Review of “A realistic physical model of the Gibraltar Strait” by Tassigny et al.

People love laboratory experiments. Even in an age where the smallest scales of turbulence are starting to become numerically resolvable, lab experiment give a sort of immediate physical connection that is hard to reproduce through simulation.  It is good to know that the large turntable in Grenoble is being put to good use.

The particular experiment described in this paper is a scale model of the Strait of Gibraltar and immediately surroundings. The exchange flow is set up using a dam break scenario with topography that is realistic except for a scale factor of 10 and a bit of smoothing.  Semidiurnal tides are imposed using oscillating plungers.  Using modern laboratory measurements, including PIV, PLIF, ADV, conductivity and temperature sensors, and interferometers to measure surface elevation, the authors are able to gather data on velocity and stratification along three parallel transects of the strait. These are used to features at different phases of the tidal cycle and to compare conditions under spring and neap tide forcing. 

For me the most interesting sections of the paper are those that describe detachment of the Mediterranean layer as it spills down the western flank of Camarinal Sill (CS) under conditions of outflow of the barotropic tide.  The authors argue that strong barotropic outflow conditions create  the adverse pressure gradient required for detachment and discuss consequences for mixing. Also interesting are insights into the role of bottom boundary layer processes in mixing, tidal rectification of the baroclinic flow and properties of the internal bore that propagates eastward.  I suppose that some of the results on mixing between the upper layer and salty lower layer must be taken with a grain of salt since the Reynolds numbers are much lower than in the ocean. 

Although the paper is lengthy, the narrative is generally easy to follow and there are just a individual points that need to be cleared up. I also have some suggestions regarding quantification of results that I hope the authors will consider.  My recommendation is for moderate revision.

Main Points

One line 55 the text mentions “uncertainties” that remain and lists a few general categories such as internal hydraulics and instabilities, but it does not specify what the uncertainties are.  The Introduction would be more helpful if it gave the reader more specific information about the issues that are unsettled and how a laboratory experiment (as opposed to a numerical simulation) will clarify or inform.

The paper does not really discuss the topic of maximal vs. submaximal exchange.  Maximal exchange stems from the Stommel and Farmer (1952 and 1953 FMR) papers on overmixing in estuaries. It has turned out that estuaries are not good candidates for overmixing, but as clarified in the Armi and Farmer papers (different Farmer), the Strait of Gibraltar appears to lie close to a state of maximal exchange, with two hydraulic controls, one at CS and the other in the Tarrifa Narrows (TN).   This picture is complicated by tides and I think the current thinking is that the mean exchange is close to maximal and is perhaps pushed intermittently into a maximal state.  The present experiments are quite interesting: Figure 14 suggests that at no point in the tidal cycle is the flow is hydraulically critical at both CW and in the Tarrifa Narrows (TN).  However, during much of the tidal cycle the flow appears to be critical at one or the other.  Generally speaking, maximal conditions mean that signals from outside of the strait are unable to propagate into and through the straight. (They are blocked but supercritical flow at each end.)  When the flow is critical at CS, only signals from the west are blocked, and when the flow is critical at TN, only signals from the east are blocked.  So this would appear to be inconsistent with maximal exchange, but I’ll let the authors weigh in on what they think. Some comment should be made on this historical debate.

A third issue is the reliance of 1D metrics to characterize a 3D flow, a practice that continues in spite of the fact that theory has moved beyond the 1D setting.  A case in point is the composite Froude number, which as the authors acknowledge, tells one something about local hydraulic criticality and says something about the ability of locally generated disturbances to propagate upstream. The local Froude number does is not by itself an indication of hydraulic control of the exchange flow as a whole.  For example, if a hydraulic control exists at the CS section, it is because the entire baroclinic exchange across that section is being choked by the topographic constriction.  If the width of the strait there were made to contract, or the topography to become shallower, a disturbance would be generated that would be felt across the whole width of the strait, would propagate into the Mediterranean, and would result in a diminished exchange rate and a deeper pycnocline.  (A terrific educational video could be created  if this exercise were set up experimentally and filmed.)  In any cases,  statements such as  “hydraulic control has been lost at CS in all three transects” (line 678) don’t make much sense: hydraulic control is not a local phenomenon or a property of a section.   It would be quite easy to use values from the three sections to at least estimate the bulk criticality of the flow at any cross sectional using the generalized composite Froude number that the authors refer to in their citation of Pratt (2008, JFM). These take into consideration the velocity distribution and stratification across the whole section.  If this value dropped below unity, the authors would be justified in claiming that control at CS has been lost.

These remarks also apply in the vertical. The separation between the pycnocline and the level of maximum shear in some locations is nicely documented (e.g. Fig. 12). The authors remark that this separation clouds the use of a composite Froude number (2-layer or 3-layer). In situations like this, the local hydraulic criticality of the flow can be assessed by calculating the continuous vertical modes of the stratified shear flow using the Taylor-Goldstein equation or one of its extensions.  This has been done in places like the Bab al Mandeb and Hood Canal (see Pratt, et al. JPO, 2000 and Gregg and Pratt, JPO, 2010) where it is sometimes difficult to identify a distinct density interface. I’m not suggesting that the authors do this now since the present manuscript is rather long, and the exercise of sorting through the modes can be a bit of work, but perhaps something to think about for the future. At one point, Bill Smyth had a nice code available through his Oregon State webpage.  It has a provision for including viscous and diffusive effect in case there are critical layers. The results are nice because they give you wave speeds and provide a stability analysis.  In general, I think modern investigators need to get away from composite Froude number is situations where the stratification and velocity are not “layered” and look at these modes.

Other Points

Figure 13 and discussion of processes east of CS:  I’m curious about a certain aspect of the tidal flow in this part of the strait: namely the stripping of high potential vorticity water from the shallow shelf on the northern side, as seen in numerical simulations (see Dias, et al., JPO, 2025 Figs. 17 and 18). Water can be  stripped away when the tide surges eastward and the advected plumes of high pv water lead to meanders in the Atlantic Jet.  Do the authors see anything like this in the laboratory model?   Also, regarding the shallowing of the Atlantic layer along the north side of the Tarrifa Narrows (light yellow regions in Fig. 13).  Armi and Farmer 1988, Fig. 11 show evidence that the pycnocline can intersect the surface, suggesting detachment of the Atlantic layer from the northern coast.  Timmermans and Pratt (JPO, 2005) reproduce this using a rotating hydraulic model.  Do the authors see this in the experiment? 

I’m curious why are there no mention of Richardson numbers? Maybe mixing is discussed in the other paper.

The separation of the Mediterranean layer on the western flank of CS is nicely documented in Fig. 12.  In many cases, the separation of a current from a rigid boundary is sensitive to details such as the boundary conditions imposed or the slope of the boundary.  The fact that the slope in the experiment is magnified by a factor up to 10 may have some effect on the location of detachment (or lack thereof) of the descending overflow.  Is this a concern?

line 32:  outlet -> natural outlet.   (don’t forget the Suez canal)

lines 81-82.  “The bottom topography is represented by the variable z=-h_b(x,y)+h(x,y,t)…”. This makes it sound as though the bottom topography is time dependent.  Some clarification or perhaps a definition sketch needed here.

Lines 126-127 suggest that the term containing the external Froude number in (3b) can be neglected, but this term is clearly much larger than the term containing the internal Froude number (Fr₀ being small and Fr being O(1)).  Perhaps the wording explanation is not clear?

Fig. 1 caption. “optical measurements” is repeated.  Also, the photo in the lower left frame is of poor quality.  There is lots of glare coming of the black bottom of the tank, making it difficult to see the actual topography.  I wonder if the photo can be retaken with different lighting, or perhaps the photo can be edited to reduce the glare?

Line 253. Delete “of”.

Line 271 “additional second” -> “second”.

Line 278.   “ADV” has not been explained yet.

Line 285:   “responding”. -> “responding to”

Lines 299-306.  I had trouble understanding the thrust of this paragraph.  It sounds like some sort of adjustment was made in the plunger’s amplitude to correct for some nonlinear process in the strait, but what is being corrected is unclear.

Line 315 I was unable to locate the Bardoel et al. (2026) reference and therefore unable to view the map.

Line 390. “layer of zero horizontal mean velocity h_u”.  Is h_u the thickness of the layer, the depth of the layer, or just a label for the layer?

Line 394.  “when the tide is applied west of CS” ->    If I understand the meaning it would be better to write “west of CS when the tide is applied”.

Line 398. “lower” -> “decrease”

Lines 420-421. I’m not surprised or worried that G² does not quite get to unity in the regions where the flow visually appears to be supercritical.  I have encountered the same issue in other straits where there is clearly a locally subcritcal-to-supercritical transition.

Line 430 states that the highest TKE values are found at the sheared interface for pure baroclinic conditions, but when I look at the bottom left panel of Fig. 4 I don’t see any elevated TKE at the interface.  It looks instead that TKE decreases monotonically from the surface to the bottom. Am I looking at the wrong thing?  Perhaps there is a tiny elevation of interfacial TKE to the east of CS.

Fig. 6 caption.  There is a reference to “vertically integrated volume transport and below salt flux” but I don’t see either of those in the figure panels.

Line 468.  It is curious that G² is maximum at CS and not immediately to the west of CS, where the Med layer spills down.  Could this be due to the definition of the Med layer, which might include low-velocity contributions from the mixed wedge of water that lies between it and the Atlantic layer.  One is probably justified in using a 1.5-layer Froude number for the overflowing layer in this case.

Line 495 claims that dilution is enhanced under neap tide conditions on both sides of the sill.  Does this mean enhanced compared to spring tide conditions?  (When I look at the 3^rd from top, left panel in Fig. 8, I don’t see much dilution in the water column east of CS, and the dilution to the west of CS does not seem to be any greater than in the lower left panel.)

Fig. 9.  The caption is a little unclear here. The bottom panel shows results from the experiment, correct?  Then what is HERCULES?

Line 510.  Why would “slightly elevated G² to the east of the sill” suggest eastward propagation?

Line 525.   By “negative” (that is, westward) do you actually mean “positive” (eastward)?

Line 534.  Has “dilution value” been formally defined?

Lines 537, 545 and 637.  When you write “along the western flank” many readers will think you mean parallel to the flank (or along-isobath), just as “along coast” means parallel to the coast.  I think you are describing the flow that is spilling down the western flank of the sill, and you might consider phrasing it that way.

Lines 521 and 544 speak of a control and hydraulic jump to the west.  It looks like these occur near x=-45. Is this the Spartel sill, and are these features due primarily to the presence of this sill?   Is there some reason it (and Tariffa narrows) is not referred to by name?

Line 598.  “x” is the zonal coordinate, as in Fig. 12.  When you say that x is the along-slope coordinate, this seems to be different.  What does “along slope” mean?  Without this understanding it is difficult to interpret eqs. (13) and (15).  Are you interested in the zonal component of pressure gradient, or the component of pressure gradient tangent to the topography, or the x-component of pressure gradient tangent to topography?   Precise mathematical definitions are nice.

1. I can see the internal bore in Fig. 13, and I think I can see the time shift, with the change in the pycnocline depth first apparent at the southern transect and later at the northern transect.There is a later assertion that this time lag is independent of Kelvin wave dynamics, but if the eastward propagating bore has some characteristic of a Kelvin wave, the signal along the southern coast would tend to lead the signal along the northern coast. This was shown by Federov and Melville (JFM,1996), who developed a solution for a “Kelvin bore”  whose leading edge curves away from the coast and would, in the case of Gibraltar, lead to the southeastward tilt cited on Line 667.  Why is this not a possible explanation?

Well, I hope these remarks improve an already-nice paper.

     This paper is a summary of rotating laboratory experiments on the 2-layer exchange through the Strait of Gibraltar carried out on the large rotating table in Grenoble.  It is an astounding paper in its comprehensive review of the scaling considerations for setting up the physical model, for its detail of the measurements carried out while the laboratory exchange flows were occurring, and for its comparisons with field observations both historical and recent.     Before making any new observations in the Strait of Gibraltar, future scientists will have to read this paper to understand the phenomena that will be encountered in the Strait environment.  I recommend that this paper be published as soon as possible.  No revisions are needed in my opinion.

     The physical model is set up to imitate the real-world environment of the Strait with detailed topography extending from the Alboran Sea to the Gulf of Cadiz and with tidal forcing to include both semi-diurnal and fortnightly variations in the currents. Analysis generally includes alongstrait transects in the northern, central and southern Strait with time series of velocity and depth of the interface between Atlantic and Mediterranean waters.  The hydraulic state of the exchange is illustrated with calculations of 2-layer Froude number at critical locations in the Strait.  Phenomena including turbulence in the descending outflow west of the sill, vertical velocities and bottom mixing near the sill, and the bore propagating eastward into the Mediterranean are identified and quantified.

     When I was making observations of the 2-layer exchange and hydraulic control characteristics in the Strait in the 1980’s and 1990’s, the field work would have greatly benefitted if we had had access to this laboratory model.   In our analyses of the observations I was always worried about unmeasured cross-strait variations in the currents at the sill, in Tarifa Narrows and downstream into the Gulf of Cadiz.  The results from this laboratory model give me reassurance that the cross-strait variations were not an overwhelming issue when interpreting our limited single point measurements.

     Our observations had an overall goal of estimating the inflow, outflow and net exchange through the Strait of Gibraltar.  Within the analysis of this paper, there is a focus on the exciting phenomena in the Strait but not on the overall exchange.  How much inflow and outflow are found in this laboratory experiment?  How do the inflow and outflow vary with the imposed density difference? With the amplitude of the tides?  A result I found fascinating in our observations was the stronger 2-layer exchange flow during Neap tides than in Spring tides, a result also found in the laboratory model here.  But the  variations in exchange were compensated by tidal fluxes so the net inflow and outflow (the overall exchange of water masses) did not vary over the fortnightly cycle.  It appeared that the net exchange was set by the density difference and could be accomplished either by the mean currents or by the tides.

     In future work with the laboratory model, it would be helpful to examine the bulk effect of the processes.  How does the exchange depend on the size of the imposed density difference?  Does the overall exchange depend on the strength of the tides?  These are questions that could be addressed by new experiments using the same physical laboratory model.

     The paper was very well written.  My only complaint was that some missing letters had to be filled in mentally in the printed version I read:  there was no “A” in the title or in “Abstract” and Vaisala came out as 3 separate phrases.  Undoubtedly this is an issue with my traditional software not being compatible with that used by the journal.  It was not an issue for my reading of the paper, but it may be important for the final online, published version.