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Khan MAI, Respondek M, Kjellström S, Deep S, Linse S, Akke M. Cu/Zn Superoxide Dismutase Forms Amyloid Fibrils under Near-Physiological Quiescent Conditions: The Roles of Disulfide Bonds and Effects of Denaturant. ACS Chem Neurosci 2017; 8:2019-2026. [PMID: 28585802 DOI: 10.1021/acschemneuro.7b00162] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Abstract
Cu/Zn superoxide dismutase (SOD1) forms intracellular aggregates that are pathological indicators of amyotrophic lateral sclerosis. A large body of research indicates that the entry point to aggregate formation is a monomeric, metal-ion free (apo), and disulfide-reduced species. Fibril formation by SOD1 in vitro has typically been reported only for harsh solvent conditions or mechanical agitation. Here we show that monomeric apo-SOD1 in the disulfide-reduced state forms fibrillar aggregates under near-physiological quiescent conditions. Monomeric apo-SOD1 with an intact intramolecular disulfide bond is highly resistant to aggregation under the same conditions. A cysteine-free variant of SOD1 exhibits fibrillization behavior and fibril morphology identical to those of disulfide-reduced SOD1, firmly establishing that intermolecular disulfide bonds or intramolecular disulfide shuffling are not required for aggregation and fibril formation. The decreased lag time for fibril formation resulting from reduction of the intramolecular disulfide bond thus primarily reflects the decreased stability of the folded state relative to partially unfolded states, rather than an active role of free sulfhydryl groups in mediating aggregation. Addition of urea to increase the amount of fully unfolded SOD1 increases the lag time for fibril formation, indicating that the population of this species does not dominate over other factors in determining the onset of aggregation. Our results contrast with previous results obtained for agitated samples, in which case amyloid formation was accelerated by denaturant. We reconcile these observations by suggesting that denaturants destabilize monomeric and aggregated species to different extents and thus affect nucleation and growth.
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Affiliation(s)
- M. Ashhar I. Khan
- Biophysical
Chemistry, Center for Molecular Protein Science, Department of Chemistry, Lund University, 221 00 Lund, Sweden
- Department
of Chemistry, Indian Institute of Technology Delhi, New Delhi 110016, India
| | - Michal Respondek
- Biophysical
Chemistry, Center for Molecular Protein Science, Department of Chemistry, Lund University, 221 00 Lund, Sweden
| | - Sven Kjellström
- Biochemistry and Structural
Biology,
Center for Molecular Protein Science, Department of Chemistry, Lund University, 221 00 Lund, Sweden
| | - Shashank Deep
- Department
of Chemistry, Indian Institute of Technology Delhi, New Delhi 110016, India
| | - Sara Linse
- Biochemistry and Structural
Biology,
Center for Molecular Protein Science, Department of Chemistry, Lund University, 221 00 Lund, Sweden
| | - Mikael Akke
- Biophysical
Chemistry, Center for Molecular Protein Science, Department of Chemistry, Lund University, 221 00 Lund, Sweden
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Khan MAI, Ali MA, Monsur MA, Kawasaki-Tanaka A, Hayashi N, Yanagihara S, Obara M, Mia MAT, Latif MA, Fukuta Y. Diversity and Distribution of Rice Blast (Pyricularia oryzae Cavara) Races in Bangladesh. Plant Dis 2016; 100:2025-2033. [PMID: 30683013 DOI: 10.1094/pdis-12-15-1486-re] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
The pathogenicity of 331 blast isolates (Pyricularia oryzae Cavara) collected from different regions and ecosystems for rice cultivation in Bangladesh was evaluated by compatibility on 23 differential varieties (DV), each harboring a single blast resistance gene, and susceptible 'Lijiangxintuanheigu' (LTH). A wide variation in virulence was found among the isolates, and 267 races were classified using a new designation system. Virulence of blast isolates against DV carrying the resistance genes Pia, Pib, Pit, Pik-s, Piz-t, Pi12(t), Pi19(t), and Pi20(t), as well as avirulence against those carrying Pish, Pi9, Pita-2, and Pita, was distributed widely in Bangladesh. Cluster analysis of the compatibility data on the DV initially classified the isolates into groups I and II. The virulence spectra of the two groups differed mainly according to the reactions of the DV to Pii, Pi3, Pi5(t), Pik-m, Pi1, Pik-h, Pik, Pik-p, and Pi7(t). Group I isolates were distributed mainly in rainfed lowlands, whereas group II isolates were found mainly in irrigated lowlands; however, there were no critical differences in geographic distribution of the blast isolates. In total, 26 isolates, which could be used to identify the 23 resistance genes of the DV on the basis of their reaction patterns, were selected as a set of standard differential blast isolates. To our knowledge, this is the first clear demonstration of the diversity and differentiation of blast races in Bangladesh. This information will be used to develop a durable blast protection system in that country.
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Affiliation(s)
- M A I Khan
- Bangladesh Rice Research Institute, Gazipur-1701, Bangladesh
| | - M A Ali
- Bangladesh Rice Research Institute, Gazipur-1701, Bangladesh
| | - M A Monsur
- Bangladesh Rice Research Institute, Gazipur-1701, Bangladesh
| | - A Kawasaki-Tanaka
- Tottori University, 4-101 Koyama-Minami Tottori, Tottori 680-8553, Japan
| | - N Hayashi
- National Institute of Agrobiological Sciences, 2-1-2 Kannondai, Tsukuba, Ibaraki, 305-8602, Japan
| | - S Yanagihara
- Japan International Research Center for Agricultural Sciences, 1-1, Ohwashi, Tsukuba, Ibaraki 305-8686, Japan
| | - M Obara
- Japan International Research Center for Agricultural Sciences, 1-1, Ohwashi, Tsukuba, Ibaraki 305-8686, Japan
| | | | | | - Y Fukuta
- Tropical Agriculture Research Front, Japan International Research Center Agricultural Sciences, 1091-1, Kawarabaru, Aza Maezato, Ishigaki, Okinawa 907-0002, Japan
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Hannan MA, Chowdhury MTH, Khan MAI, Chowdhury AFMA, Shahidullah KM, Saha AK, Anjum A. Prevalence of Gingivitis, Plaque accumulation and Decayed, Missing and Filled Teeth among slum population in Bangladesh. Bangladesh Med Res Counc Bull 2015; 40:47-51. [PMID: 26415339 DOI: 10.3329/bmrcb.v40i2.25182] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
Abstract
A cross-sectional survey, using cluster sampling technique, of slum population, was done to explore the oral health status and the prevalence of common oral diseases. A close ended questionnaire comprising Decayed, Missing and Filled Teeth (DMFT) Index, Gingival Index (Löe and Silness) and Plaque Index was applied to evaluate and record oral diseases, in both male and female population, covering a wide range of age groups. Clinical examination was carried out in different slum set ups, including slum schools by trained and calibrated examiners. Three thousand nine hundred and four (3904) slum dwellers participated in the survey. Prevalence of Caries was expressed in mean DMFT, recording of gingival status followed the method of Löe and Silness, oral hygiene status was evaluated using Plaque index. Mean decayed component, of the DMFT, was significantly higher than filling and missing component. Both decayed and missing components showed increasing trend, and filling components decreased as the age progressed. Prevalence of gingivitis and plaque accumulation was remarkably high among slum dwellers. Significantly high level of common oral diseases was found among Tongi slum dwellers.Bangladesh Med Res Counc Bull 2014; 40 (2): 47-51
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Wallerstein J, Weininger U, Khan MAI, Linse S, Akke M. Site-specific protonation kinetics of acidic side chains in proteins determined by pH-dependent carboxyl (13)C NMR relaxation. J Am Chem Soc 2015; 137:3093-101. [PMID: 25665463 DOI: 10.1021/ja513205s] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Proton-transfer dynamics plays a critical role in many biochemical processes, such as proton pumping across membranes and enzyme catalysis. The large majority of enzymes utilize acid-base catalysis and proton-transfer mechanisms, where the rates of proton transfer can be rate limiting for the overall reaction. However, measurement of proton-exchange kinetics for individual side-chain carboxyl groups in proteins has been achieved in only a handful of cases, which typically have involved comparative analysis of mutant proteins in the context of reaction network modeling. Here we describe an approach to determine site-specific protonation and deprotonation rate constants (kon and koff, respectively) of carboxyl side chains, based on (13)C NMR relaxation measurements as a function of pH. We validated the method using an extensively studied model system, the B1 domain of protein G, for which we measured rate constants koff in the range (0.1-3) × 10(6) s(-1) and kon in the range (0.6-300) × 10(9) M(-1) s(-1), which correspond to acid-base equilibrium dissociation constants (Ka) in excellent agreement with previous results determined by chemical shift titrations. Our results further reveal a linear free-energy relationship between log kon and pKa, which provides information on the free-energy landscape of the protonation reaction, showing that the variability among residues in these parameters arises primarily from the extent of charge stabilization of the deprotonated state by the protein environment. We find that side-chain carboxyls with extreme values of koff or kon are involved in hydrogen bonding, thus providing a mechanistic explanation for the observed stabilization of the protonated or deprotonated state.
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Affiliation(s)
- Johan Wallerstein
- Department of Biophysical Chemistry and ‡Department of Biochemistry and Structural Biology, Center for Molecular Protein Science, Lund University , P.O. Box 124, SE-221 00 Lund, Sweden
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Bhatia NK, Srivastava A, Katyal N, Jain N, Khan MAI, Kundu B, Deep S. Curcumin binds to the pre-fibrillar aggregates of Cu/Zn superoxide dismutase (SOD1) and alters its amyloidogenic pathway resulting in reduced cytotoxicity. Biochim Biophys Acta 2015; 1854:426-36. [PMID: 25666897 DOI: 10.1016/j.bbapap.2015.01.014] [Citation(s) in RCA: 92] [Impact Index Per Article: 10.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2014] [Revised: 12/25/2014] [Accepted: 01/31/2015] [Indexed: 12/13/2022]
Abstract
Amyotrophic Lateral Sclerosis (ALS) is a fatal neurodegenerative disease that affects motor neurons. Unfortunately, effective therapeutics against this disease is still not available. Almost 20% of familial ALS (fALS) is suggested to be associated with pathological deposition of superoxide dismutase (SOD1). Evidences suggest that SOD1-containing pathological inclusions in ALS exhibit amyloid like properties. An effective strategy to combat ALS may be to inhibit amyloid formation of SOD1 using small molecules. In the present study, we observed the fibrillation of one of the premature forms of SOD1 (SOD1 with reduced disulfide) in the presence of curcumin. Using ThT binding assay, AFM, TEM images and FTIR, we demonstrate that curcumin inhibits the DTT-induced fibrillation of SOD1 and favors the formation of smaller and disordered aggregates of SOD1. The enhancement in curcumin fluorescence on the addition of oligomers and pre-fibrillar aggregates of SOD1 suggests binding of these species to curcumin. Docking studies indicate that putative binding site of curcumin may be the amyloidogenic regions of SOD1. Further, there is a significant increase in SOD1 mediated toxicity in the regime of pre-fibrillar and fibrillar aggregates which is not evident in curcumin containing samples. All these data suggest that curcumin reduces toxicity by binding to the amyloidogenic regions of the species on the aggregation pathway and blocking the formation of the toxic species. Nanoparticles of curcumin with higher aqueous solubility show similar aggregation control as that of curcumin bulk. This suggests a potential role for curcumin in the treatment of ALS.
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Affiliation(s)
- Nidhi K Bhatia
- Department of Chemistry, Indian Institute of Technology, Delhi, Hauz Khas, New Delhi, India
| | - Ankit Srivastava
- Kusuma School of Biological Sciences, Indian Institute of Technology, Delhi, Hauz Khas, New Delhi, India
| | - Nidhi Katyal
- Department of Chemistry, Indian Institute of Technology, Delhi, Hauz Khas, New Delhi, India
| | - Nidhi Jain
- Department of Chemistry, Indian Institute of Technology, Delhi, Hauz Khas, New Delhi, India
| | - M Ashhar I Khan
- Department of Chemistry, Indian Institute of Technology, Delhi, Hauz Khas, New Delhi, India
| | - Bishwajit Kundu
- Kusuma School of Biological Sciences, Indian Institute of Technology, Delhi, Hauz Khas, New Delhi, India
| | - Shashank Deep
- Department of Chemistry, Indian Institute of Technology, Delhi, Hauz Khas, New Delhi, India.
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Saini K, Khan MAI, Chakrapani S, Deep S. Transforming growth factor receptor type II (ec-TβR II) behaves as a halophile. Int J Biol Macromol 2014; 72:1104-10. [PMID: 25316422 DOI: 10.1016/j.ijbiomac.2014.09.051] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2014] [Revised: 09/25/2014] [Accepted: 09/27/2014] [Indexed: 11/17/2022]
Abstract
The members of transforming growth factor β family (TGF-β) are multifunctional proteins but their main role is to control cell proliferation and differentiation. Polypeptides of TGF-β family function by binding to two related, functionally distinct transmembrane receptor kinases, first to the type II (TβR II) followed by type I receptor (TβR I). The paper describes, in details, the stability of wt-ec-TβR II under different conditions. The stability of wt-ec-TβR II was observed at different pH and salt concentration using fluorescence spectroscopy. Stability of ec-TβR II decreases with decrease in pH. Interestingly, the addition of salt increases the stability of the TβRII at pH 5.0 as observed for halophiles. Computational analysis using DELPHI suggests that this is probably due to the decrease in repulsion between negatively charged residues at surface on the addition of salt. This is further confirmed by the change in the stability of receptor on mutation of some of the residues (D32A) at surface.
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Pradhan S, Naik SN, Khan MAI, Sahoo PK. Experimental assessment of toxic phytochemicals in Jatropha curcas: oil, cake, bio-diesel and glycerol. J Sci Food Agric 2012; 92:511-9. [PMID: 21993892 DOI: 10.1002/jsfa.4599] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/14/2011] [Revised: 07/05/2011] [Accepted: 07/08/2011] [Indexed: 05/20/2023]
Abstract
BACKGROUND Jatropha curcas seed is a rich source of oil; however, it can not be utilised for nutritional purposes due to presence of toxic and anti-nutritive compounds. The main objective of the present study was to quantify the toxic phytochemicals present in Indian J. curcas (oil, cake, bio-diesel and glycerol). RESULTS The amount of phorbol esters is greater in solvent extracted oil (2.8 g kg⁻¹) than in expeller oil (2.1 g kg⁻¹). Liquid chromatography-mass spectroscopy analysis of the purified compound from an active extract of oil confirmed the presence of phorbol esters. Similarly, the phorbol esters content is greater in solvent extracted cake (1.1 g kg⁻¹) than in cake after being expelled (0.8 g kg⁻¹). The phytate and trypsin inhibitory activity of the cake was found to be 98 g kg⁻¹ and 8347 TIU g⁻¹ of cake, respectively. Identification of curcin was achieved by sodium dodecyl sulfate-polyacrylamide gel electrophoresis and the concentration of curcin was 0.95 g L⁻¹ of crude concentrate obtained from cake. CONCLUSION Higher amounts of phorbol esters are present in oil than cake but bio-diesel and glycerol are free of phorbol esters. The other anti-nutritional components such as trypsin inhibitors, phytates and curcin are present in cake, so the cake should be detoxified before being used for animal feed.
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Affiliation(s)
- Subhalaxmi Pradhan
- Centre for Rural Development and Technology, Indian Institute of Technology, Delhi, Hauz Khas, New Delhi-110016, India
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Hewitt RE, Mullin T, Tavener SJ, Khan MAI, Treacher PD. Nonlinear vortex development in rotating flows. Philos Trans A Math Phys Eng Sci 2008; 366:1317-1329. [PMID: 17984036 DOI: 10.1098/rsta.2007.2133] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
We present the results of a combined experimental and numerical investigation into steady secondary vortex flows confined between two concentric right circular cylinders. When the flow is driven by the symmetric rotation of both end walls and the inner cylinder, toroidal vortex structures arise through the creation of stagnation points (in the meridional plane) at the inner bounding cylinder or on the mid-plane of symmetry. A detailed description of the flow regimes is presented, suggesting that a cascade of such vortices can be created. Experimental results are reported, which visualize some of the new states and confirm the prediction that they are stable to (mid-plane) symmetry-breaking perturbations. We also present some brief results for the flows driven by the rotation of a single end wall. Vortex structures may also be observed at low Reynolds numbers in this geometry. We show that standard flow visualization methods lead to some interesting non-axisymmetric particle paths in this case.
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Affiliation(s)
- R E Hewitt
- Manchester Centre for Nonlinear Dynamics, University of Manchester, Oxford Road, Manchester M13 9PL, UK.
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Abstract
Medical thoracoscopy is a valuable tool in the investigation and management of pleural disease. It has considerable advantages over conventional blind pleural biopsy and video-assisted thoracoscopic surgery. Despite this, the practice of this technique in the UK is limited. Most operators use the rigid thoracoscope, which may be an unfamiliar instrument to respiratory physicians. A semirigid thoracoscope is available but its use has not been possible in the UK as it requires sterilisation with ethylene oxide, which is not approved in this country. The present authors describe herein their experience with the first ever autoclavable semirigid thoracoscope. Medical thoracoscopy using the new instrument was performed in 56 patients between June 2004 and May 2006. All patients had been referred with a unilateral pleural effusion of unknown aetiology, where blind pleural aspiration had failed to yield an answer. Diagnostic samples were taken and talc poudrage performed where appropriate. The instrument was easy to handle and excellent views were obtained. Histologically adequate biopsy samples were obtained in 54 patients. The combination of clinical features, computed tomography findings and thoracoscopic biopsy enabled a definite diagnosis in 49 (90.7%) of these patients. There were no complications. The autoclavable semirigid thoracoscope has immense potential in the diagnosis and management of pleural disease. Its diagnostic yield in pleural disease is comparable to the conventional rigid thoracoscope. It is similar in design to the fibreoptic bronchoscope and respiratory physicians should be able to adapt to its use easily. It is also compatible with existing video processors and light sources available in most endoscopy suites. The fact that this instrument is autoclavable should open the field for its use in the UK as well as in other countries.
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Affiliation(s)
- M Munavvar
- Dept of Respiratory Medicine, Lancashire Teaching Hospitals NHS Trust, Royal Preston Hospital, Fulwood, Preston PR2 9HT, UK.
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Hannan MA, Shahidullah KM, Khan MAI, Anjum A. Role of nutrition in common dental diseases in rural Bangladesh. Bangladesh Med Res Counc Bull 2006; 32:55-9. [PMID: 17663361] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Subscribe] [Scholar Register] [Indexed: 05/16/2023]
Abstract
A cross-sectional study was performed to evaluate whether dietary intake and nutrition contribute to the aetiology of common dental diseases in rural Bangladesh. Study subjects were selected following multi-staged stratified random sampling procedure. A total of 300 people of both sexes were included in the study with age ranging from 12-40 years. Data were collected for demographic and socio-economic condition, oral hygiene and related knowledge, dietary consumption, history and clinical findings. The study subjects were categorized as adequate nutrient and undernutrient by dichotomy based on their needed intake and the quality of diet consumed. The results showed that only 19% of the subjects had fulfilled their required intake and the rest were undernutrient. The results also showed that about 93% of the subjects were disease positive. The results between dietary intake and prevalence of diseases were statistically significant (p<0.05). From the findings of the study, it was concluded that low income, poor dietary intake, poor oral and general health may be jointly associated with higher prevalence of dental diseases in the rural community.
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Affiliation(s)
- M A Hannan
- Deptt. of children, preventive and Community Dentistry, Sapporo Dental College and Hospital, Uttara, Dhaka
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Khan MAI. Non-European doctors and change in UK policy: change is cruel and opportunistic. BMJ 2006; 332:914. [PMID: 16613976 PMCID: PMC1440657 DOI: 10.1136/bmj.332.7546.914-a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/04/2022]
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Khan MAI, Pumir A, Vassilicos JC. Kinematic simulation of turbulent dispersion of triangles. Phys Rev E Stat Nonlin Soft Matter Phys 2003; 68:026313. [PMID: 14525111 DOI: 10.1103/physreve.68.026313] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/06/2003] [Indexed: 05/24/2023]
Abstract
As three particles are advected by a turbulent flow, they separate from each other and develop nontrivial geometries, which effectively reflect the structure of the turbulence. We investigate here the geometry, in a statistical sense, of three Lagrangian particles advected, in two dimensions, by kinematic simulation (KS). KS is a Lagrangian model of turbulent diffusion that makes no use of any delta correlation in time at any level. With this approach, situations with a very large range of inertial scales and varying persistence of spatial flow structure can be studied. We first demonstrate that the model flow reproduces recent experimental results at low Reynolds numbers. The statistical properties of the shape distribution at a much higher Reynolds number is then considered. The numerical results support the existence of nontrivial shape statistics, with a high probability of having elongated triangles. Even at the highest available inertial range of scales, corresponding to a ratio between large and small scale L/eta=17,000, a perfect self-similar regime is not found. The effects of the parameters of the synthetic flow, such as the exponent of the spectrum and the effect of the sweeping affect our results, are also discussed. Special attention is given to the effects of persistence of spatial flow structure.
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Affiliation(s)
- M A I Khan
- DAMTP, University of Cambridge, Silver Street, Cambridge CB3 9EW, United Kingdom.
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Khan MAI, Vassilicos JC. Scalings of scalar structure functions in a velocity field with coherent vortical structures. Phys Rev E Stat Nonlin Soft Matter Phys 2002; 65:016304. [PMID: 11800781 DOI: 10.1103/physreve.65.016304] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/17/2000] [Revised: 09/13/2001] [Indexed: 05/23/2023]
Abstract
In planar turbulence modeled as an isotropic and homogeneous collection of two-dimensional noninteracting compact vortices, the structure functions S(p)(r) of a statistically stationary passive scalar field have the following scaling behavior in the limit where the Péclet number Pe-->infinity: S(p)(r) approximately const+ln(r/L Pe(-1/3)) for L Pe(-1/3)<<r<<L, S(p)(r) approximately (r/L Pe(-1/3))(6(1-D)) for L Pe(-1/2)<<r<<L Pe(-1/3), where L is a large scale and D is the fractal codimension of the spiral scalar structures generated by the vortices (1/2 < or =D < 2/3). Note that L Pe(-1/2) is the scalar Taylor microscale that stems naturally from our analytical treatment of the advection-diffusion equation. The essential ingredients of our theory are the locality of interscale transfer and Lundgren's time average assumption. A phenomenological theory explicitly based only on these two ingredients reproduces our results and a generalization of this phenomenology to spatially smooth chaotic flows yields (k ln k)(-1) generalized power spectra for the advected scalar fields.
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Affiliation(s)
- M A I Khan
- Department of Applied Mathematics and Theoretical Physics, Silver Street, University of Cambridge, Cambridge CB3 9EW, United Kingdom
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