Transition to turbulence in Taylor-Couette ferrofluidic flow

Y.D. was supported by Basic Science Research Program of the Ministry of Education, Science and Technology under Grant No. NRF-2013R1A1A2010067. Y.C.L. was supported by AFOSR under Grant No. FA9550-12-1-0095.Peer reviewedPublisher PD

Nonlinear Klein-Gordon and Schrodinger Equations by the Projected Differential Transform Method

The differential transform method (DTM) is based on the Taylor series for all variables, but it differs from the traditional Taylor series in calculating coefficients. Even if the DTM is an effective numerical method for solving many nonlinear partial differential equations, there are also some difficulties due to the complex nonlinearity. To overcome difficulties arising in DTM, we present the new modified version of DTM, namely, the projected differential transform method (PDTM), for solving nonlinear partial differential equations. The proposed method is applied to solve the various nonlinear Klein-Gordon and Schrodinger equations. Numerical approximations performed by the PDTM are presented and compared with the results obtained by other numerical methods. The results reveal that PDTM is a simple and effective numerical algorithm.open1

Ring bursting behavior en route to turbulence in quasi two-dimensional Taylor-Couette flows

We investigate the quasi two-dimensional Taylor-Couette system in the regime where the radius ratio is close to unity - a transitional regime between three and two dimensions. By systematically increasing the Reynolds number we observe a number of standard transitions, such as one from the classical Taylor vortex flow (TVF) to wavy vortex flow (WVF), as well as the transition to fully developed turbulence. Prior to the onset of turbulence we observe intermittent burst patterns of localized turbulent patches, confirming the experimentally observed pattern of very short wavelength bursts (VSWBs). A striking finding is that, for Reynolds number larger than the onset of VSWBs, a new type of intermittently bursting behaviors emerge: burst patterns of azimuthally closed rings of various orders. We call them ring-burst patterns, which surround the cylinder completely but remain localized and separated by non-turbulent mostly wavy structures in the axial direction. We use a number of quantitative measures, including the cross-flow energy, to characterize the ring-burst patterns and to distinguish them from the background flow. The ring-burst patterns are interesting because it does not occur in either three- or two-dimensional Taylor-Couette flow: it occurs only in the transition, quasi two-dimensional regime of the system, a regime that is less studied but certainly deserves further attention so as to obtain deeper insights into turbulence

Transient behavior between multi-cell flow states in ferrofluidic Taylor-Couette flow

Peer ReviewedPostprint (published version

Enhanced Multistage Differential Transform Method: Application to the Population Models

We present an efficient computational algorithm, namely, the enhanced multistage differential transform method (E-MsDTM) for solving prey-predator systems. Since the differential transform method (DTM) is based on the Taylor series, it is difficult to obtain accurate approximate solutions in large domain. To overcome this difficulty, the multistage differential transform method (MsDTM) has been introduced and succeeded to have reliable approximate solutions for many problems. In MsDTM, it is the key to update an initial condition in each subdomain. The standard MsDTM utilizes the approximate solution directly to assign the new initial value. Because of local convergence of the Taylor series, the error is accumulated in a large domain. In E-MsDTM, we propose the new technique to update an initial condition by using integral operator. To demonstrate efficiency of the proposed method, several numerical tests are performed and compared with ones obtained by other numerical methods such as MsDTM, multistage variational iteration method (MVIM), and fourth-order Runge-Kutta method (RK4).open4

Effects of an imposed axial flow on a ferrofluidic Taylor-Couette flow

We investigate the effects of an externally imposed axial mass flux [1, 2] (axial pressure gradient, axial through flow) on ferrofluidic Taylor-Couette flow under the influence of either an axial or a transverse magnetic field [3]. Without imposed axial through flow, due to the symmetry-conserving axial field and the symmetry-breaking transverse field, it gives rise to various vortex flows inferrofluidic Taylor-Couette flow such as wavy Taylor vortex flow (wTVF), wavy spiral vortex flow (wSPI) and wavy vortex flows (wTVFHx and wSPIHx ), which are typically produced by a non-linear interaction of rotational, shear and magnetic instabilities. In addition, when an axial through flow is imposed to a ferrofluidic Taylor-Couette flow in the presence of such a magnetic field, new helical vortex structures are born. In particular, we uncover ’modulated Mixed-Cross-Spirals’ with a combination of at least three different dominant azimuthal wavenumbers.Postprint (author's final draft

Effects of an imposed axial flow on a Ferrofluidic Taylor-Couette flow

In this paper we investigate the effects of an externally imposed axial mass flux (axial pressure gradient, axial through flow) on ferrofluidic Taylor-Couette flow under the influence of either an axial or a transverse magnetic field. Without an imposed axial through flow, due to the symmetry-conserving axial field and the symmetry-breaking transverse field, it gives rise to various vortex flows in ferrofluidic Taylor-Couette flow such as wavy Taylor vortex flow (wTVF), wavy spiral vortex flow (wSPI) and wavy vortex flows (wTVFHx and wSPIHx), which are typically produced by a nonlinear interaction of rotational, shear and magnetic instabilities. In addition, when an axial through flow is imposed to a ferrofluidic Taylor-Couette flow in the presence of either an axial or a transverse magnetic field, previously unknown new helical vortex structures are observed. In particular, we uncover ‘modulated Mixed-Cross-Spirals’ with a combination of at least three different dominant azimuthal wavenumbers. Emergence of such new flow states indicates richer but potentially more controllable dynamics in ferrofluidic flows, i.e., an imposed axial through flow will be a new controllable factor/parameter in applications of a ferrofluidic and magnetic flows flow.Peer ReviewedPostprint (published version