U.S. Dept. of Commerce / NOAA / OAR / PMEL / Publications

Buoyancy-driven plumes in rotating, stratified cross flows: Plume dependence on rotation, turbulent mixing, and cross-flow strength

J. W. Lavelle

National Oceanic and Atmospheric Administration/Pacific Marine Environmental Laboratory, Seattle, Washington

Journal of Geophysical Research, 102(C2), 3405-3420 (1997)
Not subject to U.S. copyright. Published in 1997 by the American Geophysical Union.

Results

Six model experiments are reported here. Discussion begins with a reference case followed by contrasting results of perturbed cases (Table 1). Perturbed cases refer to those at zero rotation rate ( = 0), null shear-dependent turbulent mixing intensity (CS = 0, (6)), reduced horizontal background mixing (AHMIN = 10 m s, (4)), and higher U of 3 and 6 cm s. The three velocity cases to be compared have R = wMAX /U values of 6.6, 2.8, and 1.0, where wMAX is the computed maximum upward velocity in the plume stem and U is background flow velocity. Buoyancy dominates plume development for larger R and cross flow dominates for smaller R. The parameter R is often used to classify situations of jets entering cross flows, in which case wMAX represents jet exit velocity. Sykes et al. [1986] ran numerical experiments for jets that spanned the ratio 2-8. Laboratory experiments of Ernst et al. [1994] on buoyant jets in cross flows showed plume bifurcation over the range R = 2-6.

Calculated fields in three dimensions and in time include eq-uvector.gif (872 bytes), p, , S, and AI. This paper focuses primarily on temperature and velocity/vorticity fields near temporal equilibrium as a way to describe differences caused by rotation, turbulence, and cross-flow speed.

Reference Case

Figures 2 and 3 present cross sections through the reference experiment plume at 24 hours past plume startup. With the given advection speed (U = 1.5 cm s), the advection distance over that time period is 3 times the distance (425 m) between source and outflow boundary. By 24 hours, the plume is in equilibrium; heat flux through the outflow boundary is equal to the heat input at the source. Even as early as 8 hours, corresponding to an advection distance just past the outflow boundary, the plume is in equilibrium around the source and near equilibrium at outflow, with outflow heat flux already 80% of vent heat input.

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Figure 2. Plume distributions for the reference case (experiment 21, Table 1) at t = 24 hours. The cross-stream direction is y and the along-stream direction is x. (a) on the plane y = 0; (b) on the plane y = 0; (c) on the plane z = 2280 m; (d) on the plane x = 320 m. All contours are in degrees Celsius.

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Figure 3. Velocity, , and relative vorticity patterns for the reference case (experiment 21, Table 1) at t = 24 hours. (a) (shaded) and z nondimensionalized by U/D (contoured) at z = 2350 m (z/D = 5); (b) (shaded) and u velocity (contoured) at z = 2280 (z/D = 12); (c) (shaded) and v velocity (contoured) at z = 2280 (z/D = 12). Velocity is in meters per second.

Contours of (Figure 2a) show the effect of hydrothermal heat release on the surrounding environment. Isotherms are drawn down into the source region. The inverted J-shaped isotherm and a plume stem bent ~13° with respect to the vertical evidence the effects of background flow. The well-defined stem has lateral gradients as large as 6.8 × 10 °C m. Relatively steep gradients such as these are not numerically easy to preserve; their occurrence in these calculations results from the use of the upstream corrected advection scheme of Smolarkiewicz and Clark [1986]. Downstream internal waves above the height of the convection column with wavelength of ~140-170 m are also evident in Figure 2a. These are associated with internal waves in u and w velocities with amplitudes of ~0.2 and 0.6 cm s, respectively. Lees waves in the atmosphere resulting from convective motion have been modeled by Hauf and Clark [1989] and are used to good advantage by glider pilots [Kuettner et al., 1987]. A possible explanation for their occurrence is that a convection column can act, in part, like a hill, forcing environmental flow over and around, but further numerical experimentation is required to be unequivocal about the cause in this setting.

The anomaly, = - BKG, contoured in units of 0.005°C (Figure 2b), better shows the maximum rise of the plume to be 180 m. For the given combination of U and B, the plume overshoots the neutral density level. Yet flow is strong enough, with the given source buoyancy and stratification, that the overshoot is small, and strong enough that no limb of the plume appears upstream of the source. For fixed B, an upstream limb can be expected as U is reduced [e.g., Ernst et al., 1994], and full plume symmetry about the then-vertical convection axis must occur when U = 0 [e.g., Lavelle, 1995]. In all cases reported here, U is sufficiently large (1.5 cm/s) that neither upstream nor significant cross-stem plume growth occurs. Flows in and around the stem and plume cap region, which result from the superposition of background and convective flows, are also much different than flows expected in and around convective plumes rising into a quiescent background environment [e.g., Lavelle and Baker, 1994].

Vertical velocities in the stem reach maxima of 0.1 m s in this example. The plume overshoots the equilibrium level and causes a slight positive density anomaly in the region above the stem. Just downstream of the positive region, flow has a downward directed component with vertical velocities of as much as 0.03 m s. The local maximum of centered near x = 50 m (Figure 2b) is at the terminal end of this downward directed flow. Note that > 0.02 °C extends only several hundred meters downstream because of lateral dispersion. Since resolving 0.01 °C in field data is difficult, a single hydrothermal source of the given size in this stratification environment ought to be difficult to detect thermally beyond several hundred meters from the vent source.

A planar view of the same plume at 120 m above the bottom (z = 2280 m, Figure 2c) shows the small aspect ratio of the plume for the given cross-flow strength. At the outflow boundary, the plume (i.e., the 0.005°C isopleth) at this depth is ~100 m wide. Growth of the plume in the flow transverse direction is limited by the downstream transport of plume material. The local maximum centered at x = 75 m (Figure 2c) is the same local maximum evident in Figure 2b, the consequence of initial plume overshoot with subsequent downward advection. Computations without rotation show planar distributions with perfect symmetry about the y = 0 axis. The slight asymmetry of the pattern of Figure 2c is thus caused by rotation, a topic to be taken up more fully later. No undesirable outflow boundary layer is apparent in Figures 2a-2c, evidence that supports Johansson's [1993] prescription for boundary conditions.

At the outflow boundary (x = 320 m), the equilibrium plume shows a maximum core of 0.015°C (Figure 2d). The plume (i.e., 0.005°C isopleth) has maximum width of ~200 m, about half the width of the computational domain (320 m). Cyclic boundary conditions in the y direction allow transport through the side walls of the calculational region, but little -distribution contamination by adjoining cyclic domains is apparent. A wider computational domain width would be necessitated if smaller U were used. A test experiment was performed to examine the change in results due to quadrupling the domain width. In that case the y-direction resolution was coarsened to 10 m, but all other aspects of the calculations were left intact. Results were not significantly different from those shown here. In consideration of computational costs, most experiments were run with the 320-m domain width.

Circulation in the region of the plume stem and above is considerably different from that predicted for point source convection in otherwise quiescent environments [e.g., Lavelle and Baker, 1994]. In the high -gradient region near the source, contours (shaded, Figure 3a) are kidney- or horseshoe-shaped, as found numerically, for example, of plumes in nonrotating environments by Sykes et al. [1986]. The same authors cite numerous laboratory observations of the same effect. While much of the upstream fluid enters the stem, there is also some spatial acceleration of flow around the stem. Downstream of the stem there is a u-velocity minimum and beyond that is a reconvergence of the stem-separated flow. The flow patterns result in a counterrotating z couplet (contours, Figure 3a) with a z maximum on the right (referenced to the downstream direction) and a minimum on the left, at the downstream end of the anomalies. Such a counterrotating couplet at the downstream edge of a jet entering cross flow was noted by Turner [1960] and observed by Moussa et al. [1977], for example. Besides the asymmetry caused by rotation (Figure 3a), the z pair is also much like the one found numerically by Sykes et al. [1986] for jets in nonrotating, unstratified cross flows. Not shown is the perturbation pressure (p') distribution, which has two local minima of comparable size located asymmetrically about y = 0 and slightly downstream of the isopleth tips.

The kidney-shaped pattern of extends from the seafloor to the levels of neutral buoyancy. At z = 2280 m, the pattern of in the stem region (shaded, Figures 3b and 3c) also has two lobes, the right lobe being larger. Asymmetry about y = 0 is again the consequence of Coriolis forces. Superimposed on the distributions are isopleths of u (Figure 3b) and v (Figure 3c). With background flow at 0.015 m s, Figure 3b shows a region of reduced u ahead of the convection column and a region of near-zero u some 20 m downstream. The v distribution (Figure 3c) shows maxima to both side of the column, but much higher v in the direction of positive y. Downstream, the signs of the two v lobes reverse to allow the reconvergence of the flow that was deflected to either side of the column. Though Figure 3 bears evidence that the Coriolis force does affect plume structure, the simple anticyclonic flow for the upper plume predicted when convection occurs in a quiescent background environment [Lavelle and Baker, 1994] no longer occurs. Additional differences in plume structure with and without rotation are discussed in the following section.

The Nonrotating Case

A nonrotational case was next examined. To isolate direct effects of rotation, the u profile of Figure 1a was taken as the along-stream background current, and cross-stream v was taken to be zero in experiment 22. Using (11), a P profile consistent with those velocity profiles but unique to the nonrotating case was determined. The resulting P was used to force ambient cross flow (Table 1). Using the P of experiment 21 when = 0 would have resulted in a uBKG profile with a much thicker boundary layer.

The primary difference in caused by rotation is the absence of distributional symmetry about y = 0; rise height, overshoot, and magnitudes are otherwise similar in a general sense. As expected, u and v too are symmetrical about y = 0 in experiment 22 (Figures 4a and 4b) but not in experiment 21 (Figures 4c and 4d). To allow easier comparison of these results with those of Sykes et al. [1986], velocities and distances in Figure 4 have been non-dimensionalized by U and D.

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Figure 4. Comparison of rotating (experiment 21) and nonrotating (experiment 22) cases. Velocity u nondimensionalized by U on the plane z = 2380 m (z/D = 2) when = 0 (Figure 4a) and when 0 (Figure 4c). Velocity v nondimensionalized by U on the plane z = 2380 m (z/D = 2) when = 0 (Figure 4b) and when 0 (Figure 4d). For = 0, on the plane x = -60 m (x/D = 4) (Figure 4e) and nondimensional u on the plane x = -60 m (x/D = 4) (Figure 4f).

Figures 4a ( = 0) and 4c ( 0) show u in the vicinity of the source at a vertical distance of z/D = 2, where z is distance from the seafloor. When = 0, u is nearly doubled (U/U = 1.9) on both sides of the rising plume as background flow, in part, sweeps around the ascending fluid column. The bulk of the upstream flow is undeflected; after entering the column, u momentum is displaced vertically, with the result that little of the u momentum entering upstream is found downstream at z levels where the stem is well-defined. The u velocity immediately downstream of the stem is just greater than zero, although flow of small size (u < 0) occurs in the boundary layer (z/D < 2) and at some sites above z/D = 10. Though the possibility of downstream reverse flow (u < 0) must depend on boundary layer thickness and strength of upward convection, the general result, that nearly all entrainment into the stem occurs from the upstream side of plumes under similar forcing conditions, is likely not to be significantly altered.

In the rotating case (Figure 4c), reverse flow (u < 0) occurs on the left side of the convection column (y > 0), while larger along-stream flow (u/U = 2.4) occurs on the right (y < 0). This asymmetry helps shape the distribution of, for example, Figure 3a. The region of flow affected is small. Consequently, field observations of u enhancement near a heat source may prove difficult, if only because of the small size of the region involved.

Magnitude of the transverse velocity, |v| , reaches ~0.6U in both cases (Figures 4b and 4d). For = 0, maximum |v| occurs nearly twice as far downstream as || maxima, which occur at the downstream edge of the stem. The v convergence (Figure 4b) results in u values again having magnitudes ~U within a distance of 5D downstream of x = 0. The effect of 0 on v (Figure 4d) is to skew distributions across the plane of symmetry (y = 0) so maximum |v| occurs slightly farther downstream than does maximum |-v|. Magnitudes of v at this z level are little changed by rotation.

For cases when R = 4 and R = 8, Sykes et al. [1986] provide distributions of a passive scalar and u on the cross section x/D = 4. While their study of jets involved neither background stratification nor a boundary layer, their results show horseshoe-shaped patterns for the scalar (as in Figure 4e) and u distributions with a low velocity core underlying a higher velocity high region (as in Figure 4f). Results here show larger vertical gradients above the core (Figure 4e) and maximum u velocities the distribution of which drapes less over the sides of the lower u core (Figure 4f) than it does in the results of Sykes et al. [1986]. Those differences undoubtedly reflect the presence of background stratification. In none of the panels of Figure 4 is the full domain of computation shown.

Relative vorticity distributions allow a comparison to the results of Sykes et al. [1986] as well. Nondimensionalized stream-wise vorticity in the source region at z/D = 2 appears as a counterrotating couplet (Figure 5a); even during plume development (t < 1 hour) the couplet at this level has the indicated strength and shape. Low p is found just downstream of extremal x sites. If contours were superimposed, x extrema would be seen to be just downstream of the center. When 0, the axis separating the two counterrotating vortices of the couplet is oriented clockwise of the x axis, but magnitudes are comparable to those of the = 0 case. Sykes et al. [1986] found distributions of that are similar in both length scale and intensity at this height. The similarity is not surprising, in that at z/D = 2 the background environment is well mixed (Figures 1a-1b) and by this time (t = 8.3 hours) conditions in the stem have long ago reached equilibrium. The pattern (Figure 5a) is primarily the consequence of the w/y contribution to x and, for fixed x, error function-like distributions of w in the y direction across the plume stem; the other term contributing to x, v/z, is less than 10% the size of w/y.

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Figure 5. Relative vorticity, nondimensionalized by U/D, about the x axis, , when = 0 on the planes (a) z = 2380 (z/D = 2), (b) x = -60 m (x/D = 4), and (c) x = 0 (x/D = 10). (d) Relative vorticity, nondimensionalized by U/D, about the y axis, , on the plane y = 0.

Downstream, the distribution of x grows in complexity. For example, on the plane x/D = 4, has two pairs of counterrotating cells (Figure 5b). The underlying velocity field is like that measured by Fearn and Weston [1974] for a jet entering a cross flow. It is the w distribution, similar to Figure 4e, once differentiated (i.e., w/y), much more than the distribution of v/x, that determines the form of . At this x location, x again resembles that found by Sykes et al. [1986]. At x/D = 10, where negative w at the level of neutral buoyancy is a response to the initial plume overshoot (Figure 3a), is preponderantly negative on the right side and positive on the left (Figure 5c). No similar result could be expected for jets in homogenous flow because then no vertical overshoot is possible. Stratification also broadens and flattens the x distribution at this distance.

In experiment 22 ( = 0), initially only is nonzero, and then only in the boundary layer, because background shear is at first unidirectional. Both and quickly develop, however, and is substantially changed as convectively forced flow develops. On the plane y = 0, for example, singlet becomes a couplet extending much higher into the water column (Figure 5d) with extremal values (6.5 units) that dwarf original magnitudes (-0.65 units). The distribution of in Figure 5d is also determined by the distribution of w across the stem region: w/x, the significant factor determining , is positive entering the stem on the upstream side and negative exiting the stem downstream. Sykes et al. [1986] and Klemp [1987], among others, have analyzed the growth of vorticity components as convection occurs, so a full discussion of that time development is unnecessary to repeat here. Klemp [1987] shows that when cross-stream vorticity is present, it is tilted and drawn up by buoyancy driven flow during thunderstorm development to initiate a z couplet (e.g., Figure 3a). Schlesinger [1980] suggests that no initial shear is needed for all three components to develop, but tilting by advection is a primary means of growth for downstream components during storm development.

Dominance of x and by one of the horizontal derivatives of w points to the certainty of development of both relative vorticity components starting at the time buoyancy is first generated because vertical velocity is created by buoyancy from startup. For example, without cross flow the distribution of w in the budding stem would be Gaussian in both lateral directions, and the first derivative of w would lead to counterrotating vorticity pairs in both x and y directions, i.e., x and y. Clearly no cross-stream or stream-wise vorticity is needed initially when buoyancy forcing is present to generate x and . Just as clearly does z production begin at the same time: as the convection column first deflects a fraction of the background flow to both sides, flow that subsequently converges downstream, distributions of u and v (Figures 4a-4d) are created that once differentiated lead to nonzero z. Production of all components of must occur at any location where buoyancy has begun to disturb background flow.

Sensitivity to Mixing Strength

To gauge sensitivity of results to subgrid-scale mixing, two additional experiments were performed. In the first, dependence of mixing on shear (equation (6)) was eliminated by setting CS = 0, so only constant mixing coefficients controlled turbulent diffusion (experiment 23). Those background mixing coefficients had relatively small values AZMIN (10 m2 s) and AHMIN (10 m2 s), as indicated earlier. In another experiment (experiment 26), CS was left at 0.2 so that AI (equation (6)) would be a significant factor in mixing in the stem region, where shears are larger, but the value of AHMIN that controls lateral mixing outside that region was reduced by a factor of 10. In this case AHMIN is smaller (10 m s) than even AZMAX (equation (12)). In reference experiment 21, AI in the plume stem was typically 10-20 × 10 m2 s. With a small value in experiment 26, AHMIN had little influence on mixing in the stem region and much reduced influence beyond. Effects of stirring by nonlinear advection beyond the convection region are thus highlighted in experiment 26.

Results at t = 8.3 hours for the three cases are shown in Figure 6. In both panels, isopleths are provided as solid lines (experiment 23), dotted lines (experiment 26), or shaded regions (experiment 21). Both experiments with reduced turbulent mixing show anomalies with greater spatial variability. Three plumes along y = 0 (Figure 6a) show that there is no substantial difference in the equilibrium level of the plumes. Using height of maximum averaged over each section in the downstream interval 200 < x < 320 m as indicator, average rise heights were 136, 125, and 122 m for experiments 21, 23, and 26, respectively (Table 1). Thus reduced lateral mixing leads to only slightly smaller rise heights. On the other hand, when time development of the plumes is examined, the starting pulse of anomalous water rose to a height greater by 27 m in the case of smallest stem viscosity (experiment 23) compared to the case of largest viscosity (experiment 21). Earlier work by Lavelle and Baker [1994] for plumes without cross flow had shown higher rise heights with less stem mixing. Present results agree only for the initial interval of rise to the level of neutral buoyancy, but not in the longer term. The explanation must lie in differences in entrainment when cross flow is present. In the cross flow case, background flow is forced into the plume stem region on the upstream side, while without cross flow, entrainment is caused by convection alone and occurs omnidirectionally.

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Figure 6. for experiments that differ only in the subgrid-scale parameterization (Table 1). Results are represented by dotted contours for experiment 26 (AHMIN = 10 cm s), solid contours for experiment 23 (CS = 0), and shaded contours for experiment 21, the reference case. (a) Cross sections for y = 0, (b) cross sections for z = 2280 m. All contours are in degrees Celsius at 8.3 hours.

When viewed on the horizontal plane z = 2280 m, plumes of experiments 23 and 26 show larger lateral downstream spread than in the reference experiment (Figure 6b). Counterintuitively, smaller mixing coefficients either locally in the stem (experiment 23) or globally (experiment 26) cause greater lateral dispersion. Using the 0.005°C isopleth to designate a plume edge, widths averaged over 200 < x < 320 m for the three experiments were 90, 188, and 155 m, respectively. In experiment 26, that same edge shows signs of wispiness, as if Helmholtz shear instabilities were occurring.

Statistics of z within the downstream plume ( > 0.005°C, x > 100 m ) show experiment 26 having larger relative vorticity. In experiment 26, z was more patchy downstream of the source. Mean values of |z| for the three experiments were 1.4 ×, 1.2 ×, and 2.9 × 10 s, while the standard deviation of || for experiment 26 is twice as large as for the other experiments. This suggests that resolved stirring rather than unresolved mixing is more significant as a dispersion process in experiment 26 than in the others. Thus reduced turbulent mixing in the far field, i.e., smaller AHMIN, allows stronger small-scale stirring, which in turn leads to more widespread plume dispersal.

Differences in velocities also are apparent with changes in turbulent mixing intensity. In the stem, w maxima are smallest with full mixing (experiment 21) and largest when CS = 0 (experiment 23). Downstream negative w are 40% larger in experiment 23 than experiment 21. Times series show that differences are much more than just changes in magnitude. Animations of fields show source heat, while steadily discharged at the seafloor, being pulsed to higher levels when mixing is small (experiments 23 and 26) but not when mixing is higher (experiment 21). Time series sampled at a site 120 m above and 27.5 m downstream of the source (Figure 7) show, in comparison, that quickly grows to a value of 0.06°C in all three experiments as the plume front passes but thereafter they are quite different. For largest mixing (experiment 21), smoothly seeks an equilibrium level. In experiments 23 and 26, on the other hand, values oscillate with periods of ~1300 s. The w time series at this location shows similar frequency content. Buoyancy period, based on the linear region of the profile (Figure 1b), is 1265 s. The oscillation period from model results is only a coarse estimate because model data were sampled only every 300 s. Since the amplitude of oscillations is nearly 0.03°C in experiment 26 (Figure 7), field observations of very near to hydrothermal heat sources at intervals of 1 min or less might be able to distinguish different mixing coefficient regimes.

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Figure 7. Time series of at a fixed point in the plume stem (x/D = 2.25, y = 0, z/D = 12). The dotted line represents the experiment of largest subgrid-scale mixing (experiment 21), while the other two have reduced background mixing (dashed line, experiment 26) or shear independent mixing (solid line, experiment 23).

 

Changes in Cross-Flow Strength

Effects of cross-flow strength were examined by increasing U from 1.5 cm s in experiment 21, to 3 and 6 cm s in experiments 24 and 25, while all other conditions were held fixed. That sequence of three experiments has R = wMAX/Uo values of 6.6, 2.8, and 1.0, respectively, where wMAX is maximum upward stem velocity determined empirically from results of each experiment. This range of R is comparable to that examined by Sykes et al. [1986] and is approximately the range over which Ernst et al. [1994], in laboratory experiments, found significant changes in the character of buoyant jets in cross flows.

Plumes bend increasingly with increasing cross-flow strength, as expected (Figures 8a and 8d); in all panels of Figure 8 the dotted line represents the = 0.005°C isotherm of experiment 21. Rise heights, hRISE, based on the location of maximum in vertical sections at the outflow boundary for each of the three experiments are 136, 97, and 77 m, respectively, the last value representing the higher of two maxima (Figure 8f). On the basis of those three values alone, a best fit of hRISE to U gives hRISE U-0.40. Extensive atmospheric observations have led to the canonical form hRISE = 2.6 [B/(UN)]1/3 for bent-over plumes in the stratified atmosphere [e.g., Hanna et al., 1982], where hRISE refers to distance between source level and the vertical midpoint of the plume downstream of the source. Thus, for atmospheric cases, hRISE U-0.33. The similarity of U dependence for these model results and atmospheric data is encouraging, though the paucity of model realizations, the difficulty of defining rise height when the distribution has more than a single maximum (Figure 8f), and the difference in rise height definitions between this and the atmospheric case are all causes for caution.

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Figure 8. Contours of in degrees Celsius at 8.3 hours for experiment 24 (U = 0.03 m s, Table 1) at (a) y = 0, (b) z = 2320 m, (c) x = 300 m, and for experiment 25 (U = 0.06 m s, Table 1) at (d) y = 0, (e) z = 2360 m, and (f) x = 300 m. The dotted contour in each panel represents the 0.005°C isopleth for the reference case (experiment 21).

Unexpectedly, plumes of experiments 24 and 25 have voids in the downstream distributions. For experiment 23 (R = 2.8) this occurs just downstream of the stem, but the branches merge again farther downstream (Figure 8a). In experiment 26 (R = 1.0), branching occurs farther from the stem region and extends to the outflow boundary (Figure 8d). No such voids were seen in experiment 21 (R = 6.6, Figure 2).

In neither of the two cases is branching simple. For R = 2.8, a section for z = 2320 m (Figure 8b) shows that the void does not extend laterally all the way across the plume. The core region of highest gradients has a more exaggerated kidney shape than in experiment 21, but only the right branch spawns material downstream at this level; the left branch is truncated. A sequence of horizontal sections shows the void to be tubular with the principal axis of the tube skewed from the vertical. The irregularly shaped tube cuts through the plume wall, here defined as the = 0.005°C isopleth, on the left-hand side below z = 2310 m, creating the left-side void seen in Figure 8b. Above z = 2310 m, the right-side wall of the plume is interrupted. In the x direction near the stem, is continuous on the right-hand side below z = 2310 m and continuous on the left-hand side above. Beyond x = ~100 m, the plume has no voids. At x = 300 m (Figure 8c) it is wider than high, with two local maxima. The rightmost maximum evidently buds from the lower right-hand limb of the kidney-shaped region, while the upper maximum buds from the higher-rising left-hand limb.

For the plume rising into the strongest cross flow (R = 1.0, experiment 25), the picture of a top-to-bottom bifurcation suggested by Figure 8d is also not complete. The planar view (Figure 8e) shows a plume with a strong right-hand limb and a stunted left-hand limb at z = 2360 m. A sequence of horizontal slices shows that the left-hand limb is favored below z = 2380 m and the right-hand limb is favored above. The left-hand limb is attached to the seafloor and extends to x = ~200 m before disappearing; the attachment is in part caused by the location of the source at the seafloor, but effects of the low vertical resolution of the boundary layer by the model cannot be discounted. The right-hand limb splits vertically but does not completely separate; the section at x = 300 m (Figure 8f) shows that the bifurcation in Figure 8d was apparent only; the two vertically aligned maxima are connected. The plume would be earmarked as distinctly bifurcated only if = 0.005°C were too small an anomaly to be observed. Thus an observational threshold can affect judgement as to whether a plume has bifurcated or not. This result should also serve warning that two maxima in a single vertical profile in a hydrothermal region may not mean that two venting sources, each with different B, are nearby.

Distributions of within these plumes might seem peculiar if it were not for field and laboratory observations that confirm that plumes from buoyant jets can bifurcate. Scorer [1959] noted the occurrence of plume bifurcation in ordinary chimney plumes. Observations of bifurcating industrial stack plumes are exemplified in the report of Fanaki [1975]. Volcanic plume bifurcations are summarized by Ernst et al. [1994]. Several laboratory experiments of Wu et al. [1988] on buoyant jets in unstratified flows led to vertical bifurcation of the kind seen in experiment 25 (Figure 8f), though in the laboratory it was a source configuration skewed with respect to flow direction rather than environmental rotation or shear in cross flow that broke plume symmetry about the y axis.

Mechanisms that cause jet or plume bifurcations are not completely understood, though observations have pinpointed some conditions under which bifurcation is likely to occur. In cases of jets entering unstratified flows, the ratio R has been used to classify results. Ernst et al. [1994] saw buoyant laboratory jets that clearly bifurcated when R fell in the range 2-6, but bifurcation was blurred or did not occur at higher or lower R values. In model plumes addressed here, bifurcation occurred but was not complete when R = 1.0 and 2.8, but did not occur when R = 6.6. Ernst et al. [1994] noted that sharp density interfaces, orientation of a jet orifice with respect to the flow, and latent heat release all can influence the occurrence of a bifurcation. In the case of convection during severe storms, Klemp and Wilhelmson [1978] showed that vertical shear of environmental winds and downdraft caused by precipitation are important to the storm splitting and divergence process. On the basis of results reported here, it is appropriate to add rotation, background stratification, and boundary layer shear to the list of possible factors affecting plume bifurcation. The large number of potential factors involved, however, will likely make the identification of conditions and causes leading to the bifurcation of hydrothermal plumes difficult.


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