Modal and nonmodal stability analysis for an electrified falling film

Area of Science:

• Fluid Dynamics
• Electromagnetohydrodynamics
• Nonlinear Dynamics

Background:

• Gravity-driven fluid flows over inclined planes are fundamental in various natural and industrial processes.
• The influence of external electric fields on fluid stability is a critical area of research with practical implications.

Purpose of the Study:

• To investigate the linear stability of a three-dimensional viscous incompressible fluid flow over an inclined plane under a normal electric field.
• To analyze the effects of the electric field strength (quantified by the electric Weber number) on both modal and nonmodal stability characteristics.

Main Methods:

• Derivation of time evolution equations for normal velocity, vorticity, and surface deformation.
• Numerical solution using the Chebyshev spectral collocation method.
• Modal and nonmodal stability analyses were conducted.

Main Results:

• Modal analysis revealed three unstable regions for the surface mode, which coalesce and grow with increasing electric Weber number.
• A single unstable region for the shear mode was observed, slightly attenuating with higher electric fields.
• Both modes are stabilized by spanwise wave numbers, shifting instability from long to finite wavelengths.
• Nonmodal analysis showed transient disturbance energy growth, intensifying slightly with the electric Weber number.

Conclusions:

• The electric field significantly impacts the stability of inclined fluid flows, altering the nature and extent of instabilities.
• Spanwise perturbations play a crucial role in stabilizing the flow, modifying the dominant instability wavelengths.
• Transient energy growth mechanisms persist and are slightly enhanced by the electric field.