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How waves and turbulence maintain the super-rotation of Venus’ atmosphere

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Science  24 Apr 2020:
Vol. 368, Issue 6489, pp. 405-409
DOI: 10.1126/science.aaz4439

Explaining super-rotation on Venus

The solid surface of Venus rotates very slowly, once every 243 days, but its thick atmosphere circles the planet in just 4 days. This phenomenon, known as super-rotation, requires a continuous input of angular momentum, from an unknown source, to overcome friction with the surface. Horinouchi et al. mapped the planet's winds using ultraviolet observations of Venus' clouds from the orbiting Akatsuki spacecraft (see the Perspective by Lebonnois). They incorporated these data into a global model of angular momentum transport in the atmosphere, finding that the super-rotation is maintained through thermal tides driven by solar heating.

Science, this issue p. 405; see also p. 363

Abstract

Venus has a thick atmosphere that rotates 60 times as fast as the surface, a phenomenon known as super-rotation. We use data obtained from the orbiting Akatsuki spacecraft to investigate how the super-rotation is maintained in the cloud layer, where the rotation speed is highest. A thermally induced latitudinal-vertical circulation acts to homogenize the distribution of the angular momentum around the rotational axis. Maintaining the super-rotation requires this to be counteracted by atmospheric waves and turbulence. Among those effects, thermal tides transport the angular momentum, which maintains the rotation peak, near the cloud top at low latitudes. Other planetary-scale waves and large-scale turbulence act in the opposite direction. We suggest that hydrodynamic instabilities adjust the angular-momentum distribution at mid-latitudes.

The thick atmosphere of Venus rotates at speeds up to 60 times those of the slow planetary rotation; the surface rotates westwards with a period of 243 days (throughout this paper, day refers to Earth days). The mechanism responsible for this super-rotation (SR) remains unclear (1, 2), partly because of insufficient observational evidence for hypothesis testing.

SR may also occur in tidally locked exoplanets—those that always face the same way toward their host star and are therefore heated only on one side. Zonal (east-west) flow around the rotation axis, including SR, can transport heat from the dayside to the nightside of those exoplanets (3).

SR cannot occur unless the atmospheric angular momentum with respect to the rotational axis (hereinafter, AM) is transported by axially asymmetric flows (eddies) such as waves and turbulence. Without these, AM (per unit mass) is homogenized by the latitudinal-vertical circulation (meridional circulation) induced by the pole-equator temperature difference (4). Estimates of the AM transport from observations have been attempted by tracking features in images of the cloud top (65 to 70 km in altitude) obtained by the Mariner 10 (5) and Pioneer Venus Orbiter (6, 7) spacecraft; however, the sampling proved insufficient both in space and in time.

Simulations using atmospheric general circulation models have generated SR (8–15); these simulations indicate that SR is realized by AM transport via tidal (9, 11, 13, 14) and other waves (8, 10–15). Some of these waves arise from hydrodynamic instabilities [such as the barotropic (10, 12–14), baroclinic (12, 13, 15), and Rossby-Kelvin instabilities (14)] and turbulent eddies (15). The relative contributions of each of these effects to SR differ between models.

The AM budget can be described by the following equation, which in meteorology is known as the transformed Eulerian mean equation∂M∂t = −vr · ∇M + ρ0−1 ∇ · Fwhere M is the zonal-mean (i.e., averaged along latitudinal circles) AM per unit mass, which is negative when westward, as in SR; F is (minus) the AM flux, called the Eliassen-Palm flux; vr ≡ (0, vr, wr) represents the mean meridional circulation velocities and is called the residual circulation; vr is the northward velocity; and wr is the westward velocity (16). The equation above indicates that, at steady state, AM transport by eddies (the ρ0−1 ∇ · F term) and AM transport by the mean meridional circulation (the −vr · ∇M term) compensate each other. On Venus, |M| reaches its maximum around the cloud-top altitude near the equator (17, 18). Maintenance of this maximum requires eddy AM transport to that region.

We begin by examining the mean meridional circulation and its effects. To determine the circulation directly from wind observations is difficult even for Earth’s atmosphere. For Venus, the most credible estimates are provided by observations of solar and thermal radiations, from which we constructed a model (16). The resulting wr and vr indicate an upwelling of a few millimeters per second in the equatorial upper cloud layer and a poleward flow of ~1 m s−1 at around the mid-latitude cloud top, respectively (Fig. 1).

Fig. 1 Idealized model calculation of the meridional circulation derived from solar heating and the advective acceleration of idealized zonal AM.

(A) Global-mean downward solar flux (F). (B) The mass stream function χ derived from the solar heating at ϕmax = 38.2°. The dashed line indicates interpolation and the blue dotted line indicates the value at 74 km. (C) Hemispheric structure of χ (black contours; flow directions are indicated schematically by red arrows); idealized M between 40 and 90 km (gray dashed contours); and advective zonal acceleration –(a cos ϕ)–1 vr · ∇M between 50 and 80 km (color shading). (D) vr at ϕmax (black line) and wr at the equator (blue line). Thicker lines highlight values between 50 and 80 km.

We introduce an idealized zonal wind (eastward velocity component) structure into the model (16). The upwelling in the equatorial cloud layer acts to decelerate the SR by ~1 m s−1 day−1 at the AM peak around the equatorial cloud top (Fig. 1C), which must be compensated by eddy acceleration.

At mid-to-high latitudes, negative (or positive) acceleration occurs through the −vr · ∇M term above (or below) ~65 km (Fig. 1C). We expect that hydrodynamic instabilities inevitably induced by the circulation (19, 20) compensate for these accelerations (16) (fig. S2), so we infer that the AM distribution at mid-to-high latitudes can be formed more-or-less spontaneously.

We provide further constraints using data from the Akatsuki spacecraft orbiting Venus. We analyzed observations taken between December 2015 and December 2018, divided into five subperiods, starting 7 December 2015, 21 September 2016, 21 April 2017, 1 December 2017, and 16 June 2018 (ending on 7 December 2018). Using a cloud-tracking method with quality control (21, 22), we derived wind estimates using Akatsuki’s Ultraviolet Imager (UVI) (23) at the wavelengths of 365 and 283 nm. We derived horizontal velocities near the cloud top over regions of about 1000 km by 1000 km with a time resolution of 4 hours (16) (uncertainties shown in fig. S3A). The 283-nm results capture winds at slightly higher altitudes than the 365-nm results, presumably by a few kilometers (24).

The meridional component of the Eliassen-Palm flux Fy is likely dominated by the fyv ≡ −〈u*v*〉 cos ϕ term (16), where u and v are zonal and meridional (south-to-north) winds, respectively, and the angle brackets and asterisks represent zonal mean and the deviation from it, respectively. We employ a coordinate system based on local time τL, latitude ϕ, and time t, where τL is defined by assigning 0 to 24 hours to longitudes relative to the antisolar point. Temporally averaged winds in this system (u¯, v¯) consist of zonal and temporal mean winds (u0, v0) and the flow associated with the thermal tides (ut, vt). The mean winds from the 3 years are shown in fig. S3.

We estimated (ut, vt) by subtracting the model estimated (u0, v0) from the observationally derived (u¯, v¯) for each of the UVI image subperiods (16). The resulting tidal AM flux, 〈utvt〉 cos ϕ, is shown in Fig. 2A. It is positive (negative) in the northern (southern) hemisphere, which indicates equatorward transport of westward AM in both hemispheres. The consistency between our results for different subperiods (Fig. 2A) demonstrates the robustness of our estimation. The tidal meridional AM flux convergence acts to accelerate the SR between 20°S and 20°N, reaching peak values around −0.6 (−0.9) m s−1 day−1 for the 365-nm (283-nm) case, which indicates the acceleration of westward SR (Fig. 2C). The estimates depend on u0 and v0; we performed a sensitivity study (16) (figs. S9 and S10) to verify the robustness of the estimates, although some uncertainty remains (16). Thermal tide carries eastward AM, so our result is consistent with the action-reaction law on the tide generation by solar heating, which is stronger at lower latitudes.­

Fig. 2 Meridional AM flux and its divergence due to thermal tide and transient disturbances at the cloud top and tidal heat flux.

(A) Mean tidal flux (thick lines: red, from 283-nm images; blue, from 365-nm images) obtained by averaging 〈utvt〉 cos ϕ for the second to fifth subperiods; the first subperiod was excluded because the local time coverage was too narrow to estimate u0. Shaded areas indicate the standard deviation among subperiods. Thin solid lines are like the solid lines but were obtained without subperiod division. (B) As in (A) but for transient disturbances, 〈u′v′〉¯ cos ϕ, from the five subperiods. Biases arising from the error covariance between u′ and v′ have been subtracted. Dotted lines are as the thin solid lines, except they are obtained from daily-mean winds (u#, v#). (C) Zonal acceleration by the meridional AM flux convergence by thermal tides (−∂〈utvt〉 cos2 ϕa cos2 ϕ ∂ϕ; solid lines) and transient disturbances (−∂〈u′v′〉 cos2 ϕa cos2 ϕ ∂ϕ; dashed lines) based on the thin solid lines in (A) and (B). Dotted lines are the same, but for Rossby waves obtained from the co-spectra after a 1:2:1 smoothing with latitude. Colors are as in (A). (D) Mean tidal heat flux by diurnal tides obtained by averaging 〈vtTt〉1 for the five subperiods with vt at 365 nm (thick solid line). Shaded areas indicate the standard deviation among subperiods. Thin solid line was obtained without subperiod division. (E) As in (D) but for fzT1 ≡ ζaS−1〈vtTt〉1 cos ϕ (using absolute vorticity ζa in fig. S3B and the stability S = 8 × 10−3 K m−1).

We next examine the AM transport by transient motions other than thermal tides. We use (u′, v′) ≡ (u−u˜, v−v˜), where (u˜, v˜) are the averages of (u, v) over ±15 days at fixed τL and ϕ. Figure 2B shows the AM flux 〈u′v′〉¯ cos ϕ (solid lines) after the effects of the correlation between the errors in u′ and v′ have been subtracted using the error covariance (16) (fig. S5). Prior to subtraction, the error covariance enhanced the AM flux by a factor of 1.5. However, this effect is very small (16) for 〈u#v#〉¯ cos ϕ, where (u#, v#) is (u′, v′) smoothed by daily averaging, which is time averaging over each day at fixed τL and ϕ. The UVI was typically operated for 16 hours each day, so the daily averaging smooths winds over several thousand kilometers in longitude because of the SR.

The derived AM flux (Fig. 2B) is opposite to that provided by the thermal tides (Fig. 2A). The consistency between subperiods again indicates the robustness of our method. Unlike the tidal case, both wavelengths produce quantitatively consistent results, which suggests a deceleration of the SR that is weaker than the tidal acceleration (Fig. 2C). The AM flux computed with (u#, v#) (Fig. 2B) is slightly weaker than that computed with (u′, v′), which suggests that a small fraction of the AM flux resides at high frequencies (periods shorter than 2 days) or, equivalently, at small scales.

Next, we consider the nature of transient disturbances and their roles in the AM transport. Figure 3A presents an example of the spatial distribution of wind disturbances using (u#, v#) and the absolute vorticity computed with (u#+u˜, v#+v˜), constructed by shifting by 90° per day, approximating the advection by SR; more examples are shown in figs. S6 and S7. The smooth transition over adjacent days indicates that overall temporal evolution is slow. The distribution of u# suggests the dominance of variability at zonal wave number (the wave number along the longitude direction in radians) equal to 1—i.e., a single wave extending over latitudinal circles—which is consistent with Rossby waves (25, 26). We derived power spectra of u# (Fig. 3B), which reach a maximum at a frequency of around 0.2 day−1, corresponding to a ground-based period of 5.2 days. The sign of the imaginary part of cross-spectrum (fig. S8C) that arises from quadrature-phase lags is also consistent with a Rossby wave structure. A secondary spectral peak appears in Fig. 3B at 0.24 day−1 (corresponding to a ground-based period of 4 days), which is consistent with Kelvin waves (25, 26). The equivalent signal in v# away from the equator (fig. S8B) indicates a distortion that is absent in pure Kelvin waves.

Fig. 3 Example wind disturbances (365 nm) and corresponding spectra.

(A) Daily-mean transient winds (u#, v#) (arrows; red if u# > 0) and absolute vorticity (colored shading) for the period 7 to 10 January 2017, overlaid by shifting 90° per day. (B) Power spectra of u# obtained from the second to the fourth subperiods (colored shading; the white contour is at 500 m2 s−2 day). Frequency is for observers at fixed local time (LT), τL; the corresponding ground-based period (days) and zonal propagation speed at the equator (EQ) when the disturbances have zonal wave number 1 and move westwards (negative wave number) are shown on the abscissa. (C) Same as in (B) but for co-spectra between u# and v# (white contours are at an interval of 20 m2 s−2 day).

In addition to the waves, turbulence-like motion is apparent in Fig. 3A (and fig. S6). The nonmonotonic change of absolute vorticity with latitudes around 30°N indicates overturning motion to generate turbulence. Meandering (often cross-equatorial) flows prevail near the equator where the directions of absolute-vorticity gradients vary substantially, which is difficult to explain with simple superpositions of Rossby waves. These flows are also unlike gravity waves. Therefore, we conclude that some portion of the transient wind disturbances are due to horizontal turbulence.

The real part of the cross-spectrum (co-spectrum) of u# and v# decomposes their correlation along frequencies (Fig. 3C). The signs at different frequencies almost always agree at latitudes poleward of 20°N and 20°S. The co-spectrum of two random signals has an equal probability to be positive or negative, so this agreement cannot be explained by coincidence or by noise. From the co-spectra, we computed the contribution of the Rossby-wave periods (frequencies 0.1888 to 0.2222 day−1) to the meridional AM flux (Fig. 2C). This is only a small fraction of the AM transport, at least between 30°S and 30°N. The contribution of the Kelvin waves is even smaller. We therefore suggest that horizontal turbulence at broad frequency (together with waves) collectively decelerates the SR. This idea opposes the earlier expectation that turbulent AM transport accelerates SR, which is required in the so-called classical Gierasch-Rossow-Williams mechanism in which AM transport by meridional circulation and AM transport by turbulence balance one another (1, 27, 28).

We further investigate the vertical component of F, Fz ∝ fzw + fzT, where fzw and fzT are terms proportional to 〈u*w*〉 and 〈v*T*〉, respectively (16); here, w is vertical velocity. We estimated the meridional heat flux by the diurnal (i.e., zonal wave number 1) components of the thermal tides (diurnal tides), 〈vtTt〉1 ∝ fzT, by using the brightness temperature obtained from Akatsuki’s Longwave Infrared Camera (LIR) (16). This shows that the tidal heat flux is poleward (Fig. 2D). The diurnal tides are dominated by a Rossby wave at mid-to-high latitudes (29). Theoretically, the Fz component of a Rossby wave is dominated by fzT, so its estimation (Fig. 2E) indicates that the wave transports negative AM downward. Its typical magnitude is 1 × 10−2 m2 s−2 at midlatitudes. This indicates that its effect on SR is minor because the expected acceleration is ~0.1 m s−1 day−1 (this value follows if the vertical convergence of fzT due to tidal excitation occurs over a height scale of 10 km).

The entire semidiurnal (i.e., zonal wave number 2) components of the thermal tides (semidiurnal tides) and the low-latitude portion of the diurnal tides are dominated by gravity waves (29). They are expected to transport AM to its upgradient to accelerate the SR (9, 30). Observational estimations of Fz associated with gravity waves are not available because it is dominated by fzw and thus includes vertical velocity. We instead performed an order-of-magnitude estimation (16), finding that the acceleration associated with ∂Fz∂z is likely ~1 m s−1 day−1 or smaller. Therefore, the tidal vertical AM transport can contribute to the acceleration of SR at low latitudes by an amount similar to the contribution of the horizontal transport.

The Akatsuki data have allowed us to estimate the horizontal AM transport by thermal tides, planetary-scale Rossby waves, and other transient disturbances. The thermal tides transport westward (super-rotating) AM equatorward, contributing to the maintenance of the SR against the homogenization by the meridional circulation. The other motions act in the opposite direction at low latitudes. We also estimated vertical AM transport by thermal tides. The AM balance that governs the maintenance of the SR in the cloud layer is schematically illustrated in Fig. 4. We suggest that the SR maintenance mechanism is a version of the nonclassical Gierasch-Rossow-Williams scenario (1), which extends the classical one to include AM transport by tidal waves.

Fig. 4 Schematic illustration of the suggested AM balance in the cloud layer of Venus.

(A) Processes quantified or estimated in this study. (B) Same as (A) with our suggested interpretation overlain. Wavy arrows indicate eddy transport of SR’s negative AM; those labeled with “tr” represent transport processes that we quantified (black, blue) or estimated (gray), and those with “tr?” in (B) represent suggested transport processes. Their widths crudely represent their relative contributions to the AM transport. The cyan curved arrow shows the mean meridional circulation that acts to homogenize the AM. The dotted curved arrows are expected contributions to the circulation (16). The background shows the cloud layer (pale orange shading), idealized distributions of 〈u〉 (black contours; meters per second), and M (red contours; square meters per second).

Supplementary Material

science.sciencemag.org/content/368/6489/405/suppl/DC1

Materials and Methods

Supplementary Text

Figs. S1 to S11

Table S1

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Acknowledgments: We thank numerous colleagues who supported the Akatsuki project and three anonymous reviewers who provided comments that helped improve this paper. Funding: This study was supported by the Japanese Society for Promotion of Science grants-in-aid 16H02231, 16H02225, 19H05605, and 19K14789 and by NASA grant NNX16AC79G. J.P. acknowledges the Japan Aerospace Exploration Agency’s International Top Young Fellowship. Author contributions: T.H. derived the wind estimations, conducted analysis, produced the figures, and wrote the text. K.O., S.M., M.Tak., T.K., and T.H. developed the cloud-tracking program. Y.-Y.H., J.P., S.S.L., and T.S. contributed to the interpretation. S.W., M.Y., and A.Y. calibrated the UVI radiance. T.K., M.Tag., and T.F. derived the temperatures using Akatsuki’s LIR. K.O. and M.Tak. refined the geographic data mapping. T.M.S., T.S., T.I., S.M., and M.N. coordinated Akatsuki’s observations and processed the original data. Competing interests: The authors declare no competing interests. Data and materials availability: The Akatsuki data are available at (31–33). The data derived in this paper, including the cloud tracking results and the results shown in the figures, are available at https://darts.isas.jaxa.jp/pub/akatsuki/paper/Horinouchi_2020/ and in table S1.

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