much smaller than the imposed field and scales with $Rm$ [@Zikanov_Thess98; @Willis_Barenghi02; @Liu_etal06], so we change it to ${\bf b}'\rightarrow Rm\cdot {\bf b}'$, such that the new ${\bf
b}'$ is comparable to the perturbed velocity ${\bf u}$. Substituting this into Eqs. (1)-(3), taking into account that the imposed magnetic field is current-free, and using the above normalization, we arrive at the following equations governing perturbations with arbitrary amplitude in nondimensional form to first order in $Rm$ (primes henceforth will be omitted): $$\frac{\partial {\bf u}}{\partial t}+({\bf U}_0\cdot \nabla) {\bf
u}=-\nabla p-({\bf u}\cdot \nabla) {\bf U}_0+ \frac{Ha^2}{Re}(\nabla
\times {\bf b})\times {\bf B}_0 + \frac{1}{Re}\nabla^2 {\bf u}-({\bf
u}\cdot \nabla) {\bf u},$$ $$Rm\left[\frac{\partial {\bf b}}{\partial t}-\nabla\times \left({\bf
U}_0\times {\bf b}\right)-\nabla\times \left({\bf u}\times {\bf
b}\right)\right]=\nabla\times \left({\bf u}\times {\bf
B}_0\right)+\nabla^2{\bf b},$$ $$\nabla\cdot {\bf u}=0,~~~\nabla\cdot {\bf b}=0,$$ where the terms proportional to $Rm$ on the left hand side of induction equation (6), including the time-derivative, are usually neglected in the limit of small $Rm\rightarrow 0$ (inductionless, or quasi-static approximation, see e.g., [@Willis_Barenghi02; @Szklarski_Ruediger06; @Child_Hollerbach16]). In that case, the advective derivative, or the inertial term involving the perturbed velocity, $({\bf u}\cdot \nabla) {\bf u}$, is the only nonlinearity that remains in these equations. Here we preferred to keep 