Oscillatory oblique stagnation-point flow toward a plane wall

Two-dimensional oscillatory oblique stagnation-point flow toward a plane wall is investigated. The problem is a eneralisation of the steady oblique stagnation-point flow examined by previous workers. Far from the wall, the flow is composed of an irrotational orthogonal stagnation-point flow with a time-periodic strength, a simple shear flow of constant vorticity, and a time-periodic uniform stream. An exact solution of the Navier-Stokes equations is sought for which the flow streamfunction depends linearly on the coordinate parallel to the wall. The problem formulation reduces to a coupled pair of partial differential equations in time and one spatial variable. The first equation describes the oscillatory orthogonal stagnation-point flow discussed by previous workers. The second equation, which couples to the first, describes the oblique component of the flow. A description of the flow velocity field, the instantaneous streamlines, and the particle paths is sought through numerical solutions of the governing equations and via asymptotic analysis

Effects of a synthetic jet acting on a separated flow over a hump

The effects of an oscillatory zero-net-mass-flux jet (i.e. synthetic jet) acting on a separated flow over a hump are investigated in terms of two actuation parameters – actuator position and forcing frequency. By considering the vorticity flux balance and introducing a centroid of vorticity production over the hump surface, lift and drag acting on the hump can be expressed as a function of this centroid and the rate of vorticity production. To study the parametric dependence of lift and drag, direct numerical simulation (DNS) is performed by solving compressible, unsteady, laminar flows over a half-cylindrical hump in two dimensions. The DNS results show that periodic actuation significantly reduces the rate of vorticity production at the wall and shifts the centroid upstream so that the drag is reduced and the lift is increased, respectively. When the actuation parameters are varied, it is found that the lift is governed by the horizontal coordinate of the vorticity-production centroid, while the drag is determined by both the vertical coordinate of the centroid and the rate of vorticity production over the hump. This paper explains by using ideal flow models that the vorticity-production centroid is controlled by two factors: one is the actuator position at which clockwise vorticity is generated, and the other is the point where the separation vortex is pinched off, thereby the clockwise vorticity being absorbed

Oscillatory Flows Induced by Microorganisms Swimming in Two-dimensions

We present the first time-resolved measurements of the oscillatory velocity field induced by swimming unicellular microorganisms. Confinement of the green alga C. reinhardtii in stabilized thin liquid films allows simultaneous tracking of cells and tracer particles. The measured velocity field reveals complex time-dependent flow structures, and scales inversely with distance. The instantaneous mechanical power generated by the cells is measured from the velocity fields and peaks at 15 fW. The dissipation per cycle is more than four times what steady swimming would require.Comment: 4 pages, 4 figure

Heat transfer in steady-periodic flows over heated microwires

Effects of Reynolds number (Re), nondimensional drive frequency (Srp) and amplitude of yoscillations in the flow on the heat transfer coefficient and its frequency response characteristics for oscillatory flows over a micro wire are presented here. Time-averaged Nusselt numbers (Nu) at the stagnation point and averaged over the cylinder are calculated for Re = 10, 30 and 50, .001 < Srp < 1., and oscillation amplitudes, Vp, of 0.1 and 0.2 (for Re = 50). We used a formulation that allows decomposition of the flow into mean and periodic components, and used finite-element simulations to solve for the mean flow over the cylinder. Periodic component of the flow contributes to an artificial body force in the Navier-Stokes equation. According to our simulations, time-averaged Nusselt numbers are not strongly affected by oscillations. Largest increase in the time-averaged average Nu is only 3% larger than its unforced value. Nusselt oscillations have multiple modes and we used Fourier Transform to identify each mode and calculate its corresponding amplitude. The mode for which the frequency is twice as much as the driving frequency is the dominant mode for Srp up to 0.1 for all Reynolds numbers studied here. For larger drive frequencies, the second mode dies off; for Re = 30 and 50 amplitude of the first mode at the drive frequency takes over. For large drive frequencies (Srp~1) all modes tend to diminish

Fractional Fourier approximations for potential gravity waves on deep water

In the framework of the canonical model of hydrodynamics, where fluid is assumed to be ideal and incompressible, waves are potential, two-dimensional, and symmetric, the authors have recently reported the existence of a new type of gravity waves on deep water besides well studied Stokes waves (Phys. Rev. Lett., 2002, v. 89, 164502). The distinctive feature of these waves is that horizontal water velocities in the wave crests exceed the speed of the crests themselves. Such waves were found to describe irregular flows with stagnation point inside the flow domain and discontinuous streamlines near the wave crests. Irregular flows produce a simple model for describing the initial stage of the formation of spilling breakers when a localized jet is formed at the crest following by generating whitecaps. In the present work, a new highly efficient method for computing steady potential gravity waves on deep water is proposed to examine the above results in more detail. The method is based on the truncated fractional approximations for the velocity potential in terms of the basis functions $1/\bigr(1-\exp(y_0-y-ix)\bigl)^n$, $y_0$ being a free parameter. The non-linear transformation of the horizontal scale $x = \chi - \gamma \sin\chi, 0<\gamma<1,$ is additionally applied to concentrate a numerical emphasis on the crest region of a wave for accelerating the convergence of the series. Fractional approximations were employed for calculating both steep Stokes waves and irregular flows. For lesser computational time, the advantage in accuracy over ordinary Fourier expansions in terms the basis functions $\exp\bigl(n (y+ix)\bigr)$ was found to be from one to ten decimal orders depending on the wave steepness and flow parameters.Comment: 14 pages, 8 figures, submitted to Nonlinear Processes in Geophysic

Polymer stress growth in viscoelastic fluids in oscillating extensional flows with applications to micro-organism locomotion

Simulations of undulatory swimming in viscoelastic fluids with large amplitude gaits show concentration of polymer elastic stress at the tips of the swimmers.We use a series of related theoretical investigations to probe the origin of these concentrated stresses. First the polymer stress is computed analytically at a given oscillating extensional stagnation point in a viscoelastic fluid. The analysis identifies a Deborah number (De) dependent Weissenberg number (Wi) transition below which the stress is linear in Wi, and above which the stress grows exponentially in Wi. Next, stress and velocity are found from numerical simulations in an oscillating 4-roll mill geometry. The stress from these simulations is compared with the theoretical calculation of stress in the decoupled (given flow) case, and similar stress behavior is observed. The flow around tips of a time-reversible flexing filament in a viscoelastic fluid is shown to exhibit an oscillating extension along particle trajectories, and the stress response exhibits similar transitions. However in the high amplitude, high De regime the stress feedback on the flow leads to non time-reversible particle trajectories that experience asymmetric stretching and compression, and the stress grows more significantly in this regime. These results help explain past observations of large stress concentration for large amplitude swimmers and non-monotonic dependence on De of swimming speeds

Marangoni instability of a heated liquid layer in the presence of a soluble surfactant

We consider the influence of adsorption kinetics on a longwave oscillatory instability in a layer of a binary liquid heated from below. It is shown that an advection of the adsorbed surfactant leads to a strong stabilization of the mode. Qualitative explanation of the numerical results is provided