The DOI matches its Crossref record; 11 of the 11 references it cites were found in a registry or an index.
Camassa-Holm Equations as a Closure Model for Turbulent Channel and Pipe Flow
Open accessAbstract
We propose the viscous Camassa-Holm equations as a closure approximation for the Reynolds-averaged equations of the incompressible Navier-Stokes fluid. This approximation is tested on turbulent channel and pipe flows with steady mean. Analytical solutions for the mean velocity and the Reynolds shear stress are consistent with experiments in most of the flow region.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Handbook of Mathematical Functions
McQuarrie, D. A. (1966) · American Journal of Physics · doi:10.1119/1.1972842 · Cited by 40,433
Turbulence statistics in fully developed channel flow at low Reynolds number
Kim, J., Moin, P., & Moser, R. (1987) · Journal of Fluid Mechanics · doi:10.1017/s0022112087000892 · Cited by 4,873
An integrable shallow water equation with peaked solitons
Camassa, R., & Holm, D. D. (1993) · Physical Review Letters · doi:10.1103/physrevlett.71.1661 · Cited by 3,624
Self-citationLandau, L. D., Lifshitz, E. M., Sykes, J. B., Reid, W. H., & Feshbach, H. (1961) · Physics Today · doi:10.1063/1.3057567 · Cited by 786
The structure of the viscous sublayer and the adjacent wall region in a turbulent channel flow
Eckelmann, H. (1974) · Journal of Fluid Mechanics · doi:10.1017/s0022112074001479 · Cited by 405
A new Reynolds stress algebraic equation model
Shih, T. H., Zhu, J., & Lumley, J. L. (1995) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/0045-7825(95)00796-4 · Cited by 311
Euler-Poincaré Models of Ideal Fluids with Nonlinear Dispersion
Holm, D. D., Marsden, J. E., & Ratiu, T. S. (1998) · Physical Review Letters · doi:10.1103/physrevlett.80.4173 · Cited by 292
Self-citationLow-Reynolds-number effects in a fully developed turbulent channel flow
Antonia, R. A., Teitel, M., Kim, J., & Browne, L. W. B. (1992) · Journal of Fluid Mechanics · doi:10.1017/s002211209200154x · Cited by 221
Nonlinear Reynolds stress models and the renormalization group
Rubinstein, R., & Barton, J. M. (1990) · Physics of Fluids A: Fluid Dynamics · doi:10.1063/1.857595 · Cited by 204
Messungen turbulenter Schwankungen
Reichardt, H. (1938) · Die Naturwissenschaften · doi:10.1007/bf01772950 · Cited by 71
Metadata
- Authors
- Chen, S., Foias, C., Holm, D. D., Olson, E., Titi, E. S., & Wynne, S.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1998-12-14
- Volume
- 81
- Issue
- 24
- Pages
- 5338-5341
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2001944648
- Cited by
- 347
- References
- 11
- FWCI
- 9.89
- Type
- journal article
- Language
- en
- Open access
- green
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Camassa-Holm Equations as a Closure Model for Turbulent Channel and Pipe Flow. https://app.cochat.ai/papers/10.1103/physrevlett.81.5338
- The paper
- Chen, S., Foias, C., Holm, D. D., Olson, E., Titi, E. S., & Wynne, S. (1998). Camassa-Holm Equations as a Closure Model for Turbulent Channel and Pipe Flow. Physical Review Letters. https://doi.org/10.1103/physrevlett.81.5338
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
