Ferrofluidic wavy Taylor vortices under alternating magnetic field

Abstract

Many natural and industrial flows are subject to time-dependent boundary conditions and temporal modulations (e.g. driving frequency), which significantly modify the dynamics compared with their static counterparts. The present problem addresses ferrofluidic wavy vortex flow in Taylor–Couette geometry, with the outer cylinder at rest in a spatially homogeneous magnetic field subject to an alternating modulation. Using a modified Niklas approximation, the effect of frequency modulation on nonlinear flow dynamics and appearing resonance phenomena are investigated in the context of either period doubling or inverse period doubling. This article is part of the theme issue ‘Taylor–Couette and related flows on the centennial of Taylor’s seminal Philosophical Transactions paper (part 1)’.

Suppressing Vortex Generation in Ferrofluidic Couette Flow Via Alternating Magnetic Fields

“…However, τ pers (TVFs) always remains below the corresponding time τ sz(t)=0 pers (TVFs) in the absence of any magnetic field. One possible speculation for this detected non-monotonous behavior may be the appearance of resonance effects, which could be supported by similar recent observations [23]. The decrease in τ pers (TVF) for Ω H = 1100 (Fig.…”

“…To realise a periodic forcing in the system, we apply a sinusoidal modulation signal to the external magnetic field, which is orientated parallel to the system symmetry (z) axis, uniform in space and harmonic in time [22,23]. It is important to mention that such a pure axial-oriented magnetic field does not change the basic system symmetry, only the stability thresholds are shifted [27,30,31].…”

“…with s z,S being the static contribution of the driving s z,M the modulation amplitude, and Ω H the modulation frequency. The exact procedure of how to solve the ferrohydrodynamical equations of motion (2.1) is explained in detail in earlier works [22,23,35].…”

“…ferrofluids [21], offer an alternative method to realise such a periodic forcing. The great advantage lies in the fact that the forcing can be introduced directly into the system via a periodic modulation of the external magnetic field [22,23].…”

Taylor–Couette and related flows on the centennial of Taylor’s seminalPhilosophical Transactionspaper: part 2

“…Part 1 of this two-part theme issue explored contemporary topics related to Taylor-Couette flow including turbulent, convective and two-phase flows as well as extensions to magnetohydrodynamic, ferrofluidic and viscoelastic flows and flow geometries that are closely related to the Taylor-Couette problem [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. Part 2 of this theme issue continues with review articles and research articles having their origin in Taylor's 1923 paper.…”