{"title":"Numerical Study on Randomization in Late Boundary Layer Transition","authors":"P. Lu, M. Thapa, Chaoqun Liu","doi":"10.2514/6.2012-748","DOIUrl":"https://doi.org/10.2514/6.2012-748","url":null,"abstract":"The mechanism of randomization in late boundary layer transition is a key issue of late boundary layer transition and turbulence theory. We studied the mechanism carefully by high order DNS. The randomization was originally considered as a result of large background noise and non-periodic spanwise boundary conditions. It was addressed that the large ring structure is affected by background noises first and then the change of large ring structure affects the small length scale quickly, which directly leads to randomization and formation of turbulence. However, what we observed is that the loss of symmetry starts from the middle level rings while the top and bottom rings are still symmetric. The nonsymmetric structure of second level rings will influence the small length scales at the boundary layer bottom quickly. The symmetry loss at the bottom of the boundary layer is quickly spread to up level through ejections. This will lead to randomization of the whole flow field. Therefore, the internal instability of multiple level ring structure, especially the middle ring cycles, is the main reason for flow randomization, but not the background noise. A hypothesis is given that the loss of symmetry may be caused by the shift from C-type transition to K-type transition or reverses.","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129984567","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Coupled nonlinear oscillators: metamorphoses of amplitude profiles for the approximate effective equation - the case of 1:3 resonance","authors":"J. Kyzioł, A. Okniński","doi":"10.5506/APhysPolB.43.1275","DOIUrl":"https://doi.org/10.5506/APhysPolB.43.1275","url":null,"abstract":"We study dynamics of two coupled periodically driven oscillators. An important example of such a system is a dynamic vibration absorber which consists of a small mass attached to the primary vibrating system of a large mass. Periodic solutions of the approximate effective equation (derived in our earlier papers) are determined within the Krylov-Bogoliubov-Mitropolsky approach to compute the amplitude profiles $A(Omega)$. In the present paper we investigate metamorphoses of the function $A(Omega)$ induced by changes of the control parameters in the case of 1:3 resonances.","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124576176","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Collisionless kinetic theory of rolling molecules","authors":"Darryl D. Holm, V. Putkaradze, C. Tronci","doi":"10.3934/krm.2013.6.429","DOIUrl":"https://doi.org/10.3934/krm.2013.6.429","url":null,"abstract":"We derive a collisionless kinetic theory for an ensemble of molecules undergoing nonholonomic rolling dynamics. We demonstrate that the existence of nonholonomic constraints leads to problems in generalizing the standard methods of statistical physics. In particular, we show that even though the energy of the system is conserved, and the system is closed in the thermodynamic sense, some fundamental features of statistical physics such as invariant measure do not hold for such nonholonomic systems. Nevertheless, we are able to construct a consistent kinetic theory using Hamilton's variational principle in Lagrangian variables, by regarding the kinetic solution as being concentrated on the constraint distribution. A cold fluid closure for the kinetic system is also presented, along with a particular class of exact solutions of the kinetic equations.","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131760516","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Pseudo resonance induced quasi-periodic behavior in stochastic threshold dynamics","authors":"P. Ditlevsen, H. Braun","doi":"10.1142/S0219493711003309","DOIUrl":"https://doi.org/10.1142/S0219493711003309","url":null,"abstract":"Here we present a simple stochastic threshold model consisting of a deterministic slowly decaying term and a fast stochastic noise term. The process shows a pseudo-resonance, in the sense that for small and large intensities of the noise the signal is irregular and the distribution of threshold crossings is broad, while for a tuned intermediate value of noise intensity the signal becomes quasi-periodic and the distribution of threshold crossings is narrow. The mechanism captured by the model might be relevant for explaining apparent quasi-periodicity of observed climatic variations where no internal or external periodicities can be identified.","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115531114","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Non Hamiltonian Chaos from Nambu Dynamics of Surfaces","authors":"M. Axenides","doi":"10.1142/9789814350341_0012","DOIUrl":"https://doi.org/10.1142/9789814350341_0012","url":null,"abstract":"We discuss recent work with E.Floratos (JHEP 1004:036,2010) on Nambu Dynamics of Intersecting Surfaces underlying Dissipative Chaos in $R^{3}$. We present our argument for the well studied Lorenz and R\"{o}ssler strange attractors. We implement a flow decomposition to their equations of motion. Their volume preserving part preserves in time a family of two intersecting surfaces, the so called {em Nambu Hamiltonians}. For dynamical systems with linear dissipative sector such as the Lorenz system, they are specified in terms of Intersecting Quadratic Surfaces. For the case of the R\"{o}ssler system, with nonlinear dissipative part, they are given in terms of a Helicoid intersected by a Cylinder. In each case they foliate the entire phase space and get deformed by Dissipation, the irrotational component to their flow. It is given by the gradient of a surface in $R^{3}$ specified in terms of a scalar function. All three intersecting surfaces reproduce completely the dynamics of each strange attractor.","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133870635","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Enstrophy bounds and the range of space-time scales in the hydrostatic primitive equations","authors":"J. Gibbon, Darryl D. Holm","doi":"10.1103/PHYSREVE.87.031001","DOIUrl":"https://doi.org/10.1103/PHYSREVE.87.031001","url":null,"abstract":"The hydrostatic primitive equations (HPE) form the basis of most numerical weather, climate and global ocean circulation models. Analytical (not statistical) methods are used to find a scaling proportional to $(Nu,Ra,Re)^{1/4}$ for the range of horizontal spatial sizes in HPE solutions, which is much broader than currently achievable computationally. The range of scales for the HPE is determined from an analytical bound on the time-averaged enstrophy of the horizontal circulation. This bound allows the formation of very small spatial scales, whose existence would excite unphysically large linear oscillation frequencies and gravity wave speeds.","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131583077","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Complete Chaotic Mixing in an Electro-osmotic Flow by Destabilization of Key Periodic Pathlines","authors":"R. Chabreyrie, C. Chandre, P. Singh, N. Aubry","doi":"10.1063/1.3596127","DOIUrl":"https://doi.org/10.1063/1.3596127","url":null,"abstract":"The ability to generate complete, or almost complete, chaotic mixing is of great interest in numerous applications, particularly for microfluidics. For this purpose, we propose a strategy that allows us to quickly target the parameter values at which complete mixing occurs. The technique is applied to a time periodic, two-dimensional electro-osmotic flow with spatially and temporally varying Helmoltz-Smoluchowski slip boundary conditions. The strategy consists of following the linear stability of some key periodic pathlines in parameter space (i.e., amplitude and frequency of the forcing), particularly through the bifurcation points at which such pathlines become unstable.","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129961284","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A hierarchy of length scales for weak solutions of the three-dimensional Navier-Stokes equations","authors":"J. Gibbon","doi":"10.4310/CMS.2012.V10.N1.A7","DOIUrl":"https://doi.org/10.4310/CMS.2012.V10.N1.A7","url":null,"abstract":"Moments of the vorticity are used to define and estimate a hierarchy of time-averaged inverse length scales for weak solutions of the three-dimensional, incompressible Navier-Stokes equations on a periodic box. The estimate for the smallest of these inverse scales coincides with the inverse Kolmogorov length but thereafter the exponents of the Reynolds number rise rapidly for correspondingly higher moments. The implications of these results for the computational resolution of small scale vortical structures are discussed.","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"212 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122841563","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Stretching and folding diagnostics in solutions of the three-dimensional Euler and Navier-Stokes equations","authors":"J. Gibbon, Darryl D. Holm","doi":"10.1017/CBO9781139235792.010","DOIUrl":"https://doi.org/10.1017/CBO9781139235792.010","url":null,"abstract":"Two possible diagnostics of stretching and folding (S&F) in fluid flows are discussed, based on the dynamics of the gradient of potential vorticity ($q = bomcdotnablatheta$) associated with solutions of the three-dimensional Euler and Navier-Stokes equations. The vector $bdB = nabla q times nablatheta$ satisfies the same type of stretching and folding equation as that for the vorticity field $bom $ in the incompressible Euler equations (Gibbon & Holm, 2010). The quantity $theta$ may be chosen as the potential temperature for the stratified, rotating Euler/Navier-Stokes equations, or it may play the role of a seeded passive scalar for the Euler equations alone. The first discussion of these S&F-flow diagnostics concerns a numerical test for Euler codes and also includes a connection with the two-dimensional surface quasi-geostrophic equations. The second S&F-flow diagnostic concerns the evolution of the Lamb vector $bsD = bomtimesbu$, which is the nonlinearity for Euler's equations apart from the pressure. The curl of the Lamb vector ($boldsymbol{varpi} := bsD$) turns out to possess similar stretching and folding properties to that of the $bdB$-vector.","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"70 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121229637","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}