75 deg. as shown by dashed lines in Fig. 7c. In terms of angular velocity, a large meridional shear emerges in high-latitudes in ZS0 (Fig. 7c), but not in ZS4 (Fig. 7g). Recall that the intensity of baroclinic disturbances is strong in ZS0 and quite small in ZS4 as shown in Fig. 5b and d, the baroclinic instability must play an important role for producing those features. The structure of the baroclinic disturbances in the model, however, is yet to be fully investigated. We just try to discuss the possible structure briefly in the next section.