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Measurements and interpretation of a Jovian, near-equatorial feature
&net. @ace Sci., Vol. 33, No. 9, pp. 987-991,198s print& in Great Britain.
00320633/85 S3.00 + 0.00 Q 1985 Per~amon Press Ltd.
MEASUREMENTS AND INTERPRETATION OF A JOVIAN, NEAR-EQUATORIAL FEATURE T. MAXWORTHY’
Division of Earth and Planetary Sciences, Jet Propulsion Laboratory, Pasadena, CA 91109, U.S.A. (Received19 November1984) Ahstzact-We present evidence to suggest that the large, rapidly moving features in Jupiter’s equatorial currents are manifestations of Rossby solitary waves. Their morphological and dynamical similarity to the great red spot and the white ovals is revealed and discussed in the context of the available theory.
INTRODUCTION
The historical, ground-based record shows a persistent feature in the South Equatorial region moving at about 95 m s- ’ which has interacted many times with the Red Spot in a very complicated manner. With the acquisition of Voyager I and II images of this region, its morphology and flow field can be carefully documented(Beebe, 1983,priv. comm.). One such image is shown in Fig. f. Here we present some new measurements of this near-equatorial feature and discuss an interpretation which is insistent with its identification as a solitary Rossby wave (M~worthy and Redekopp, 1976; Redekopp, 1977; Maxworthy, Redekopp and Weidman, 1978; Maxworthy and Redekopp, 1980; and Maxworthy 1979).t MEASUREMENT
TECHNIQUES
This work makes use of the raw data gathered by the Voyager Imaging Team and methods of measuring the velocity of cloud marker particles developed by the personnel ofthe Image ProcessingLaboratory at J.P.L. A pair of images of appro~mately the same region of the planet but taken about 1Oh apart were analysed using this system and the resulting velocity vectors plotted manually. We also reconstructed a high resolutionphotographicmosaicoftheregionofinterest using standard, shaded and filtered, J.P.L.-format output without further enhancement or processing. RESULTS
AND COMMENTS
As pointed out in the majority of our reports listed in the Introduction, the morphology of planetary solitary * Permanent address: Departments of Mechanical and Aerospace En~n~~n~ Unive~ity of Southern California, Los Angeles, CA 90089-1453, U.S.A. t Designated MRl, R, MRW, MR2 and M in what follows.
waves in a jet-like shear fiow is quite distinctive. The anticyclonic shear can support a compact, recirculating flow, designated an E-wave; while the cyclonic shear is able to support a wave of depression or D-wave in which the streamlines, relative to the moving wave, have a hair-pin-like shape with the bend ofthe hair-pin close to the wave centre. Furthermore when combined together on a jet such waves require two critical layers at which the wave-speed equals the local flow velocity.’ In all of the examples considered up to now, e.g. the Great Red Spot (G.R.S.), the White Ovals (W.0.s) and “B-spots” to the south of the W.0.s the velocity profiles have been almost symmetric so that the critical levels occurred at velocities close to (i.e. within + 10 m s- * of) the mean rotational speed of the planet. What is particularly exciting about the present observations is that the mean velocity profiles are asymmetric (see Fig. 2) and in order for two critical levels to exist the wave velocity has to be very large (of order 90 m s- ’ in this case). In Fig. 3 we show a sketch of the type of solitary wave we would expect to findin this type of flow field’ in which streamlines are drawn with respect to {w.r.t.) a coordinate system moving with the wave. In Fig. 1 a photo~aphic mosaic of the feature is shown for comparison to the expected shape, Fig. 3. We see, as will be re-emphasized 53 the velocity measurements, that the similarities are remarkable except for a lack of visual E-W symmetry. The Ieft-hand part of the feature clearly has both the distorted oval shape and the hair-pin-shaped region to the South. On the right-hand side this latter structure is less in evidence but still exists, while the anticyclonic oval to the North is distorted into a tear-drop shaped cloud 1The existence of such double structures has recently been confirmed by Beaumont (1980) for jet-iike flows foliowing their q~itative discussion in MRl. * Detailed calculations based on the actual velocity profile are currently underway.
987
T.
988 -40
0
40
VELOClTYtys, 120
MAXWORTHY
160
FIG.2.DETAILSOFTHEVELOCITYPROFILETOTHESOUTHOFTHE JOVIANFZQUATOR,FARREMOWDFROMTHECENTREOF~WAVE UNDER INVESTIGATION.
Open circles taken from the left-hand side of the wave and closed circles from the right. The chain-dotted line is the propagation velocity of the equatorial feature as a whole.
pattern. There is some evidence of this tear-drop patternon theleft-handsideofthestructure, butitisnot as extensive or obvious. In defense of our solitary wave explanation we note two important differences between the theory, as presently formulated, and the observations. Firstly the theory does not include the
cl
g-s 8 -10 -15 FIG.3. EXPECTEDSTRRAMLINESOFASOLITARYWAVEWITHTWO CRITICAL LEVEL.9 ON AN ASYMMETR IC JET-LIKE VELOCITY PROFILE.
Streamlines drawn with respect to a coordinate system moving with the wave. Here and in Fig. 2 the chain-dotted line shows the velocity of the wave in System III.
Measurements and interpretation of a Jovian, near-equatorial feature
FIG.~.~~~PA~RNS~IA~DWI~WA~
arrow A points to the centre of the recirculating flow, identified as a wave of elevation in the text. B lies along the region ofhair-pin streamlines, a wave ofdepression. The small insert shows an inverted picture of one of the White Ovals in order to point out the similarity in cloud structure between it and the feature under discussion.
The
FIG.~.~OD~~~YPR~~~IONSOF Voyager PAPER (1) ANDo~OFA~~OFVIR~ALLY~DE~CAL~~~~~
ZFRAHES~OWING~WA~DI~U~~IN~S NoRTHOFTKEEQ~ATOR~~).
989
Measurements and interpretation of a Jovian, near-equatorial feature
effects that clouds, and their possible energy source, may have on the dynamics. Secondly these same clouds may also distort the observations by behaving unsymmetrically as fluid parcels rise on one side of the wave and fall on the other. As part ofFig. 1 we also show an inverted picture of one of the W.0.s to emphasis the similarities in morphology and explanation between these features. In M.R.W., M.R.2 and M we have already applied our solitary wave ideas to the W.0.s and note again here that such blobs (E-waves) are always anti-cyclonic while hair-pins (D-waves) are always cyclonic. The velocity measurements (Fig. 4) tend to confirm this tentative explanation. Velocity vectors drawn with respect to the moving wave (heavy lines in the figure) show exactly the pattern one would expect from theoretical considerations. Points near the centre of the wave are moving with the wave speed. Flows into and out of the “hair-pin” regions are clearly shown. The weak rotation within the oval region is shown less clearly because of the lack of well-defined marker particles within this relatively featureless region. These velocity measurements (as also shown in Fig. 2) also indicate that the same velocity field exists in the hair-pin shaped regions on either side of the centre of the feature despite a lack of similarity in their visual appearance. CONCLUSIONS
We have shown that morphology and flow-field of one particular near-equatorial Jovian feature is consistent with its explanation as a planetary solitary wave. In particular, in order to exist on the asymmetric jet structure found in this region a large eastward wave
991
speed is to be expected so that two critical layers exist. That the observations bear out this expectation is a strong argument in favor of the model. We further note that at least one other structure of this general type exists on the same jet approx. 180” removed from it in longitude, while the similar jet on the northern edge of the equatorial region also contains numerous features with similar morphologies (Fig. 5). Acknowledgements-Theinvaluable help ofGlen W. Gameau and Jimmy L. Mitchell, of J.P.L., in the preparation of the images from which the reported data were taken is gratefully acknowledged. Discussions with Prof. Reta Beebe of N.M.S.U.were also of great help in putting this work into the correct historical perspective. Support came from the Planetary Atmospherei Section of J.P.L. under contract NASW 7; in particular the encouragement of Dr. Moustafa Chahine is acknowledged with gratitude. REFERENCES
Beaumont, D. N. (1980) Solitary waves on an unsymmetrical shear flow with applications to Jupiter’s Great Red Spot. Icarus 41,400. Maxworthy, T. (1979) Dynamics of the Jovian Atmosphere. Proc. 13th Biennial Symp. on Fluid Dynamics, Polish Academy of Sciences, Warsaw, Poland. Maxworthy, T. and Redekopp, L. G. (1976) A solitary wave theory of the Great Red Spot and other observed features in the Jovian Atmosphere. Icarus 29,261. Maxworthy, T. and Redekopp, L. G. (1980) Possible fluid dynamical interpretation of some reported features in the Jovian Atmosphere. Science 210,135O. Maxworthy, T., Redekopp, L. G. and Weidman, P. D. (1978) On the production and interaction of planetary solitary waves: applications to the Jovian Atmosphere. Icarus 33, 388. Redekopp, L. G. (1977) On the theory of solitary Rossby waves. J. Fluid Mechs 19,543.
00320633/85 S3.00 + 0.00 Q 1985 Per~amon Press Ltd.
MEASUREMENTS AND INTERPRETATION OF A JOVIAN, NEAR-EQUATORIAL FEATURE T. MAXWORTHY’
Division of Earth and Planetary Sciences, Jet Propulsion Laboratory, Pasadena, CA 91109, U.S.A. (Received19 November1984) Ahstzact-We present evidence to suggest that the large, rapidly moving features in Jupiter’s equatorial currents are manifestations of Rossby solitary waves. Their morphological and dynamical similarity to the great red spot and the white ovals is revealed and discussed in the context of the available theory.
INTRODUCTION
The historical, ground-based record shows a persistent feature in the South Equatorial region moving at about 95 m s- ’ which has interacted many times with the Red Spot in a very complicated manner. With the acquisition of Voyager I and II images of this region, its morphology and flow field can be carefully documented(Beebe, 1983,priv. comm.). One such image is shown in Fig. f. Here we present some new measurements of this near-equatorial feature and discuss an interpretation which is insistent with its identification as a solitary Rossby wave (M~worthy and Redekopp, 1976; Redekopp, 1977; Maxworthy, Redekopp and Weidman, 1978; Maxworthy and Redekopp, 1980; and Maxworthy 1979).t MEASUREMENT
TECHNIQUES
This work makes use of the raw data gathered by the Voyager Imaging Team and methods of measuring the velocity of cloud marker particles developed by the personnel ofthe Image ProcessingLaboratory at J.P.L. A pair of images of appro~mately the same region of the planet but taken about 1Oh apart were analysed using this system and the resulting velocity vectors plotted manually. We also reconstructed a high resolutionphotographicmosaicoftheregionofinterest using standard, shaded and filtered, J.P.L.-format output without further enhancement or processing. RESULTS
AND COMMENTS
As pointed out in the majority of our reports listed in the Introduction, the morphology of planetary solitary * Permanent address: Departments of Mechanical and Aerospace En~n~~n~ Unive~ity of Southern California, Los Angeles, CA 90089-1453, U.S.A. t Designated MRl, R, MRW, MR2 and M in what follows.
waves in a jet-like shear fiow is quite distinctive. The anticyclonic shear can support a compact, recirculating flow, designated an E-wave; while the cyclonic shear is able to support a wave of depression or D-wave in which the streamlines, relative to the moving wave, have a hair-pin-like shape with the bend ofthe hair-pin close to the wave centre. Furthermore when combined together on a jet such waves require two critical layers at which the wave-speed equals the local flow velocity.’ In all of the examples considered up to now, e.g. the Great Red Spot (G.R.S.), the White Ovals (W.0.s) and “B-spots” to the south of the W.0.s the velocity profiles have been almost symmetric so that the critical levels occurred at velocities close to (i.e. within + 10 m s- * of) the mean rotational speed of the planet. What is particularly exciting about the present observations is that the mean velocity profiles are asymmetric (see Fig. 2) and in order for two critical levels to exist the wave velocity has to be very large (of order 90 m s- ’ in this case). In Fig. 3 we show a sketch of the type of solitary wave we would expect to findin this type of flow field’ in which streamlines are drawn with respect to {w.r.t.) a coordinate system moving with the wave. In Fig. 1 a photo~aphic mosaic of the feature is shown for comparison to the expected shape, Fig. 3. We see, as will be re-emphasized 53 the velocity measurements, that the similarities are remarkable except for a lack of visual E-W symmetry. The Ieft-hand part of the feature clearly has both the distorted oval shape and the hair-pin-shaped region to the South. On the right-hand side this latter structure is less in evidence but still exists, while the anticyclonic oval to the North is distorted into a tear-drop shaped cloud 1The existence of such double structures has recently been confirmed by Beaumont (1980) for jet-iike flows foliowing their q~itative discussion in MRl. * Detailed calculations based on the actual velocity profile are currently underway.
987
T.
988 -40
0
40
VELOClTYtys, 120
MAXWORTHY
160
FIG.2.DETAILSOFTHEVELOCITYPROFILETOTHESOUTHOFTHE JOVIANFZQUATOR,FARREMOWDFROMTHECENTREOF~WAVE UNDER INVESTIGATION.
Open circles taken from the left-hand side of the wave and closed circles from the right. The chain-dotted line is the propagation velocity of the equatorial feature as a whole.
pattern. There is some evidence of this tear-drop patternon theleft-handsideofthestructure, butitisnot as extensive or obvious. In defense of our solitary wave explanation we note two important differences between the theory, as presently formulated, and the observations. Firstly the theory does not include the
cl
g-s 8 -10 -15 FIG.3. EXPECTEDSTRRAMLINESOFASOLITARYWAVEWITHTWO CRITICAL LEVEL.9 ON AN ASYMMETR IC JET-LIKE VELOCITY PROFILE.
Streamlines drawn with respect to a coordinate system moving with the wave. Here and in Fig. 2 the chain-dotted line shows the velocity of the wave in System III.
Measurements and interpretation of a Jovian, near-equatorial feature
FIG.~.~~~PA~RNS~IA~DWI~WA~
arrow A points to the centre of the recirculating flow, identified as a wave of elevation in the text. B lies along the region ofhair-pin streamlines, a wave ofdepression. The small insert shows an inverted picture of one of the White Ovals in order to point out the similarity in cloud structure between it and the feature under discussion.
The
FIG.~.~OD~~~YPR~~~IONSOF Voyager PAPER (1) ANDo~OFA~~OFVIR~ALLY~DE~CAL~~~~~
ZFRAHES~OWING~WA~DI~U~~IN~S NoRTHOFTKEEQ~ATOR~~).
989
Measurements and interpretation of a Jovian, near-equatorial feature
effects that clouds, and their possible energy source, may have on the dynamics. Secondly these same clouds may also distort the observations by behaving unsymmetrically as fluid parcels rise on one side of the wave and fall on the other. As part ofFig. 1 we also show an inverted picture of one of the W.0.s to emphasis the similarities in morphology and explanation between these features. In M.R.W., M.R.2 and M we have already applied our solitary wave ideas to the W.0.s and note again here that such blobs (E-waves) are always anti-cyclonic while hair-pins (D-waves) are always cyclonic. The velocity measurements (Fig. 4) tend to confirm this tentative explanation. Velocity vectors drawn with respect to the moving wave (heavy lines in the figure) show exactly the pattern one would expect from theoretical considerations. Points near the centre of the wave are moving with the wave speed. Flows into and out of the “hair-pin” regions are clearly shown. The weak rotation within the oval region is shown less clearly because of the lack of well-defined marker particles within this relatively featureless region. These velocity measurements (as also shown in Fig. 2) also indicate that the same velocity field exists in the hair-pin shaped regions on either side of the centre of the feature despite a lack of similarity in their visual appearance. CONCLUSIONS
We have shown that morphology and flow-field of one particular near-equatorial Jovian feature is consistent with its explanation as a planetary solitary wave. In particular, in order to exist on the asymmetric jet structure found in this region a large eastward wave
991
speed is to be expected so that two critical layers exist. That the observations bear out this expectation is a strong argument in favor of the model. We further note that at least one other structure of this general type exists on the same jet approx. 180” removed from it in longitude, while the similar jet on the northern edge of the equatorial region also contains numerous features with similar morphologies (Fig. 5). Acknowledgements-Theinvaluable help ofGlen W. Gameau and Jimmy L. Mitchell, of J.P.L., in the preparation of the images from which the reported data were taken is gratefully acknowledged. Discussions with Prof. Reta Beebe of N.M.S.U.were also of great help in putting this work into the correct historical perspective. Support came from the Planetary Atmospherei Section of J.P.L. under contract NASW 7; in particular the encouragement of Dr. Moustafa Chahine is acknowledged with gratitude. REFERENCES
Beaumont, D. N. (1980) Solitary waves on an unsymmetrical shear flow with applications to Jupiter’s Great Red Spot. Icarus 41,400. Maxworthy, T. (1979) Dynamics of the Jovian Atmosphere. Proc. 13th Biennial Symp. on Fluid Dynamics, Polish Academy of Sciences, Warsaw, Poland. Maxworthy, T. and Redekopp, L. G. (1976) A solitary wave theory of the Great Red Spot and other observed features in the Jovian Atmosphere. Icarus 29,261. Maxworthy, T. and Redekopp, L. G. (1980) Possible fluid dynamical interpretation of some reported features in the Jovian Atmosphere. Science 210,135O. Maxworthy, T., Redekopp, L. G. and Weidman, P. D. (1978) On the production and interaction of planetary solitary waves: applications to the Jovian Atmosphere. Icarus 33, 388. Redekopp, L. G. (1977) On the theory of solitary Rossby waves. J. Fluid Mechs 19,543.