This paper presents numerical linear stability analysis of a cylindrical Taylor-Couette flow of l... more This paper presents numerical linear stability analysis of a cylindrical Taylor-Couette flow of liquid metal carrying axial electric current in a generally helical external magnetic field. Axially symmetric disturbances are considered in the inductionless approximation corresponding to zero magnetic Prandtl number. Axial symmetry allows us to reveal an entirely new electromagnetic instability. First, we show that the electric current passing through the liquid can extend the range of helical magnetorotational instability (HMRI) indefinitely by transforming it into a purely electromagnetic instability. Two different electromagnetic instability mechanisms are identified. The first is an internal pinch-type instability, which is due to the interaction of the electric current with its own magnetic field. Axisymmetric mode of this instability requires a free-space component of the azimuthal magnetic field. When the azimuthal component of the magnetic field is purely rotational and the ax...
This paper presents numerical analysis a pinch-type instability in a semi-infinite planar layer o... more This paper presents numerical analysis a pinch-type instability in a semi-infinite planar layer of inviscid conducting liquid bounded by solid walls and carrying a uniform electric current. The instability resembles the Tayler instability in astrophysics and can presumably disrupt the operatio n of the recently developed liquid metal batteries (Wang et al. 2014 Nature 514 348). We show that the instability in liquid metals, which are relatively poor conductors, significantly differs from that in a well conducting fluid. In the latter, instability is dominated by the current perturbation resulting from the advection of the magnetic field. In the former, the instability is dominated by the magnetic field perturbation resulting from the diffusion of the electric current perturbation. As a result, in liquid metals, instability develops on the magnetic response time scale, which depends on the conductivity, and is much longer than the Alfvén time scale, on which the instability develops ...
ABSTRACT We analyze weakly nonlinear stability of a flow of viscous conducting liquid driven by p... more ABSTRACT We analyze weakly nonlinear stability of a flow of viscous conducting liquid driven by pressure gradient in the channel between two parallel walls subject to a transverse magnetic field. Using a non-standard numerical approach, we compute the linear growth rate correction and the first Landau coefficient, which in a sufficiently strong magnetic field vary with the Hartmann number as $\mu_{1}\sim(0.814-\mathrm{i}19.8)\times10^{-3}\textit{Ha}$ and $\mu_{2}\sim(2.73-\mathrm{i}1.50)\times10^{-5}\textit{Ha}^{-4}$. These coefficients describe a subcritical transverse velocity perturbation with the equilibrium amplitude $|A|^{2}=\Re[\mu_{1}]/\Re[\mu_{2}](\textit{Re}_{c}-\textit{Re})\sim29.8\textit{Ha}^{5}(\textit{Re}_{c}-\textit{Re})$ which exists at Reynolds numbers below the linear stability threshold $\textit{Re}_{c}\sim 4.83\times10^{4}\textit{Ha}.$ We find that the flow remains subcritically unstable regardless of the magnetic field strength. Our method for computing Landau coefficients differs from the standard one by the application of the solvability condition to the discretized rather than continuous problem. This allows us to bypass both the solution of the adjoint problem and the subsequent evaluation of the integrals defining the inner products, which results in a significant simplification of the method.
This paper presents numerical linear stability analysis of a cylindrical Taylor-Couette flow of l... more This paper presents numerical linear stability analysis of a cylindrical Taylor-Couette flow of liquid metal carrying axial electric current in a generally helical external magnetic field. Axially symmetric disturbances are considered in the inductionless approximation corresponding to zero magnetic Prandtl number. Axial symmetry allows us to reveal an entirely new electromagnetic instability. First, we show that the electric current passing through the liquid can extend the range of helical magnetorotational instability (HMRI) indefinitely by transforming it into a purely electromagnetic instability. Two different electromagnetic instability mechanisms are identified. The first is an internal pinch-type instability, which is due to the interaction of the electric current with its own magnetic field. Axisymmetric mode of this instability requires a free-space component of the azimuthal magnetic field. When the azimuthal component of the magnetic field is purely rotational and the ax...
This paper presents numerical analysis a pinch-type instability in a semi-infinite planar layer o... more This paper presents numerical analysis a pinch-type instability in a semi-infinite planar layer of inviscid conducting liquid bounded by solid walls and carrying a uniform electric current. The instability resembles the Tayler instability in astrophysics and can presumably disrupt the operatio n of the recently developed liquid metal batteries (Wang et al. 2014 Nature 514 348). We show that the instability in liquid metals, which are relatively poor conductors, significantly differs from that in a well conducting fluid. In the latter, instability is dominated by the current perturbation resulting from the advection of the magnetic field. In the former, the instability is dominated by the magnetic field perturbation resulting from the diffusion of the electric current perturbation. As a result, in liquid metals, instability develops on the magnetic response time scale, which depends on the conductivity, and is much longer than the Alfvén time scale, on which the instability develops ...
ABSTRACT We analyze weakly nonlinear stability of a flow of viscous conducting liquid driven by p... more ABSTRACT We analyze weakly nonlinear stability of a flow of viscous conducting liquid driven by pressure gradient in the channel between two parallel walls subject to a transverse magnetic field. Using a non-standard numerical approach, we compute the linear growth rate correction and the first Landau coefficient, which in a sufficiently strong magnetic field vary with the Hartmann number as $\mu_{1}\sim(0.814-\mathrm{i}19.8)\times10^{-3}\textit{Ha}$ and $\mu_{2}\sim(2.73-\mathrm{i}1.50)\times10^{-5}\textit{Ha}^{-4}$. These coefficients describe a subcritical transverse velocity perturbation with the equilibrium amplitude $|A|^{2}=\Re[\mu_{1}]/\Re[\mu_{2}](\textit{Re}_{c}-\textit{Re})\sim29.8\textit{Ha}^{5}(\textit{Re}_{c}-\textit{Re})$ which exists at Reynolds numbers below the linear stability threshold $\textit{Re}_{c}\sim 4.83\times10^{4}\textit{Ha}.$ We find that the flow remains subcritically unstable regardless of the magnetic field strength. Our method for computing Landau coefficients differs from the standard one by the application of the solvability condition to the discretized rather than continuous problem. This allows us to bypass both the solution of the adjoint problem and the subsequent evaluation of the integrals defining the inner products, which results in a significant simplification of the method.
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Papers by Janis Priede