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The improvement of next-generation sequencing technologies has promoted the field of immunogenetics and produced numerous immunogenomics data. Modern data-driven research has the power to promote novel biomedical discoveries through secondary analysis of such data. Therefore, it is important to ensure data-driven research with great reproducibility and robustness for promoting a precise and accurate secondary analysis of the immunogenomics data. In scientific research, rigorous conduct in designing and conducting experiments is needed, specifically in scientific and articulate writing, reporting and interpreting results. It is also crucial to make raw data available, discoverable, and well described or annotated in order to promote future re-analysis of the data. In order to assess the data availability of published T cell receptor (TCR) repertoire data, we examined 11,918 TCR-Seq samples corresponding to 134 TCR-Seq studies ranging from 2006 to 2022. Among the 134 studies, only 38.1% had publicly available raw TCR-Seq data shared in public repositories. We also found a statistically significant association between the presence of data availability statements and the increase in raw data availability (p=0.014). Yet, 46.8% of studies with data availability statements failed to share the raw TCR-Seq data. There is a pressing need for the biomedical community to increase awareness of the importance of promoting raw data availability in scientific research and take immediate action to improve its raw data availability enabling cost-effective secondary analysis of existing immunogenomics data by the larger scientific community.

The ability to identify and track T cell receptor (TCR) sequences from patient samples is becoming central to the field of cancer research and immunotherapy. Tracking genetically engineered T cells expressing TCRs that target specific tumor antigens is important to determine the persistence of these cells and quantify tumor responses. The available high-throughput method to profile T cell receptor repertoires is generally referred to as TCR sequencing (TCR-Seq). However, the available TCR-Seq data is limited compared to RNA sequencing (RNA-Seq). In this paper, we have benchmarked the ability of RNA-Seq-based methods to profile TCR repertoires by examining 19 bulk RNA-Seq samples across four cancer cohorts including both T cell rich and poor tissue types. We have performed a comprehensive evaluation of the existing RNA-Seq-based repertoire profiling methods using targeted TCR-Seq as the gold standard. We also highlighted scenarios under which the RNA-Seq approach is suitable and can provide comparable accuracy to the TCR-Seq approach. Our results show that RNA-Seq-based methods are able to effectively capture the clonotypes and estimate the diversity of TCR repertoires, as well as to provide relative frequencies of clonotypes in T cell rich tissues and monoclonal repertoires. However, RNA-Seq-based TCR profiling methods have limited power in T cell poor tissues, especially in polyclonal repertoires of T cell poor tissues. The results of our benchmarking provide an additional appealing argument to incorporate the RNA-Seq into immune repertoire screening of cancer patients as it offers broader knowledge into the transcriptomic changes that exceed the limited information provided by TCR-Seq.

The scientific community has accumulated enormous amounts of genomic data stored in specialized public repositories. Genomic data is easily accessible and available from public genomic repositories allowing the biomedical community to effectively share the omics datasets. However, improperly annotated or incomplete metadata accompanying the raw omics data can negatively impact the utility of shared data for secondary analysis. In this study, we perform a comprehensive analysis under 137 studies over 18,559 samples across six therapeutics fields to assess the completeness of metadata accompanying omics studies in both publication and its related online repositories across and make observations about how the process of data sharing could be made reliable. This analysis involved finding studies based on the six therapeutic fields, that are Alzheimer’s disease, acute myeloid leukemia, cystic fibrosis, cardiovascular diseases, inflammatory bowel disease, sepsis, and tuberculosis. We carefully examined the availability of metadata over nine clinical variables, that included disease condition, age, organism, sex, tissue type, ethnicity, country, mortality, and clinical severity. By comparing the metadata availability in both original publications and online repositories, we observed discrepancies in sharing the metadata. We determine that the overall availability of metadata is 72.8%, where the most complete reported phenotypes are disease condition and organism, and the least is mortality. Additionally, we examined the completeness of metadata reported separately in original publications and online repositories. The completeness of metadata from the original publication across the nine clinical phenotypes is 71.1%. In contrast, the overall completeness of metadata information from the public repositories is 48.6%. Our study is the first one to systematically assess the completeness of metadata accompanying raw data across a large number of studies and phenotypes and opens a crucial discussion about solutions to improve completeness and accessibility of metadata accompanying omics studies.

To quickly and accurately measure psychological well-being has been a challenging task. Traditionally, this is done with self-report surveys, which can be time-consuming and burdensome. In this work, we demonstrate the use of short voice recordings on smartphones to automatically predict well-being. In a 5-day study, 35 participants used their smartphones to make short voice recordings of what they were doing throughout the day. Using these recordings, our model can predict the participants’ well-being scores with a mean absolute error of 14%, relative to the self-reported well-being (“ground truth”). Both audio and text features from the recordings, especially, MFCC and semantic features, are important for prediction accuracy. Based on the work, we provide suggestions for future research to further improve the prediction result.

Recent advancement from low-throughput sequencing techniques to high-throughput sequencing gives the public more efficient ways to acquire human adaptive immune receptor repertoire sequences (AIRR-seq). The advanced high-throughput sequencing techniques allow scientists to comprehensively examine and characterize the T cell receptors’ and B cell receptors’ genetic sequences efficiently. The development of multi-powerful platforms in AIRR-seq studies and advanced bioinformatic tools also boosts the AIRR community’s richness. However, although high-throughput sequencing technologies have been well-developed, most AIRR-seq studies have not taken ancestries or populations in their research into consideration. In the study, we investigate the ancestry distribution in the T cell receptor sequencing(TCR-seq) studies to initial estimate the ancestry distribution in the open AIRR-seq studies. The result disclosed that 84.08% of the studies with reported ancestries are conducted under European ancestries, which omit other populational ancestries’ diversity in the open TCR-Seq studies.

Replication of the genotype 2 hepatitis C virus (HCV) requires hyper-phosphorylation of the nonstructural protein NS5A. It has been known that NS5A hyper-phosphorylation results from the phosphorylation of a cluster of highly conserved serine residues (S2201, S2208, S2211, and S2214) in a sequential manner. It has also been known that NS5A hyper-phosphorylation requires an NS3 protease encoded on one single NS3-5A polyprotein. It was unknown whether NS3 protease participates in the above sequential phosphorylation process. Using an inventory of antibodies specific to S2201, S2208, S2211, and S2214 phosphorylation, we found that protease-dead S1169A mutation abrogated NS5A hyper-phosphorylation and phosphorylation at all serine residues measured, consistent with the role of NS3 in NS5A sequential phosphorylation. These effects were not rescued by a wildtype NS3 protease provided in trans by another molecule. Mutations (T1661R, T1661Y, or T1661D) that prohibited proper cleavage at the NS3-4A junction, too, abolished NS5A hyper-phosphorylation and phosphorylation at all serine residues, whereas mutations at the other cleavage sites, NS4A-4B (C1715S) or NS4B-5A (C1976F), did not. In fact, any combinatory mutations that prohibited NS3-4A cleavage (T1661Y/C1715S or T1661Y/C1976F) abrogated NS5A hyper-phosphorylation and phosphorylation at all serine residues. In the C1715S/C1976F double mutant that resulted in an NS4A-NS4B-NS5A fusion polyprotein, a hyper-phosphorylated band was observed and was phosphorylated at all serine residues. We conclude that NS3-mediated auto-cleavage at the NS3-4A junction is critical to NS5A hyper-phosphorylation at S2201, S2208, S2211, and S2214 and that NS5A hyper-phosphorylation could occur in an NS4A-NS4B-NS5A polyprotein.Importance For twenty some years, the HCV protease NS3 was implicated in NS5A hyper-phosphorylation. We now show that it was the NS3-mediated cis-cleavage at the NS3-4A junction that permits NS5A hyper-phosphorylation at serine 2201, 2208, 2211, and 2214, leading to hyper-phosphorylation, which is a necessary condition for genotype 2 HCV replication. We further show that NS5A may already be phosphorylated at the above serine residues right after NS3-4A cleavage and before NS5A was released from the NS4A-5A polyprotein. Our data suggest that the dual functional NS3, a protease and an ATP-binding RNA helicase, could have a direct or indirect role in NS5A hyper-phosphorylation.

The spiked-helmet sign is a marker for high mortality in critical patients. It is characterised as a dome-shaped ST-segment elevation accompanied by an upward shift of the baseline before the onset of the QRS complex. We present two patients with the spiked-helmet sign on electrocardiogram. Patient A showed a potential relationship between the spiked-helmet sign and hyper-osmolar hyper-glycaemic state, whereas patient B had clinically suspected viral myocarditis.

A 36-year-old woman who presented with upper limb distal weakness since the age of 15 years, with gradual progression to the lower limbs, is reported. Hereditary motor neuropathy was initially suspected based on distal weakness and hyporeflexia; however, whole exome sequencing accidentally revealed a compound heterozygous variant in the GNE gene, and ultrasound revealed increased homogeneous echogenicity in the involved muscles, which is characteristic of myopathic changes. Muscle magnetic resonance imaging revealed fatty infiltration in all limb muscles, sparing the triceps brachii, vastus lateralis and vastus medialis. Muscle biopsy revealed intracytoplasmic rimmed vacuole, supporting the diagnosis of GNE myopathy.

Objective: Total knee arthroplasty (TKA) is usually associated with moderate-to-severe postoperative pain. Our study investigated the possible benefits of the use of nerve blocks (NBs), including pain score reduction, the rescuing dosage of morphine, the timing of ambulation, and the length of stay (LOS) in the hospital. Materials and Methods: We included patients who underwent unilateral primary TKA due to primary knee osteoarthritis under general anesthesia with laryngeal mask airway. The control group only received oral pain medication with rescuing morphine injections, whereas the NB group received oral pain medication with an NB and rescuing morphine injections. We collected data on the patients' basic characteristics, postoperative visual analog scale (VAS), the dosage of rescuing morphine over 3 days, time to ambulation, and LOS in the hospital. Results: The NB group received significantly fewer morphine dose compared with the control group during postoperative days 1 to 3. There were no statistically significant differences between the NB and control groups on days 1 and 2 in the VAS score, and the VAS score was significantly lower in the NB group on postoperative day 3. The NB group had a significantly shorter time to ambulation compared with the control group. LOS did not differ significantly between the NB and control groups. Conclusion: Patients, who underwent TKA under general anesthesia with laryngeal mask airway (LMAGA) receiving NB for postoperative pain, needed less dosage of morphine and had the trend of having lower VAS. There was no association with LOS between two groups, but time to ambulation might be decreased with NB group. Some limitations might need to be further investigated in future study, such as NB regimens, knee function after TKA, muscle power, information after discharge, and NB-related complications.

Background: The smartphone-based whole slide imaging (WSI) system represents a low-cost and effective alternative to automatic scanners for telepathology. In a previous study, the development of one such solution, named scalable whole slide imaging (sWSI), was presented and analyzed. A clinical evaluation of its iOS version with 100 frozen section samples verified the diagnosis-readiness of the produced virtual slides. Objective: The first aim of this study was to delve into the quantifying issues encountered in the development of an Android version. It should also provide insights into future high-resolution real-time feedback medical imaging apps on Android and invoke the awareness of smartphone manufacturers for collaboration. The second aim of this study was to further verify the clinical value of sWSI with cytology samples. This type is different from the frozen section samples in that they require finer detail on the cellular level. Methods: During sWSI development on Android, it was discovered that many models do not support uncompressed camera pixel data with sufficient resolution and full field of view. The proportion of models supporting the optimal format was estimated in a test on 200 mainstream Android models. Other factors, including slower processing speed and camera preview freezing, also led to inferior performance of sWSI on Android compared with the iOS version. The processing speed was mostly determined by the central processing unit frequency in theory, and the relationship was investigated in the 200-model simulation experiment with physical devices. The camera preview freezing was caused by the lag between triggering photo capture and resuming preview. In the clinical evaluation, 100 ThinPrep cytology test samples covering 6 diseases were scanned with sWSI and compared against the ground truth of optical microscopy. Results: Among the tested Android models, only 3.0% (6/200) provided an optimal data format, meeting all criteria of quality and efficiency. The image-processing speed demonstrated a positive relationship with the central processing unit frequency but to a smaller degree than expected and was highly model-dependent. The virtual slides produced by sWSI on Android and iOS of ThinPrep cytology test samples achieved similar high quality. Using optical microscopy as the ground truth, pathologists made a correct diagnosis on 87.5% (175/200) of the cases with sWSI virtual slides. Depending on the sWSI version and the pathologist in charge, the kappa value varied between .70 and .82. All participating pathologists considered the quality of the sWSI virtual slides in the experiment to be adequate for routine usage. Conclusions: Limited by hardware and operating system support, the performance of sWSI on mainstream Android smartphones did not fully match the iOS version. However, in practice, this difference was not significant, and both were adequate for digitizing most of the sample types for telepathology consultation. [JMIR Mhealth Uhealth 2018;6(4):e82]

The purpose of this study was to explore the effects of a flipped English classroom intervention on high school students’ information and communication technology (ICT) and English reading comprehension in Taiwan. Forty 10th graders were randomly selected from a representative senior high school as an experimental group (EG) to attend a 12-h flipped English classroom intervention while another 37 10th graders were randomly selected from the same school to be the comparison group. All participants completed the high school student questionnaire that assessed students’ ICT, English reading comprehension at the beginning and end of this study. In addition, 4 target students with the lowest pretest scores on ICT from the EG were selected to be observed weekly and interviewed following the posttest. The findings showed that the EG students’ ICT, and English reading comprehension improved significantly during the intervention. The interview and observation results were consistent with the quantitative findings. Educational implications and research recommendations are discussed.

p65 is a transcription factor that is involved in many physiological and pathologic processes. Here we report that p65 strongly binds to the miR-23a-27a-24 cluster promoter to up-regulate its expression. As bone marrow-derived cells differentiate into red blood cells in vitro, p65/miR-23a-27a-24 cluster expression increases sharply and then declines before the appearance of red blood cells, suggesting that this cluster is negatively related to erythroid terminal differentiation. Bioinformatic and molecular biology experiments confirmed that the miR-23a-27a-24 cluster inhibited the expression of the erythroid proteome and contributed to erythroleukemia progression. In addition, high level of the p65/miR-23a-27a-24 cluster was found in APL and AML cell lines and in nucleated peripheral blood cells from leukemia patients. Furthermore, anti-leukemia drugs significantly inhibited the expression of the p65/miR-23a-27a-24 cluster in leukemia cells. Administration of the p65 inhibitor parthenolide significantly improved hematology and myelogram indices while prolonging the life span of erythroleukemia mice. Meanwhile, stable overexpression of these three miRNAs in mouse erythroleukemia cells enhanced cell malignancy. Our findings thus connect a novel regulation pathway of the p65/miR-23a-27a-24 cluster with the erythroid proteome and provide an applicable approach for treating leukemia.

BACKGROUND The smartphone-based whole slide imaging (WSI) system represents a low-cost and effective alternative to automatic scanners for telepathology. In a previous study, the development of one such solution, named scalable whole slide imaging (sWSI), was presented and analyzed. A clinical evaluation of its iOS version with 100 frozen section samples verified the diagnosis-readiness of the produced virtual slides. OBJECTIVE The first aim of this study was to delve into the quantifying issues encountered in the development of an Android version. It should also provide insights into future high-resolution real-time feedback medical imaging apps on Android and invoke the awareness of smartphone manufacturers for collaboration. The second aim of this study was to further verify the clinical value of sWSI with cytology samples. This type is different from the frozen section samples in that they require finer detail on the cellular level. METHODS During sWSI development on Android, it was discovered that many models do not support uncompressed camera pixel data with sufficient resolution and full field of view. The proportion of models supporting the optimal format was estimated in a test on 200 mainstream Android models. Other factors, including slower processing speed and camera preview freezing, also led to inferior performance of sWSI on Android compared with the iOS version. The processing speed was mostly determined by the central processing unit frequency in theory, and the relationship was investigated in the 200-model simulation experiment with physical devices. The camera preview freezing was caused by the lag between triggering photo capture and resuming preview. In the clinical evaluation, 100 ThinPrep cytology test samples covering 6 diseases were scanned with sWSI and compared against the ground truth of optical microscopy. RESULTS Among the tested Android models, only 3.0% (6/200) provided an optimal data format, meeting all criteria of quality and efficiency. The image-processing speed demonstrated a positive relationship with the central processing unit frequency but to a smaller degree than expected and was highly model-dependent. The virtual slides produced by sWSI on Android and iOS of ThinPrep cytology test samples achieved similar high quality. Using optical microscopy as the ground truth, pathologists made a correct diagnosis on 87.5% (175/200) of the cases with sWSI virtual slides. Depending on the sWSI version and the pathologist in charge, the kappa value varied between .70 and .82. All participating pathologists considered the quality of the sWSI virtual slides in the experiment to be adequate for routine usage. CONCLUSIONS Limited by hardware and operating system support, the performance of sWSI on mainstream Android smartphones did not fully match the iOS version. However, in practice, this difference was not significant, and both were adequate for digitizing most of the sample types for telepathology consultation.

The β-L-arabinofuranosidase (HypBA1) fromBifidobacterium longumJCM 1217 hydrolyzes the β-1,2-linked arabinofuranose disaccharide to release L-arabinoses. HypBA1 was classified into glycoside hydrolase family 127 (GH127) by the CAZy website (http://www.cazy.org/). The enzyme was expressed inEscherichia coliand the purified recombinant protein was crystallized. Crystals belonging to the primitive hexagonal space groupP3x21, with unit-cell parametersa=b= 75.9,c= 254.0 Å, were obtained by the sitting-drop vapour-diffusion method and diffracted to 2.78 Å resolution. ABLASTPsearch (http://blast.ncbi.nlm.nih.gov/) of the Protein Data Bank did not reveal any similar crystal structures. Structural determination by using SeMet MAD and MIR methods is in progress.

In this paper, we put forth a generalized Bradshaw–Richardson number BΣ, which applies to the turbulence in any arbitrary rotating frame of reference and includes as a special case its classical form defined in 1969 by Bradshaw [“The analogy between streamline curvature and buoyancy in turbulent shear flow,” J. Fluid Mech. 36, 177–191 (1969)]. We show that the physical importance of BΣ lies in the fact that it classifies the absolute mean vorticity (ω¯+2Ω) in an arbitrary rotating frame of reference into three disjoint classes and ranges from −∞ to ∞, displaying the kinematical features of the mean vorticity in relation to the rotating frame of reference. As a kinematical parameter, BΣ not only measures the mean rigid rotation effects of turbulence as the mean stretching tensor (rate of strain tensor) D¯→0 but also indicates the amount of the absolute mean vorticity (ω¯+2Ω) that is aligned, partly or completely (in the same or the opposite direction), with the angular velocity Ω of the rotating frame of r...

We investigate the role of extended intrinsic mean spin tensor introduced in this work for turbulence modelling in a non-inertial frame of reference. It is described by the Euclidean group of transformations and, in particular, its significance and importance in the approach of the algebraic Reynolds stress modelling, such as in a nonlinear K-ɛ model. To this end and for illustration of the effect of extended intrinsic spin tensor on turbulence modelling, we examine several recently developed nonlinear K-ɛ models and compare their performance in predicting the homogeneous turbulent shear flow in a rotating frame of reference with LES data. Our results and analysis indicate that, only if the deficiencies of these models and the like be well understood and properly corrected, may in the near future, more sophisticated nonlinear K-ɛ models be developed to better predict complex turbulent flows in a non-inertial frame of reference.

In this note we show that the setting up of the “principle of material frame-indifference in the limit of two-dimensional turbulence” by Speziale in the 1980s, which has been applied to turbulence modelling for the past two decades as seen from the literature, is unsound—in fact, there is an inconsistency in dealing with the fluctuating pressure which leads to contradicting the physical facts of turbulence. We conclude that this so-called “principle of material frame-indifference in the limit of two-dimensional turbulence” for turbulence modelling should be discarded.

We investigate the principal aspects of modelling the fully-developed turbulent swirling flows based on the algebraic two-equation (K–e) modelling approach. As a typical example, the characteristics of modelling the turbulent swirling flow in an axially rotating pipe based on the non-linear cubic K–e models of Craft et al. (Int. J. Heat Fluid Flow 1996; 17:108–115), Shih et al. (Proceedings of 11th Symposium on Turbulent Shear Flows, Grenoble, France, 1997; 31.1–31.6), and Huang and Ma (Phys. Rev. E 2004; 70:036302) are analysed and discussed in detail. Moreover, we carry out the numerical simulations by using the above three cubic models for the turbulent swirling flows in an axially rotating pipe and in an axisymmetric chamber, respectively, in comparison with the experimental data concerned. The numerical results indicate that, in addition to the frame-indifferent mean stretching tensor (the mean strain-rate tensor), the frame-dependent mean spin tensor actually plays an effective and important role as well in predicting the turbulent swirling flows. Copyright © 2005 John Wiley & Sons, Ltd.

We explore an approach to the constitutive equations for the Reynolds stress, assuming that it is determined by the history of the mean deformation of turbulence but has a fading memory. By considering the first and the subsequent higher order approximations to the mean deformation of turbulence, we further assume that the Reynolds stress depends on the history of the mean relative deformation gradient of turbulence and its higher gradients up to some finite order. To exemplify this approach, a simple but nonlinear constitutive equation for the Reynolds stress is proposed with emphasis on some history effects of turbulence; its approximate form is shown to include as special cases a few previously proposed models, which however were developed based on different approaches and reasoning.

The β-L-arabinofuranosidase from Bifidobacterium longum JCM 1217 (HypBA1), a DUF1680 family member, was recently characterized and classified to the glycoside hydrolase family 127 (GH127) by CAZy. The HypBA1 exerts exo-glycosidase activity to hydrolyze β-1,2-linked arabinofuranose disaccharides from non-reducing end into individual L-arabinoses. In this study, the crystal structures of HypBA1 and its complex with L-arabinose and Zn2+ ion were determined at 2.23-2.78 A resolution. HypBA1 consists of three domains, denoted N-, S- and C-domain. The N-domain (residues 1-5 and 434-538) and C-domain (residues 539-658) adopt β-jellyroll architectures, and the S-domain (residues 6-433) adopts an (α/α)6-barrel fold. HypBA1 utilizes the S- and C-domain to form a functional dimer. The complex structure suggests that the catalytic core lies in the S-domain where Cys417 and Glu322 serve as nucleophile and general acid/base, respectively, to cleave the glycosidic bonds via a retaining mechanism. The enzyme contains a restricted carbohydrate-binding cleft, which accommodates shorter arabino oligosaccharides exclusively. In addition to the complex crystal structures, we have one more interesting crystal which contains the apo HypBA1 structure without Zn2+ ion. In this structure, the Cys417-containing loop is shifted away due to the disappearance of all coordinate bonds in the absence of Zn2+ ion. Cys417 is thus diverted from the attack position, and probably is also protonated, disabling its role as the nucleophile. Therefore, Zn2+ ion is indeed involved in the catalytic reaction through maintaining the proper configuration of active site. Thus the unique catalytic mechanism of GH127 enzymes is now well elucidated.

Within the framework of rational thermodynamics set forth by Truesdell and Toupin [In: S. Flugge, C. Truesdell (Eds.), Handbuch der Physik III/1, Springer, Berlin, 1960], and Coleman and Noll [Arch. Rational Mech. Anal. 13 (1963) 167–178], among others, we study thermodynamic restriction on turbulence modelling. First, we show that the turbulent kinetic energy equation is a direct consequence of the first law of thermodynamics, and in view of the second law of thermodynamics the turbulent dissipation rate is in nature a thermodynamic internal variable. Second, we show that the principle of entropy growth expressed in the forms of the Clausius–Duhem and the Clausius–Planck inequalities, places a restriction on turbulence modelling, wherein the turbulent dissipation rate as a thermodynamic internal variable plays a key role in ensuring the modelling adopted to be thermodynamically admissible.

We use Noether's theorem to derive energy-momentum tensors for a simple elastic material, a nonsimple elastic material of grade two, a simple elastic dielectric and a nonsimple elastic dielectric of grade two. The technique is easily extendable to a nonsimple elastic dielectric of any grade.

In this work, we extend the notion of natural viscosity introduced by Truesdell in 1964 for the simple fluid in a viscometric flow to the study of homogeneous turbulent shear flow of a Navier–Stokes fluid. Within the framework of Navier–Stokes equations, first, we prove the existence of the natural viscosity of turbulence of a Navier–Stokes fluid in the limit of zero shear rate in homogeneous turbulent shear flow and derive its exact expression. Secondly, we show that, in contrast with the simple fluid in which case its natural viscosity is a material constant, the natural viscosity of turbulence is a function of time and always non-negative, different from the eddy viscosity introduced by Boussinesq in 1877, which could take on negative values as shown in experiments and differs from one model to another in turbulence modelling. In addition, we analyse Prandtl's mixing length model and a few linear and non-linear K–e models related to the concept of eddy viscosity and compare their performance in approxi...

In this work, we develop a Reynolds stress model along the line of the approach presented by Huang [Commun. Nonlinear Sci. Numer. Simul. 9, 543 (2004)], aiming to assess the role and contribution of the mean spin tensor in turbulence modeling. Here, the constitutive functional for the Reynolds stress depends on the mean spin tensor as well as the mean stretching tensor and its Jaumann derivative, the turbulent kinetic energy $K$, and the turbulent dissipation rate $\ensuremath{\epsilon}$, which is at the complexity level of $p=1,m=1$, and $n=0$ of a rate-type constitutive equation for the Reynolds stress proposed in the aforementioned paper. The explicit form for the Reynolds stress is obtained with recourse to the representation theorem and the theory of invariants developed in modern rational continuum mechanics, and, as an approximation, a nonlinear cubic $K\text{\ensuremath{-}}\ensuremath{\epsilon}$ model is worked out in which the model coefficients are analytically identified based on the experimental results of Tavoularis and Corrsin [J. Fluid Mech. 104, 311 (1981)]. In addition, numerical results based on this model, in the forms of employing the Jaumann derivative and the Oldroyd derivative, respectively, for homogeneous turbulent shear flow and fully developed turbulent flow over a backward-facing step, are presented in comparison with those obtained based on a few previously proposed linear and nonlinear $K\text{\ensuremath{-}}\ensuremath{\epsilon}$ models, showing reasonably good agreement with the experimental results and the DNS data concerned and a better performance than the previously developed quadratic models.

In this paper, we study the characteristics of the Reynolds stress under a change of frame, as defined by the Euclidean group of transformation. We show that being subject to the dynamical processes induced from the mean Navier-Stokes equations, the invariance group of the fluctuating velocity and the Reynolds stress is no longer the Euclidean group of transformation, which is merely a kinematical aspect, but reduces to the extended Galilean group of transformation. As a consequence, in contrast to developing the constitutive equations for the Cauchy stress in continuum mechanics, wherein the principle of material frame-indifference is a guiding principle, the frame-dependent kinematical quantities, e.g., the mean spin tensor, may be allowed to play an effective role as the constitutive variable in turbulence modeling.

This note presents a theoretical study on Kolmogorov's −5/3 scaling law under a change of frame of reference and, in particular, its corresponding form in a non-inertial frame of reference. First, we show that the Kolmogorov scales in the universal equilibrium range and the turbulent kinetic energy spectrum function E(κ, t) are not frame-indifferent, i.e., frame-dependent, in the sense of Truesdell and Noll (1965). Moreover, we investigate the aspects of the scaling coefficient C K under a change of frame of reference and arrive at a generalized Kolmogorov's −5/3 scaling law in a non-inertial frame of reference, which is frame-dependent and in an inertial frame of reference reduces to the form stemming from Kolmogorov's 1941 paper.