Sergey A. Suslov

Sun Cable posed several questions related to the bio-fouling of submarine transmission cablesfor their installation between Darwin and Singapore. The group considered growth factors,hydrodynamic effects and heating and insulation impact on the cables across the range ofdifferent conditions over the proposed path. The Coral Triangle as it is known has a greatbio-diversity and a range of different seabed and physical conditions, leading to highly variableconditions.

Circular flow can be induced electromagnetically in a horizontal unsupported film of an electrolyte fluid attached to concentric cylindrical electrodes and placed in an external orthogonal magnetic field. In the presence of a surfactant, the film remains approximately undeformed, and the flow is effectively two-dimensional. We study the linear stability of the base azimuthal flow and nonlinear flow dynamics induced by direct and alternating sinusoidal currents. For a direct current, precessing vortices are formed for Reynolds numbers above the critical. We follow such nonlinear solutions by numerical continuation in parameter space and determine the metastability boundary for the base flow. The classical plane Poiseuille flow (PPF) is recovered in the limit of infinite annulus radius. In channels with a small width-to-radius ratio, we find a signature of temporal intermittency in a fully developed nonlinear flow. Contrary to PPF, subcritical transition to turbulence in a circular channel is not found. In the case of a sinusoidal current, the time-periodic base flow is calculated analytically, and its stability is studied using the Floquet theory. The first azimuthal mode that gives rise to a single precessing vortex is known to be linearly stable for a dc forcing. However, we show that this mode can be destabilized under the ac forcing. The linear stability of azimuthal modes with larger wavenumbers follows a qualitatively similar scenario as known for periodically driven PPF: high frequency forcing stabilizes the base flow, while moderate and low frequency forcing is destabilizing.

This study investigates the mechanical and thermodynamic effects of the evaporating ocean spray on the structure and dynamics of a hurricane marine atmospheric boundary layer using Eulerian multifluid and mixture model approaches coupled with the E−ϵ turbulence closure. The multifluid framework treats air and spray as interpenetrating phases, enabling a physically consistent representation of air–droplet interactions governing momentum transfer, enthalpy exchange, and turbulence modulation. The mixture approach is based on a simplified description that captures only part of the underlying physics, yet offers an advantage in its ability to yield analytical insight. Mechanically, spray produces competing effects: on one hand, droplet inertia causes wind deceleration, on the other, the spray-induced turbulence attenuation, primarily resulting from the air–droplet friction, leads to strengthening the wind. Analytical and numerical results show that the latter effect prevails for typical spray droplet sizes leading to wind acceleration and drag reduction at hurricane wind speeds. Thermodynamically, evaporating droplets redistribute total heat flux in favor of its latent component, with effects strongly dependent on the droplet size. Small droplets suppress turbulence and reduce the total enthalpy flux, whereas large ones enhance it. Furthermore, spray significantly increases the total enthalpy-to-drag coefficient ratio with wind speed, which agrees with field observations.

We study the influence of a low-frequency harmonic vibration on the formation of the two-dimensional rolling solitary waves in vertically co-flowing two-layer liquid films. The system consists of two adjacent layers of immiscible fluids with the first layer being sandwiched between a vertical solid plate and the second fluid layer. The solid plate oscillates harmonically in the horizontal direction inducing Faraday waves at the liquid–liquid and liquid–air interfaces. We use a reduced hydrodynamic model derived from the Navier–Stokes equations in the long-wave approximation. Linear stability of the base flow in a flat two-layer film is determined semi-analytically using Floquet theory. We consider sub-millimetre-thick films and focus on the competition between the long-wavelength gravity-driven and finite wavelength Faraday instabilities. In the linear regime, the range of unstable wave vectors associated with the gravity-driven instability broadens at low and shrinks at high vibration frequencies. In nonlinear regimes, we find multiple metastable states characterized by solitary-like travelling waves and short pulsating waves. In particular, we find the range of the vibration parameters at which the system is multistable. In this regime, depending on the initial conditions, the long-time dynamics is dominated either by the fully developed solitary-like waves or by the shorter pulsating Faraday waves.

The asymptotic analysis of steady azimuthally invariant electromagnetically driven flows occurring in a shallow annular layer of electrolyte undertaken in Part 1 of this study (McCloughan & Suslov, J. Fluid Mech., vol. 980, 2024, A59) predicted the existence of a two-tori flow state that has not been detected previously. In Part 2 of the study we confirm its existence by numerical time integration of the governing equations. We observe a hysteresis, where the type of solution obtained for the same set of governing parameters depends on the choice of the initial conditions and the way the governing parameters change, which is fully consistent with the analytic results of Part 1. Subsequently, we perform a linear stability analysis of the newly obtained steady state and deduce that the experimentally observed anti-cyclonic free-surface vortices appear on its background as a result of a centrifugal (Rayleigh-type) instability of the interface separating two counter-rotating toroidal structures that form the newly found flow solution. The quantitative characteristics of such instability structures are determined. It is shown that such structures can only exist in sufficiently thin layers with the depth not exceeding a certain critical value.

We study the effect of a dynamic contact angle on an electromagnetically driven flow in a horizontal free electrolyte film stretched between two coaxial cylindrical electrodes and placed in a uniform magnetic field. The flow dynamics and film deformation are described using the reduced hydrodynamic model derived in the lubrication approximation in [A. Pototsky and S. A. Suslov, J. Fluid Mech., 984, A75 (2024)]. The linearized molecular kinetic model is used to relate the dynamic and static contact angles to the wetting-line friction coefficient. Steady azimuthal flow is found for arbitrary static contact angles. Linear stability of the base azimuthal flow with respect to azimuthally invariant perturbations is studied using the numerical continuation method. We find that the flow stability is highly sensitive to variations of the wetting-line friction coefficient and the static contact angle. The least stable azimuthal flow is found for the frictionless contact line corresponding to a free film that remains perpendicular to the surface of the electrodes. The azimuthal flows are found to experience a supercritical Hopf bifurcation upon which they transition to a stable oscillatory dynamic regime characterized by alternating squeezing and swelling of the film near the inner and outer electrodes.

We consider a thin horizontal layer of a non-magnetic electrolyte containing a bulk solution of salt and carrying an electric current. The layer is bounded by two deformable free surfaces loaded with an insoluble surfactant and is placed in a vertical magnetic field. The arising Lorentz force drives the electrolyte in the plane of the layer. We employ the long-wave approximation to derive general two-dimensional hydrodynamic equations describing symmetric pinching-type deformations of the free surfaces. These equations are used to study the azimuthal flow in an annular film spanning the gap between two coaxial cylindrical electrodes. In weakly deformed films, the base azimuthal flow and its linear stability with respect to azimuthally invariant perturbations are studied analytically. For relatively thick layers and weak magnetic fields, the leading mode with the smallest decay rate is found to correspond to a monotonic azimuthal velocity perturbation. The Marangoni effect leads to further stabilisation of the flow while perturbations of the solute concentration in the bulk of the fluid have no influence on the flow stability. In strongly deformed films in the diffusion-dominated regime, the azimuthal flow becomes linearly unstable with respect to an oscillatory mixed mode characterised by the combination of radial and azimuthal velocity perturbations when the voltage applied between electrodes exceeds the critical value.

This study extends our previous work (McCloughan & Suslov, J. Fluid Mech., vol. 887, 2020, A23), where the existence of a saddle-node bifurcation of steady axisymmetric electrolyte flows driven by the Lorentz force in a shallow annular domain was first reported. Here we perform further weakly nonlinear analysis over a wider range of the governing parameters to demonstrate that the previously reported saddle-node bifurcation is a local feature of a global fold catastrophe, which, in turn, is a part of cusp catastrophe occurring as the thickness of the fluid layer increases. The amplitude equation characterising multiple flow solutions in the finite vicinity of catastrophe points is derived. The sensitivity of its coefficients and solutions to the distance from the catastrophe points is assessed demonstrating the robustness of the used analytical procedure. The asymptotic flow solution past the catastrophe point is subsequently obtained and its topology is explored confirming the existence of the secondary circulation in the bulk of flow (two-tori background flow structure). The latter is argued to lead to the appearance of experimentally observable vortices on the fluid surface. The rigorous justification of this conjecture is to be given in Part 2 of the study.