Fluid Dynamics Research

Publisher: Nihon Ryūtai Rikigakkai


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    Fluid dynamics research (Online), FDR
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Publications in this journal

  • Fluid Dynamics Research 02/2015; 47(1).
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    ABSTRACT: The effects of inertia on miscible displacements in a Hele-Shaw cell are analyzed. Both linear stability analysis and nonlinear simulations are performed. The results reveal that inertia tends to attenuate viscous fingering. An analysis based on the quasi-steady-state approximation (QSSA) revealed that the growth rate at initial time decreases monotonically as a modified Reynolds number Re* increases, while the most dangerous wavenumber tends to shift toward smaller values. It was also found that the cutoff wavenumber is not affected by inertia and that inertial effects are very limited for longwave instabilities. Initial value calculations extended the QSSA and confirmed the decrease of the growth rate with Re* for long times. Full nonlinear simulations based on a spectral method showed that inertial effects tend to delay the initial development of the instability and result in wider fingers at later breakthrough times. Furthermore, a quantitative analysis of the mixing area shows that inertia can extend the dispersive regime. A re-scaling of the mixing area and time is proposed and the curves at any Peclet and modified Reynolds numbers were superposed onto a single universal curve. With this, the mixing area of any flow with different inertial effects can be predicted.
    Fluid Dynamics Research 02/2015; 47(1).
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    ABSTRACT: The erosion of a granular layer due to the normal impact of a vortex ring was investigated experimentally. We observed two characteristic surface patterns, grooves and dimples, depending on the magnitude of the vortex ring, its travelling distance, and the properties of the granular material. In order to clarify these pattern formation mechanisms, we measured the temporal variation of the layer thickness using the transmitted light intensity, as well as the velocity field using particle image velocimetry. These patterns are found to be generated by successive collisions of the primary vortex ring and the secondary vortex ring which develops on the granular layer.
    Fluid Dynamics Research 11/2014; 46(6):061421.
  • Fluid Dynamics Research 11/2014; 46(6):060001.
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    ABSTRACT: Numerical simulations of viscous flow past a flat plate moving in the direction normal to itself reveal details of the vortical structure of the flow. At early times, most of the vorticity is attached to the plate. This paper introduces a definition of the shed circulation at all times and shows that it indeed represents vorticity that separates and remains separated from the plate. During a large initial time period, the shed circulation satisfies the scaling laws predicted for self-similar inviscid separation. Various contributions to the circulation shedding rate are presented. The results show that during this initial time period, viscous diffusion of vorticity out of the vortex is significant but appears to be independent of the value of the Reynolds number. At later times, the departure of the shed circulation from its large Reynolds number behaviour is significantly affected by diffusive loss of vorticity through the symmetry axis. A timescale is proposed that describes when the viscous loss through the axis becomes relevant. The simulations provide benchmark results to evaluate simpler separation models such as point vortex and vortex sheet models. A comparison with vortex sheet results is included.
    Fluid Dynamics Research 11/2014; 46(6):061420.
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    ABSTRACT: The correction to the propagation velocity of point vortex equilibria caused by allowing the vortices to have finite core size is calculated. A matched asymptotic expansion in the small parameter , given by the ratio of the core size to the dimension of the equilibrium configuration, is carried out. The resulting velocity correction is found to be of order and arises from the interaction of second- and third-order terms in the inner expansion, which are themselves forced by the strain and strain derivatives of the outer field.
    Fluid Dynamics Research 11/2014; 46(6):061419.
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    ABSTRACT: We review research aimed at the development of an analytical and numerical framework for tracking the evolution, in an incompressible viscous fluid, of scalar fields, called 'vortex surface fields' (VSFs), whose instantaneous isosurfaces always contain continuous vortex lines. A set of equations describing the evolution of VSFs starting from a known initial condition is proposed and discussed. Non-uniqueness in the initial-value problem is resolved with the introduction of evolution in a pseudo-time variable where the vorticity, frozen in real time, plays the role of an advecting field. A numerical method for following both the real and pseudo-time evolution is described and its regularization properties are discussed. Examples are given of following VSFs in a viscous Taylor–Green flow (Taylor and Green 1937 Proc. R. Soc. A 158 499–521). The prospects for extending these ideas to fully turbulent flows are discussed.
    Fluid Dynamics Research 11/2014; 46(6):061418.
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    ABSTRACT: The free surface flow in a cylindrical tank over a rotating bottom is known to support spectacular three-dimensional patterns, including deformation of the inner free surface into the shape of rotating polygons and sloshing behavior of the upper free surface (e.g. Iga et al 2014 Fluid Dyn. Res. 46 031409). Through a stability analysis of a simplified model of this flow, we show that such patterns can be explained as a resonance mechanism involving different families of waves. The approach extends a previous work (Tophøj et al 2013 Phys. Rev. Lett. 110 194502) which explained the rotating polygons as an interaction between gravity waves and centrifugal waves, under the assumption that the base flow can be modeled as a potential vortex. We show that this previous model is justified for strong rotation rates (Dry-Potential case), and that for weaker rotations it can be improved by introducing an inner vortex core in solid-body rotation, which either extends to the center of the plate (Wet case) or surrounds a dry central region (Dry-Composite case). The study of this improved model predicts two new kinds of instabilities. The first occurs at low rotations (Wet case) and results from an interaction between gravity waves and the Kelvin–Kirchhoff wave (namely, oscillation of the boundary of the vortex core). This instability is proposed to be at the origin of the sloshing phenomenon. The second new instability occurs, for moderate rotations, (Dry-Composite case) as an interaction between gravity waves and a 'Kelvin-Centrifugal' wave characterized by deformation of the inner surface and the vortex core boundary in opposite directions. This instability exists for all azimuthal wave numbers starting from m = 1, this case corresponding to a 'monogon' pattern.
    Fluid Dynamics Research 10/2014; 46(6):061415.
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    ABSTRACT: Geophysical turbulent flows are characterized by their self-organization into large scale coherent structures, in particular parallel jets. We will present a theory in order to describe the effective statistics and dynamics of these jets. We prove that this closure is exact in the limit of a timescale separation between the forcing and the inertial dynamics, which is rare in a turbulent flow. The equation obtained describes the attractors for the dynamics (alternating zonal jets) and the relaxation towards those attractors. At first order, these attractors are the same as the ones obtained from a quasi-Gaussian closure, already studied. Our work thus justifies this approximation and the corresponding asymptotic limit. We also present a new, very efficient algorithm to compute the terms appearing in this equation. The theory also goes beyond the quasi-Gaussian approximation, and indeed it can also describe the stationary distribution of the jets (fluctuations and large deviations).
    Fluid Dynamics Research 10/2014; 46(6):061416.
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    ABSTRACT: A new method based on the use of the Jones polynomial, a well-known topological invariant of knot theory, is introduced to tackle and quantify topological aspects of structural complexity of vortex tangles in ideal fluids. By re-writing the Jones polynomial in terms of helicity, the resulting polynomial becomes then function of knot topology and vortex circulation, providing thus a new invariant of topological fluid dynamics. Explicit computations of the Jones polynomial for some standard configurations, including the Whitehead link and the Borromean rings (whose linking numbers are zero), are presented for illustration. In the case of a homogeneous, isotropic tangle of vortex filaments with same circulation, the new Jones polynomial reduces to some simple algebraic expression, that can be easily computed by numerical methods. This shows that this technique may offer a new setting and a powerful tool to detect and compute topological complexity and to investigate relations with energy, by tackling fundamental aspects of turbulence research.
    Fluid Dynamics Research 10/2014; 46(6):061412.
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    ABSTRACT: The quasi-cyclic evolution of turbulence driven by a steady force in a periodic cube is investigated by means of large-eddy simulations with vanishing kinematic viscosity. By constraining the domain size so that only a single series of energy cascade events can take place, quasi-cyclic motions of multi-scale coherent vortices with a period of about 20T are realized. (Here, T denotes the turnover time of the largest eddies.) The observed cycle is composed of four periods characterized by activities of the largest- and smallest-resolvable-scale eddies. Vigorous energy cascade events, which last for about 2T, are observed between the two moments when large- and small-scale eddies are active. Even though we have examined only a special case of steady forces, such cyclic behavior of turbulence is likely to capture the essential dynamics of the regeneration cycle of multi-scale coherent structures, that is, the energy cascade in homogeneous isotropic turbulence at high Reynolds numbers.
    Fluid Dynamics Research 10/2014; 46(6):061413.
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    ABSTRACT: In order to study the generation of (aerodynamic) sound in flue instruments, we numerically apply Howeʼs energy corollary for a two-dimensional model of a flue instrument. Howeʼs energy corollary enables us to estimate the energy transfer between the fluid flow and acoustic field. To implement it, separating the acoustic field from the fluid flow is needed. However the complete method to numerically achieve it has not been established yet. In this work, we develop an approximate method, which has been recently proposed in their experimental studies by Yoshikawa et al (2012 J. Sound Vib. 331 2558–77) and others, and we apply it to the simulation of the model instrument. We first calculate fluid flow and acoustic oscillation simultaneously by a compressible fluid solver. Next referring to the information on the acoustic oscillation obtained we set up a pressure source on an acoustic solver and reproduce almost the same acoustic oscillation with it. Combining those results, we are able to calculate Howeʼs energy corollary. The numerical result shows that the aerodynamic sound is generated from the oscillating jet rather than the vortices shed by the collision of it with the edge of the mouth opening, namely vortex shedding.
    Fluid Dynamics Research 10/2014; 46(6):061411.
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    ABSTRACT: Non-trivial bright patterns of reflective flakes recently observed experimentally and numerically in a precessing sphere are reproduced theoretically by the use of a small flat-plate model of flakes with diffusion effects of Brownian motion and the asymptotic velocity field in the double limit of large Reynolds numbers and small Poincar? numbers. It is shown that what is visualized by flakes is not the local flow field but the overall contribution of the velocity gradient, induced by the conical shear layers, over the whole orbit of flakes. It is suggested that Brownian motion plays a significant role to the orientation distribution of flakes.
    Fluid Dynamics Research 10/2014; 46(6):061404.
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    ABSTRACT: In this paper, we study the linear stability of an infinite vortex ring array with respect to the pairing instability, using a spectral code. The base flow solution, obtained after a short relaxation process, is composed of rings with a Gaussian azimuthal vorticity profile. The temporal stability properties are first obtained and compared to the theoretical predictions obtained by Levy and Forsedyke (1927 Proc. R. Soc. Lond. A 114 594–604). The spatio-temporal evolution of a localized perturbation is then computed. The growth rate of the perturbation in the frame moving at the speed v is obtained for all v. The variation of with respect to the parameters of the flow is provided.
    Fluid Dynamics Research 10/2014; 46(6):061405.
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    ABSTRACT: Spontaneous thermoacoustic oscillations of a gas in a closed cylindrical tube are studied. Numerical simulations of the flow field in the tube on which a temperature gradient along the axis is imposed are performed by solving the axisymmetric compressible Navier?Stokes equations. The wall temperature of the hot part near both ends (300 K) and that of the cold part near the center (20 K) are fixed. The computations are done for various values of the length ratio ? of the hot part to the cold part between 0.3 and 1.0, and steady oscillatory states are obtained. These states are divided into three groups according to the magnitude of the pressure amplitude. The state in each group has distinguished features of the flow field. We analyze the effect of vortices on the structure of the temperature distribution. The difference of the boundary layer thickness between the hot part and the cold part is shown to play an important role.
    Fluid Dynamics Research 10/2014; 46(6):061408.
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    ABSTRACT: This paper details a generalized method to, within some numerical tolerance, compute vortex equilibria in the presence of many obstacles. Given a conformal mapping between a pre-image circular domain and the physical domain, stationary conditions for the point vortices and the desired Kutta conditions are constructed and then solved using a Brownian Ratchets scheme. The method is applied to a Kasper Wing (three plate) configuration and results are compared to those of a single plate. The lift experienced by the main plate is seen to be sensitive to the placement of the two additional plates but their presence can be force enhancing for certain configurations.
    Fluid Dynamics Research 10/2014; 46(6):061402.
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    ABSTRACT: Exact partial differential equations are derived to describe Görtler instability, caused by a weakly concave wall, of axisymmetric boundary layers with similar velocity profiles that are decomposed into a sequence of ordinary differential systems on the assumption that the solution can be expanded into inverse powers of local Reynolds number. The leading terms of the series solution are determined by solving a non-parallel version of Görtler’s eigenvalue problem and lead to a neutral stability curve and finite values of critical Görtler number and wave number for stationary and longitudinal vortices. Higher-order terms of the series solution indicate Reynolds-number dependence of Görtler instability and a limited validity of Görtler’s approximation based on the leading terms only. The present formulation is simply applicable to two-dimensional boundary layers of similar profiles, and critical Görtler number and wave number of the Blasius boundary layer on a flat plate are given by G 2c = 1.23 and β 2c = 0.288, respectively, if the momentum thickness is chosen as the reference length.
    Fluid Dynamics Research 10/2014; 46(5).