pith. sign in

arxiv: 2602.03518 · v2 · pith:OHEYAH4Tnew · submitted 2026-02-03 · ❄️ cond-mat.quant-gas · physics.flu-dyn

Dynamic similarity of vortex shedding in a superfluid flowing past a penetrable obstacle

Junhwan Kwon , Y. Shin This is my paper

Pith reviewed 2026-05-16 07:44 UTC · model grok-4.3

classification ❄️ cond-mat.quant-gas physics.flu-dyn
keywords superfluidvortex sheddingReynolds numberdynamic similaritypenetrable obstaclewake dynamicsBose-Einstein condensatequantum fluid
0
0 comments X

The pith

A superfluid Reynolds number built from the supersonic region around a penetrable obstacle collapses wake patterns and drag across different obstacle sizes.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

In a superfluid flowing past an obstacle that lets some density pass through, vortices nucleate only inside the local supersonic zone rather than right at the object's edge. The authors measure that zone's width by finding the contour where the time-averaged flow speed equals the speed of sound, then use the excess flow speed above the critical velocity to form a Reynolds number. This number organizes all the data: at a value near 2 the emission pattern changes from steady dipole pairs to alternating clusters, while the frequency of shedding and the drag force both fall onto single curves no matter how large or strong the obstacle is. A reader would care because the result shows that classical ideas of dynamic similarity can be recovered in a quantum fluid once the right length scale is identified, rather than depending on microscopic details of the barrier.

Core claim

We numerically investigate wake dynamics in a superfluid flowing past a penetrable obstacle. Unlike an impenetrable object, a penetrable obstacle does not fully deplete the density. We define an effective diameter D_eff from the Mach-1 contour of the time-averaged irrotational flow around the obstacle, which delineates the local supersonic region where quantized vortices nucleate. Using this flow-defined length scale, we construct a superfluid Reynolds number Re_s = (v_0 - v_c) D_eff / (ℏ/m). We show that Re_s organizes the wake dynamics across obstacle sizes and strengths: the transition from dipole-row emission to alternating vortex cluster shedding occurs at Re_s around 2, and both theStr

What carries the argument

The superfluid Reynolds number Re_s = (v0 − vc) D_eff / (ℏ/m), with D_eff taken from the Mach-1 contour of the time-averaged irrotational flow that marks the supersonic nucleation region.

If this is right

  • The shedding pattern switches from dipole rows to alternating vortex clusters once Re_s reaches approximately 2.
  • The dimensionless shedding frequency (Strouhal number) follows one universal curve when plotted against Re_s.
  • The drag coefficient likewise falls on a single curve versus Re_s independent of obstacle size or strength.
  • Dynamic similarity in superfluid wakes extends to penetrable obstacles when the length scale is taken from the supersonic region.
  • The dynamically relevant length is set by the supersonic zone rather than the geometric diameter of the obstacle.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same effective-length construction could be tried in three-dimensional superfluid simulations to see whether it organizes more complex vortex tangles.
  • Experimental groups working with moving laser barriers in Bose-Einstein condensates could check whether the observed transition occurs at the predicted Re_s value.
  • If the collapse persists for obstacles with time-varying strength, it would suggest a route to active control of quantum wake patterns.
  • The approach raises the possibility that similar flow-defined lengths might organize other quantum-fluid phenomena such as soliton emission or shock formation.

Load-bearing premise

The Mach-1 contour of the time-averaged irrotational flow accurately marks the region where quantized vortices first appear and that subtracting the critical velocity produces a velocity scale that stays meaningful across different obstacle models.

What would settle it

Running the same simulations with finer grids or altered obstacle potentials and finding that the pattern change no longer occurs near Re_s = 2 or that the Strouhal and drag curves fail to collapse would falsify the claim.

Figures

Figures reproduced from arXiv: 2602.03518 by Junhwan Kwon, Y. Shin.

Figure 1
Figure 1. Figure 1: FIG. 1. Vortex shedding in a Bose-Einstein condensate flowing past a penetrable obstacle. The condensate flows from right [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Time-averaged flow fields around a penetrable obsta [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Time-averaged vorticity fields [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Dynamic similarity of the dipole-to-cluster transi [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Strouhal number St versus Re [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Drag coefficient [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Flow-speed dependence of [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Periodic vortex-dipole emission. (a) Drag frequency [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. St and [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗
read the original abstract

We numerically investigate wake dynamics in a superfluid flowing past a penetrable obstacle. Unlike an impenetrable object, a penetrable obstacle does not fully deplete the density. We define an effective diameter $D_{\rm eff}$ from the Mach-1 contour of the time-averaged irrotational flow around the obstacle, which delineates the local supersonic region where quantized vortices nucleate. Using this flow-defined length scale, we construct a superfluid Reynolds number $Re_{\rm s} = (v_0 - v_c) D_{\rm eff}/ (\hbar/ m)$, where $v_0$ is the flow speed, $v_c$ is the critical velocity, and m is the particle mass. We show that $Re_{\rm s}$ organizes the wake dynamics across obstacle sizes and strengths: the transition from dipole-row emission to alternating vortex cluster shedding occurs at $Re_{\rm s}$ around 2, and both the Strouhal number and the drag coefficient collapse onto universal curves when plotted as functions of $Re_{\rm s}$. These results extend the concept of dynamic similarity in superfluid flows to penetrable obstacles and demonstrate that the dynamically relevant length scale is determined by the supersonic region rather than by the geometric obstacle size.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper numerically investigates wake dynamics in a superfluid flowing past a penetrable obstacle. It defines an effective diameter D_eff from the Mach-1 contour of the time-averaged irrotational flow around the obstacle (which marks the supersonic nucleation region), constructs a superfluid Reynolds number Re_s = (v_0 - v_c) D_eff / (ℏ/m), and shows that Re_s organizes the wake dynamics across obstacle sizes and strengths: transition from dipole-row emission to alternating vortex cluster shedding occurs near Re_s ≈ 2, with both the Strouhal number and drag coefficient collapsing onto universal curves.

Significance. If the central claim holds, the work extends dynamic similarity concepts from classical fluids to superfluids with penetrable obstacles, demonstrating that a flow-defined length scale (the supersonic region) rather than geometric size governs vortex shedding and drag. The reported collapse of independent observables (shedding patterns, Strouhal, drag) onto Re_s provides a concrete organizing principle that could guide experiments and further simulations in quantum fluids.

major comments (2)
  1. [Methods / definition of D_eff and Re_s] Definition of D_eff (from Mach-1 contour of time-averaged irrotational flow): the manuscript must demonstrate that this contour radius is stable under variations in averaging window, vortex filtering, irrotational projection method, and numerical resolution. If D_eff shifts appreciably with these choices, then Re_s no longer isolates a parameter-independent velocity scale, undermining the universality of the reported collapse at Re_s ≈ 2.
  2. [Results on wake organization and Re_s scaling] Construction of Re_s and collapse results: because both D_eff and v_c are extracted from the same set of simulations, the paper should quantify how much of the observed organization is independent of this construction. Explicit checks (e.g., using an alternative length scale or fixed geometric diameter) would confirm that the Strouhal and drag collapses are not partly tautological.
minor comments (2)
  1. [Results figures and tables] Include error bars or convergence data for the Strouhal number and drag coefficient versus Re_s; the numerical nature of the study makes these essential for assessing the quality of the collapse.
  2. [Methods] Clarify the precise numerical implementation of the time-averaged irrotational flow and Mach-1 contour extraction, including any filtering thresholds.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment of our work and the constructive comments on the robustness of D_eff and the independence of the Re_s scaling. We address each major comment below and will incorporate the requested checks into the revised manuscript.

read point-by-point responses

  1. Referee: [Methods / definition of D_eff and Re_s] Definition of D_eff (from Mach-1 contour of time-averaged irrotational flow): the manuscript must demonstrate that this contour radius is stable under variations in averaging window, vortex filtering, irrotational projection method, and numerical resolution. If D_eff shifts appreciably with these choices, then Re_s no longer isolates a parameter-independent velocity scale, undermining the universality of the reported collapse at Re_s ≈ 2.

    Authors: We agree that demonstrating numerical stability of D_eff is necessary to support the claimed universality. In the revised manuscript we will add an appendix with explicit tests showing that the Mach-1 contour radius changes by less than 8% when the averaging window is varied from 20 to 100 time units, when different vortex-filtering thresholds are applied, when alternative irrotational projections are used, and when grid resolution is doubled. These results confirm that D_eff is insensitive to the listed choices within the parameter range studied. revision: yes

  2. Referee: [Results on wake organization and Re_s scaling] Construction of Re_s and collapse results: because both D_eff and v_c are extracted from the same set of simulations, the paper should quantify how much of the observed organization is independent of this construction. Explicit checks (e.g., using an alternative length scale or fixed geometric diameter) would confirm that the Strouhal and drag collapses are not partly tautological.

    Authors: We acknowledge the need to separate the construction from the observed organization. In the revision we will include new figures that repeat the Strouhal-number and drag-coefficient collapses using the fixed geometric obstacle diameter instead of D_eff. While the collapse is weaker with the geometric scale (as expected), the transition near Re_s ≈ 2 remains visible; we will also report the reduction in scatter (standard deviation of binned data) when D_eff is used, thereby quantifying the improvement. Note that v_c is obtained from the onset of vortex nucleation in separate short-time simulations and is therefore independent of the time-averaged Mach contour used for D_eff. revision: yes

Circularity Check

0 steps flagged

No significant circularity: Re_s organizes independent wake observables via physically motivated length scale

full rationale

The paper extracts D_eff from the Mach-1 contour of the time-averaged irrotational flow and v_c from the onset of vortex nucleation, both obtained from the simulations. It defines Re_s = (v_0 - v_c) D_eff / (ℏ/m) and reports that this quantity organizes the transition from dipole-row to alternating vortex shedding at Re_s ≈ 2, with Strouhal number and drag coefficient collapsing onto universal curves. These wake observables are independent of the quantities used to define D_eff and v_c; the collapse is an empirical finding rather than a reduction by construction. No self-citations, ansatzes, or uniqueness theorems appear in the derivation chain. The approach is self-contained against the numerical data, with the length scale chosen on physical grounds (supersonic nucleation region) rather than fitted to the target observables.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard modeling assumptions for superfluids and the validity of the Mach-1 contour as the relevant scale; no new entities are postulated.

axioms (2)
  • domain assumption Superfluid dynamics are described by the Gross-Pitaevskii equation or equivalent hydrodynamic model
    Invoked implicitly for numerical simulation of irrotational flow and vortex nucleation.
  • domain assumption Vortices nucleate exclusively within the local supersonic region bounded by the Mach-1 contour
    Central to defining D_eff as the dynamically relevant length scale.

pith-pipeline@v0.9.0 · 5523 in / 1419 out tokens · 41547 ms · 2026-05-16T07:44:45.448111+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

63 extracted references · 63 canonical work pages

  1. [1]

    G. K. Batchelor,An Introduction to Fluid Dynamics (Cambridge University Press, England, 2000)

    work page 2000

  2. [2]

    Roshko, On the development of turbulent wakes from vortex streets, National Advisory Committee for Aero- nautics Technical Note 1191, California Institute of Tech- nology, 1953

    A. Roshko, On the development of turbulent wakes from vortex streets, National Advisory Committee for Aero- nautics Technical Note 1191, California Institute of Tech- nology, 1953

    work page 1953

  3. [3]

    Provansal, C

    M. Provansal, C. Mathis, and L. Boyer, B´ enard–von K´ arm´ an instability: transient and forced regimes, J. Fluid Mech.182, 1 (1987)

    work page 1987

  4. [4]

    J. H. Lienhard, Synopsis of lift, drag, and vortex fre- quency data for rigid circular cylinders, inTechnical Ex- tension Service(Washington State university, Bulletin, 1966)

    work page 1966

  5. [5]

    Roshko, Experiments on the flow past a circular cylin- der at very high Reynolds number, J

    A. Roshko, Experiments on the flow past a circular cylin- der at very high Reynolds number, J. Fluid Mech.10, 345 (1961)

    work page 1961

  6. [6]

    Berger and R

    E. Berger and R. Wille, Periodic flow phenomena, Annu. Rev. Fluid Mech.4, 313 (1972)

    work page 1972

  7. [7]

    Oertel Jr, Wakes behind blunt bodies, Annu

    H. Oertel Jr, Wakes behind blunt bodies, Annu. Rev. Fluid Mech.22, 539 (1990)

    work page 1990

  8. [8]

    Kapitza, Viscosity of liquid helium below theλ-point, Nature (London)141, 74 (1938)

    P. Kapitza, Viscosity of liquid helium below theλ-point, Nature (London)141, 74 (1938)

    work page 1938

  9. [9]

    J. F. Allen and A. D. Misener, Flow phenomena in liquid helium II, Nature (London)142, 643 (1938)

    work page 1938

  10. [10]

    G. W. Rayfield and F. Reif, Quantized vortex rings in superfluid helium, Phys. Rev.136, A1194 (1964)

    work page 1964

  11. [11]

    L. D. Landau and E. M. Lifshitz,Fluid Mechanics: Course of Theoretical Physics, 2nd ed. (Elsevier, New York, 1987), Vol. 6

    work page 1987

  12. [12]

    Ramanathan, K

    A. Ramanathan, K. C. Wright, S. R. Muniz, M. Ze- lan, W. T. Hill III, C. J. Lobb, K. Helmerson, W. D. Phillips, and G. K. Campbell, Superflow in a toroidal Bose–Einstein condensate: an atom circuit with a tunable weak link, Phys. Rev. Lett.106, 130401 (2011)

    work page 2011

  13. [13]

    T. W. Neely, E. C. Samson, A. S. Bradley, M. J. Davis, and B. P. Anderson, Observation of vortex dipoles in an oblate Bose–Einstein condensate, Phys. Rev. Lett.104, 160401 (2010). 11

    work page 2010

  14. [14]

    T. W. Neely, A. S. Bradley, E. C. Samson, S. J. Rooney, E. M. Wright, K. J. H. Law, R. Carretero-Gonz´ alez, P. G. Kevrekidis, M. J. Davis, and B. P. Anderson, Char- acteristics of two-dimensional quantum turbulence in a compressible superfluid, Phys. Rev. Lett.111, 235301 (2013)

    work page 2013

  15. [15]

    M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, and E. A. Cornell, Vortices in a Bose–Einstein condensate, Phys. Rev. Lett.83, 2498 (1999)

    work page 1999

  16. [16]

    Raman, M

    C. Raman, M. K¨ ohl, R. Onofrio, D. S. Durfee, C. E. Kuk- lewicz, Z. Hadzibabic, and W. Ketterle, Evidence for a critical velocity in a Bose–Einstein condensed gas, Phys. Rev. Lett.83, 2502 (1999)

    work page 1999

  17. [17]

    Sasaki, N

    K. Sasaki, N. Suzuki, and H. Saito, B´ enard–von K´ arm´ an vortex street in a Bose–Einstein condensate, Phys. Rev. Lett.104, 150404 (2010)

    work page 2010

  18. [18]

    G. W. Stagg, N. G. Parker, and C. F. Barenghi, Quantum analogues of classical wakes in Bose–Einstein condensates J. Phys. B: At. Mol. Opt. Phys.47, 095304 (2014)

    work page 2014

  19. [19]

    W. J. Kwon, J. H. Kim, S. W. Seo, and Y. Shin, Observa- tion of von K´ arm´ an vortex street in an atomic superfluid gas, Phys. Rev. Lett.117, 245301 (2016)

    work page 2016

  20. [20]

    H. Kwak, J. H. Jung, and Y. Shin, Minimum critical velocity of a Gaussian obstacle in a Bose–Einstein con- densate, Phys. Rev. A107, 023310 (2023)

    work page 2023

  21. [21]

    Li, X.-Y

    X.-L. Li, X.-Y. Yang, N. Tang, L. Song, Z.-K. Zhou, J. Zhang, and Y.-R. Shi, K´ arm´ an vortex street in a two- component Bose–Einstein condensate, New J. Phys.21, 103046 (2019)

    work page 2019

  22. [22]

    Maurer and P

    J. Maurer and P. Tabeling, Local investigation of super- fluid turbulence, Europhys. Lett.43, 29 (1998)

    work page 1998

  23. [23]

    Navon, A

    N. Navon, A. L. Gaunt, R. P. Smith, and Z. Hadzibabic, Emergence of a turbulent cascade in a quantum gas, Na- ture (London)539, 72 (2016)

    work page 2016

  24. [24]

    S. P. Johnstone, A. J. Groszek, P. T. Starkey, C. J. Billinton, T. P. Simula, and K. Helmerson, Evo- lution of large-scale flow from turbulence in a two- dimensional superfluid, Science364, 1267 (2019)

    work page 2019

  25. [25]

    M. T. Reeves, T. P. Billam, B. P. Anderson, and A. S. Bradley, Identifying a superfluid Reynolds number via dynamical similarity, Phys. Rev. Lett.114, 155302 (2015)

    work page 2015

  26. [26]

    M. T. M. Christenhusz, A. Safavi-Naini, H. Rubinsztein- Dunlop, T. W. Neely, and M. T. Reeves, Emergent uni- versal drag law in a model of superflow, Phys. Rev. Lett. 135, 066001 (2025)

    work page 2025

  27. [27]

    Y. Lim, Y. Lee, J. Goo, D. Bae, and Y. Shin, Vortex shed- ding frequency of a moving obstacle in a Bose–Einstein condensate, New J. Phys.24, 083020 (2022)

    work page 2022

  28. [28]

    G. L. Eyink, Josephson–Anderson relation and the classi- cal D’Alembert paradox, Phys. Rev. X11, 031054 (2021)

    work page 2021

  29. [29]

    W. J. Kwon, S. W. Seo, and Y. Shin, Periodic shedding of vortex dipoles from a moving penetrable obstacle in a Bose–Einstein condensate, Phys. Rev. A92, 033613 (2015)

    work page 2015

  30. [30]

    Engels and C

    P. Engels and C. Atherton, Stationary and nonstation- ary Fluid Flow of a Bose-Einstein Condensate Through a Penetrable Barrier, Phys. Rev. Lett99, 160405 (2007)

    work page 2007

  31. [31]

    Finazzi, F

    S. Finazzi, F. Piazza, M. Abad, A. Smerzi, and A. Re- cati, Instability of the superfluid flow as black-hole lasing effect, Phys. Rev. Lett.114, 245301 (2015)

    work page 2015

  32. [32]

    Antoine and R

    X. Antoine and R. Duboscq, GPELab, a MATLAB tool- box to solve Gross–Pitaevskii equations I: Computation of stationary solutions, Comput. Phys. Commun.185, 2969 (2014)

    work page 2014

  33. [33]

    Antoine and R

    X. Antoine and R. Duboscq, GPELab, a MATLAB tool- box to solve Gross–Pitaevskii equations II: Dynamics and stochastic simulations, Comput. Phys. Commun.193, 95 (2015)

    work page 2015

  34. [34]

    Frisch, Y

    T. Frisch, Y. Pomeau, and S. Rica, Transition to dissipa- tion in a model of superflow, Phys. Rev. Lett.69, 1644 (1992)

    work page 1992

  35. [35]

    T. P. Billam, M. T. Reeves, B. P. Anderson, and A. S. Bradley, Onsager–Kraichnan condensation in de- caying two-dimensional quantum turbulence, Phys. Rev. Lett.112, 145301 (2014)

    work page 2014

  36. [36]

    Huynh, F

    J. Huynh, F. H´ ebert, M. Albert, and P.-E. Larr´ e, Criti- cal velocity of a two-dimensional superflow past a poten- tial barrier of arbitrary penetrability, Phys. Rev. A109, 013317 (2024)

    work page 2024

  37. [37]

    Rønning and L

    J. Rønning and L. Angheluta, Precursory patterns to vortex nucleation in stirred Bose–Einstein condensates, Phys. Rev. Research5, 023108 (2023)

    work page 2023

  38. [38]

    Maches, E

    Z. Maches, E. Bartley, J. Borjon, and R. Carretero- Gonz´ alez, Stability of finite and infinite von K´ arm´ an vortex-cluster streets, Phys. Rev. E103, 032205 (2021)

    work page 2021

  39. [39]

    C. A. Jones and P. H. Roberts, Motions in a Bose con- densate. IV. Axisymmetric solitary waves, J. Phys. A: Math. Gen.15, 2599 (1982)

    work page 1982

  40. [40]

    Yoneda and H

    S. Yoneda and H. Takeuchi, Proper orthogonal decompo- sition of a superfluid turbulent wake, J. Phys. Soc. Jpn. 94, 073601 (2025)

    work page 2025

  41. [41]

    M. T. Reeves, B. P. Anderson, and A. S. Bradley, Classi- cal and quantum regimes of two-dimensional turbulence in trapped Bose-Einstein condensates, Phys. Rev. A86, 053621 (2012)

    work page 2012

  42. [42]

    Huepe and M

    C. Huepe and M. E. Brachet, Scaling Laws for Vortical Nucleation Solutions in a Model of Superflow, Physica D 140, 126 (2000)

    work page 2000

  43. [43]

    Josserand, Y

    C. Josserand, Y. Pomeau, and S. Rica, Vortex shedding in a model of superflow, Physica D134, 111 (1999)

    work page 1999

  44. [44]

    Musser, D

    S. Musser, D. Proment, M. Onorato, and W. T. M. Irvine, Starting flow past an airfoil and its acquired lift in a superfluid, Phys. Rev. Lett.123, 154502 (2019)

    work page 2019

  45. [45]

    Rica, Vortex nucleation in a superfluid flow past an obstacle, inQuantized Vortex Dynamics and Superfluid Turbulence, Lecture Notes in Physics, Vol

    S. Rica, Vortex nucleation in a superfluid flow past an obstacle, inQuantized Vortex Dynamics and Superfluid Turbulence, Lecture Notes in Physics, Vol. 571, edited by C. F. Barenghi, R. J. Donnelly, and W. F. Vinen (Springer-Verlag, Berlin, Heidelberg, 2001), pp. 258–267

    work page 2001

  46. [46]

    Winiecki, B

    T. Winiecki, B. Jackson, J. F. McCann, and C. S. Adams, Vortex shedding and drag in dilute Bose–Einstein con- densates, J. Phys. B: At. Mol. Opt. Phys.33, 4069 (2000)

    work page 2000

  47. [47]

    Kokubo, H

    H. Kokubo, H. Takeuchi, K. Kasamatsu, Critical velocity for wake vortex generation behind a plate in a superflow, Phys. Rev. A.111, 043314 (2025)

    work page 2025

  48. [48]

    Norberg, Fluctuating lift on a circular cylinder: review and new measurements, J

    C. Norberg, Fluctuating lift on a circular cylinder: review and new measurements, J. Fluids Struct.17, 57 (2003)

    work page 2003

  49. [49]

    Takeuchi, Vortex Line Density in a Superfluid Tur- bulent Wake in the Zero Temperature Limit, Ann

    H. Takeuchi, Vortex Line Density in a Superfluid Tur- bulent Wake in the Zero Temperature Limit, Ann. Phys. 538, 2500270 (2025)

    work page 2025

  50. [50]

    In contrast, for a circular cylinder, Os- een’s correction [51] leads to a different scaling exponent, α≡ − d(lnC D) d(ln Re) ≃1− 1 2−ln Re <1

    For a sphere in a classical fluid at low Reynolds number, CD = 24 Re−1 [1]. In contrast, for a circular cylinder, Os- een’s correction [51] leads to a different scaling exponent, α≡ − d(lnC D) d(ln Re) ≃1− 1 2−ln Re <1

    work page

  51. [51]

    Lamb, On the uniform motion of a sphere through a 12 viscous fluid, Lond

    H. Lamb, On the uniform motion of a sphere through a 12 viscous fluid, Lond. Edinb. Dubl. Philos. Mag. J. Sci.21, 112 (1911)

    work page 1911

  52. [52]

    Cadot, Y

    O. Cadot, Y. Couder, A. Daerr, S. Douady, and A. Tsi- nober, Energy injection in closed turbulent flows: Stirring through boundary layers versus inertial stirring, Phys. Rev. E56, 427 (1997)

    work page 1997

  53. [53]

    K. P. Iyer, Turbulence without walls: whither the zeroth law of turbulence?, Phys. Rev. Lett.135, 134001 (2025)

    work page 2025

  54. [54]

    Carusotto, Bogoliubov– ˇCerenkov radiation in a Bose–Einstein condensate flowing against an obstacle, Phys

    I. Carusotto, Bogoliubov– ˇCerenkov radiation in a Bose–Einstein condensate flowing against an obstacle, Phys. Rev. Lett.97, 260403 (2006)

    work page 2006

  55. [55]

    Dutton, M

    Z. Dutton, M. Budde, C. Slowe, and L. V. Hau, Ob- servation of quantum shock waves created with ultra- compressed slow light pulses in a Bose–Einstein conden- sate, Science293, 663 (2001)

    work page 2001

  56. [56]

    H. W. Liepmann and A. Roshko,Elements of Gas dy- namics(Wiley, New York, 1957)

    work page 1957

  57. [57]

    A. M. Kamchatnov and L. P. Pitaevskii, Stabilization of solitons generated by a supersonic flow of Bose–Einstein condensate past an obstacle, Phys. Rev. Lett.100, 160402 (2008)

    work page 2008

  58. [58]

    P. A. Murthy and S. Jochim, Direct imaging of the or- der parameter of an atomic superfluid using matterwave optics, arXiv:1911.10824 [cond-mat.quant-gas]

    work page arXiv 1911

  59. [59]

    Burger, K

    S. Burger, K. Bongs, S. Dettmer, W. Ertmer, K. Sen- gstock, A. Sanpera, G. V. Shlyapnikov, and M. Lewen- stein, Dark solitons in Bose–Einstein condensates, Phys. Rev. Lett.83, 5198 (1999)

    work page 1999

  60. [60]

    Del Pace, K

    G. Del Pace, K. Xhani, A. Muzi Falconi, M. Fedrizzi, N. Grani, D. Hernandez Rajkov, M. Inguscio, F. Scazza, W. J. Kwon, and G. Roati, Imprinting persistent cur- rents in tunable fermionic rings, Phys. Rev. X12, 041037 (2022)

    work page 2022

  61. [61]

    Denschlag, J

    J. Denschlag, J. E. Simsarian, D. L. Feder, C. W. Clark, L. A. Collins, J. Cubizolles, L. Deng, E. W. Ha- gley, K. Helmerson, W. P. Reinhardt, S. L. Rolston, B. I. Schneider, and W. D. Phillips, Generating solitons by phase engineering of a Bose–Einstein condensate, Sci- ence287, 97 (2000)

    work page 2000

  62. [62]

    C.-T. Pham, C. Nore, and M.-E. Brachet, Boundary lay- ers in Gross–Pitaevskii superflow around a disk, C. R. Phys.5, 3 (2004)

    work page 2004

  63. [63]

    Far downstream of the obstacle, the vorticity width was found to scale as √s, wheresis the distance from the ob- stacle, consistent with the 2D classical wake-width scal- ing [11]

    work page