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Öğe Effect of slip on the linear stability of the rotating disk boundary layer(Aip Publishing, 2023) Thomas, Christian; Alveroglu, Burhan; Stephen, Sharon O.; Al-Malki, Mushrifah A. S.; Hussain, ZahirThe linear stability of the rotating disk boundary layer with surface roughness is investigated. Surface roughness is modeled using slip boundary conditions [M. Miklavc?ic? and C. Y. Wang, Z. Angew. Math. Phys. 55, 235-246 (2004)], which establish concentric grooves, radial grooves, and isotropic roughness. The effect on the stationary crossflow and Coriolis instabilities is analyzed by applying slip conditions to the undisturbed flow and linear disturbances. This analysis builds on the work of Cooper et al. [Phys. Fluids 27, 014107 (2015)], who modeled slip effects on the base flow but applied the no-slip condition to the linear perturbations. Neutral stability curves and critical parameter settings for linearly unstable behavior are computed for several radial and azimuthal slip length settings. The application of slip on the linear disturbances has a significant impact on the flow stability. In particular, the Coriolis instability undergoes considerable destabilization in the instance of concentric grooves (i.e., radial slip) and radial grooves with sufficiently large azimuthal slip lengths. In addition, concentric grooves destabilize the crossflow instability when the radial slip length is small. Moreover, in the instance of isotropic roughness, the stabilizing effect is markedly less than the observations of Cooper et al. [Phys. Fluids 27, 014107 (2015)]. Finally, an energy analysis is undertaken to ascertain the physical mechanisms brought about by surface roughness.Öğe Hydrodynamic stability of Bödewadt flow of a Newtonian fluid over a stationary stretchable disk subject to uniform suction in presence of heat transfer(Elsevier, 2025) Mukherjee, Dip; Alveroglu, Burhan; Sahoo, BikashThis study examines the hydrodynamic stability of an incompressible, Newtonian viscous fluid rotating above a stationary disk within a three-dimensional B & ouml;dewadt boundary layer, with a focus on the critical role of stability in practical applications involving rotating machinery and thermal management systems. The investigation explores the combined effects of surface stretching and induced suction on flow behaviour and convective instability characteristics, addressing a key challenge in ensuring stable operational conditions. The lower disk undergoes uniform radial expansion with an induced suction system, and similarity transformations convert the Navier-Stokes equations into a system of coupled ordinary differential equations (ODEs). The mean flow velocity profiles were numerically obtained, and the stability curves were derived through linear stability analysis using a Chebyshev polynomial discretisation approach. Results demonstrate that surface stretching and induced suction significantly enhance stability, particularly in mitigating Type I (cross-flow) instability, a crucial factor in optimising engineering systems reliant on rotating flows. The local stability analysis confirmed the flow stability across the examined parameter range, while the energy analysis the maximum amplification points further supports these findings. By providing a deeper understanding of the flow stabilisation mechanisms, this study offers novel insights with direct implications for industrial and engineering applications requiring precise control of the rotational fluid dynamics.Öğe Investigation of Power-Law Fluid on a Decelerated Rotating Disk(2024) Ayan, Serkan; Alveroglu, BurhanThis study explores the behaviour of power-law fluids over decelerating rotating disks. The disk’s angular velocity decreases inversely with time, and the unsteady governing equations modeling this flow yield similarity transformations that depend on the nondimensional parameter ?ˆ =??0. These transformations, introduced here for the first time in the literature, allow for a comprehensive analysis of the fluid dynamics for shear-thinning fluids within the range 0.5 < n ? 1. We examine the no-slip boundary condition alongside the dimensionless unsteadiness parameter, which quantifies the initial deceleration or acceleration of the disk. We present velocity profiles and the viscosity function for various values of ?ˆ . The boundary layer problem, formulated through dimensionless momentum and continuity equations derived via similarity transformations, is solved using the bvp4c function in MATLAB. This numerical method, employing the 4th-order RungeKutta algorithm, provides approximate solutions for the U, V, and W velocity profiles and the µ viscosity function, considering different deceleration parameters and the power-law index n. Our findings contribute novel insights into the fluid dynamics of power-law fluids in decelerating rotational systems, offering potential applications in industrial and engineering processes where such conditions are prevalent.Öğe On the hydrodynamic instabilities in boundary-layer flows induced by rotating tori(Aip Publishing, 2025) Samad, Abdul; Nawaz, Arab; Ullah, Latif; Alveroglu, BurhanWe present a linear instability analysis of three-dimensional laminar boundary-layer flows over the outer surfaces of rotating families of tori in a quiescent, incompressible fluid using toroidal-poloidal coordinates. The torus, defined by its aspect ratio (major radius to tube radius), includes spindle, horn, and ring tori. With azimuthal symmetry, the analysis is local in the poloidal angle, beginning at a pole or hub circle. The perturbation equations are reduced to sixth-order ordinary differential equations, solved as an eigenvalue problem by a fourth-order Runge-Kutta shooting method with the Gram-Schmidt orthonormalization. A Newton-Raphson procedure then satisfies the dispersion relation to determine spatial stability. Neutral curves for stationary vortices are computed for poloidal angles up to 70 degrees from a pole or hub using a Reynolds number based on the sphere's equatorial radius for aspect ratios from 0 to 7. For an aspect ratio of 0, we reproduce the convective instability results of the rotating sphere. For each fixed torus, higher rotation rates are needed near the pole or hub, while lower rates suffice near the equator. As the aspect ratio increases, lower rotation rates trigger instability at all angles. For aspect ratios below 0.15, crossflow modes dominate up to 60 degrees, with streamline-curvature modes prevailing beyond. For aspect ratios above 0.15, curvature effects vanish but reappear weakly below -30 degrees for aspect ratios above 1.5. Vortex counts and their variation with rotation rates are discussed for all families of tori. Finally, the assumption of non-stationary vortices is considered for the spindle tori.
