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Hideshi Hanazaki - One of the best experts on this subject based on the ideXlab platform.
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velocity distribution around a sphere descending in a linearly Stratified Fluid
Journal of Fluid Mechanics, 2017Co-Authors: Shinya Okino, Shinsaku Akiyama, Hideshi HanazakiAbstract:The flow around a sphere descending at constant speed in a salt-Stratified Fluid is observed by particle image velocimetry. A unique characteristic of this flow is the appearance of a thin and high-speed rear jet whose maximum velocity can reach more than five times the sphere velocity. In this study we have investigated how the velocity distributions, especially those in the jet and in the boundary layer of the sphere, vary when the Froude number or the Reynolds number ( : vertical velocity of the sphere, : Brunt–Vaisala frequency, : radius of the sphere, : kinematic viscosity of the Fluid) is changed. The results show that the radius of the jet and the thickness of the boundary layer are comparable, and they decrease for smaller Froude numbers and larger Reynolds numbers. Both of them are estimated at moderate Reynolds numbers by the primitive length scale of the Stratified Fluid ( ), or in non-dimensional form by . The overall velocity distribution in the lee of the sphere is measured to identify the internal wave patterns and their effect on the velocity variation along the jet. Corresponding numerical simulation results using the axisymmetry assumption are in agreement with the experimental results.
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velocity distribution around a sphere descending in a linearly Stratified Fluid
Journal of Fluid Mechanics, 2017Co-Authors: Shinya Okino, Shinsaku Akiyama, Hideshi HanazakiAbstract:The flow around a sphere descending at constant speed in a salt-Stratified Fluid is observed by particle image velocimetry. A unique characteristic of this flow is the appearance of a thin and high-speed rear jet whose maximum velocity can reach more than five times the sphere velocity. In this study we have investigated how the velocity distributions, especially those in the jet and in the boundary layer of the sphere, vary when the Froude number $Fr(=W^{\ast }/N^{\ast }a^{\ast })$ or the Reynolds number $Re(=W^{\ast }(2a^{\ast })/\unicode[STIX]{x1D708}^{\ast })$ ( $W^{\ast }$ : vertical velocity of the sphere, $N^{\ast }$ : Brunt–Vaisala frequency, $a^{\ast }$ : radius of the sphere, $\unicode[STIX]{x1D708}^{\ast }$ : kinematic viscosity of the Fluid) is changed. The results show that the radius of the jet and the thickness of the boundary layer are comparable, and they decrease for smaller Froude numbers and larger Reynolds numbers. Both of them are estimated at moderate Reynolds numbers by the primitive length scale of the Stratified Fluid ( $l_{\unicode[STIX]{x1D708}}^{\ast }=\sqrt{\unicode[STIX]{x1D708}^{\ast }/N^{\ast }}$ ), or in non-dimensional form by $l_{\unicode[STIX]{x1D708}}^{\ast }/2a^{\ast }=(Fr/2Re)^{1/2}$ . The overall velocity distribution in the lee of the sphere is measured to identify the internal wave patterns and their effect on the velocity variation along the jet. Corresponding numerical simulation results using the axisymmetry assumption are in agreement with the experimental results.
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numerical simulation of jets generated by a sphere moving vertically in a Stratified Fluid
Journal of Fluid Mechanics, 2015Co-Authors: Hideshi Hanazaki, S Nakamura, Hiroyasu YoshikawaAbstract:The flow past a sphere moving vertically at constant speeds in a salt-Stratified Fluid is investigated numerically at moderate Reynolds numbers . Time development of the flow shows that the violation of density conservation is the key process for the generation of the buoyant jet observed in the experiments. For example, if the sphere moves downward, isopycnal surfaces are simply deformed and dragged down by the sphere while the density is conserved along the flow. (The flow pattern is inverted if the sphere moves upward. Some explanations are given in the introduction.) Then, the flow will never become steady. As density diffusion becomes effective around the sphere surface and generates a horizontal hole in the isopycnal surface, Fluid with non-conserved density is detached from the isopycnal surface and moves upward to generate a buoyant jet. These processes will constitute a steady state near the sphere. With lengths scaled by the sphere diameter and velocities by the downward sphere velocity, the duration of density conservation at the rear/upper stagnation point, or the maximum distance that the isopycnal surface is dragged downward, is proportional to the Froude number , and estimated well by for and , corresponding to a constant potential energy. The radius of a jet defined by the density and velocity distributions, which would have correlations with the density and velocity boundary layers on the sphere, is estimated well by and respectively for , where is the Schmidt number. Numerical results agree well with the previous experiments, and the origin of the conspicuous bell-shaped structure observed by the shadowgraph method is identified as an internal wave.
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numerical simulation of jets generated by a sphere moving vertically in a Stratified Fluid
Journal of Fluid Mechanics, 2015Co-Authors: Hideshi Hanazaki, S Nakamura, Hiroyasu YoshikawaAbstract:The flow past a sphere moving vertically at constant speeds in a salt-Stratified Fluid is investigated numerically at moderate Reynolds numbers $\mathit{Re}$ . Time development of the flow shows that the violation of density conservation is the key process for the generation of the buoyant jet observed in the experiments. For example, if the sphere moves downward, isopycnal surfaces are simply deformed and dragged down by the sphere while the density is conserved along the flow. (The flow pattern is inverted if the sphere moves upward. Some explanations are given in the introduction.) Then, the flow will never become steady. As density diffusion becomes effective around the sphere surface and generates a horizontal hole in the isopycnal surface, Fluid with non-conserved density is detached from the isopycnal surface and moves upward to generate a buoyant jet. These processes will constitute a steady state near the sphere. With lengths scaled by the sphere diameter and velocities by the downward sphere velocity, the duration of density conservation at the rear/upper stagnation point, or the maximum distance that the isopycnal surface is dragged downward, is proportional to the Froude number $\mathit{Fr}$ , and estimated well by ${\rm\pi}\mathit{Fr}$ for $\mathit{Fr}\gtrsim 1$ and $\mathit{Re}\gtrsim 200$ , corresponding to a constant potential energy. The radius of a jet defined by the density and velocity distributions, which would have correlations with the density and velocity boundary layers on the sphere, is estimated well by $\sqrt{\mathit{Fr }/2\mathit{Re }\mathit{ Sc}}$ and $\sqrt{\mathit{Fr }/2\mathit{Re}}$ respectively for $\mathit{Fr}\lesssim 1$ , where $\mathit{Sc}$ is the Schmidt number. Numerical results agree well with the previous experiments, and the origin of the conspicuous bell-shaped structure observed by the shadowgraph method is identified as an internal wave.
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jets generated by a sphere moving vertically in a Stratified Fluid
Journal of Fluid Mechanics, 2009Co-Authors: Hideshi Hanazaki, K Kashimoto, Tohru OkamuraAbstract:Experiments are performed on the flow past a sphere moving vertically at constant speeds in a salt-Stratified Fluid. Shadowgraph method and fluorescent dye are used for the flow visualization, and particle image velocimetry is used for the velocity measurement in the vertical plane. Vertical ‘jets’ or columnar structures are observed in the shadowgraph for all the Froude numbers Fr (0.2 ≲ Fr ≲ 70) investigated, and the wake structures in the whole parameter space of Fr and the Reynolds number Re (30 ≲ Re ≲ 4000) are classified into seven types, five of which are newly found. Those include two types of thin jets, one of which is short with its top disturbed by internal waves to have a peculiar ‘bell-shaped’ structure, while the other has an indefinitely long length. There are two other new types of jet with periodically generated ‘knots’, one of which is straight, while the other has a spiral structure. A simply meandering jet has also been found. These wake structures are significantly different from those in homogeneous Fluids except under very weak stratification, showing that the stratification effects on vertical motion are much more significant than those on horizontal motion.
Jörg Imberger - One of the best experts on this subject based on the ideXlab platform.
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nonlinear effects in the unsteady critical withdrawal of a Stratified Fluid
Dynamics of Atmospheres and Oceans, 1996Co-Authors: S R Clarke, Jörg ImbergerAbstract:Abstract The evolution of the withdrawal through a line sink of an initially quiescent, Stratified Fluid in a semi-infinite, horizontal duct is investigated in the inviscid, nondiffusive limit. A weakly nonlinear, long-wave formulation of the problem of critical withdrawal is presented, which is then used to study the critical withdrawal of a two-layer Fluid from a sink at the base of the duct. Solutions for the evolution of the interfacial shear front are presented and related to the steady solutions for the critical withdrawal of a two-layer Fluid.
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axisymmetric selective withdrawal in a rotating Stratified Fluid
Journal of Fluid Mechanics, 1993Co-Authors: Stephen G Monismith, Robb N Mcdonald, Jörg ImbergerAbstract:In this paper we consider the axisymmetric flow of a rotating Stratified Fluid into a point sink. Linear analysis of the initial value problem of flow of a linearly Stratified Fluid into a point sink that is suddenly switched on shows that a spatially variable selective withdrawal layer is established through the outward propagation of inertial shear waves. The amplitude of these waves decays with distance from the sink; the e-folding scale of a given mode is equal to the Rossby radius of that mode. As a consequence, the flow reaches an asymptotic state, dependent on viscosity and species diffusion, in which the withdrawal-layer structure only exists for distances less than the Rossby radius based on the wave speed of the lowest mode, R 1 . If the Prandtl number, Pr , is large, then the withdrawal layer slowly re-forms in a time that is O (δ 2 i κ -1 ), such that it extends out much farther to a distance that is O ( R 1 Pr δ 2 i δ -2 e ) rather than O ( R 1 ). Because there is no azimuthal pressure gradient to balance the Coriolis force associated with the radial, sinkward flow, a strong swirling flow develops. Using scaling arguments, we conclude that this swirl causes the withdrawal-layer thickness to grow like $(ft)^{\frac{1}{3}}$ , such that eventually there is no withdrawal layer anywhere in the flow domain. Scaling arguments also suggest that this thickening takes place in finite-size basins. These analyses of swirl-induced thickening and diffusive thinning can be combined to yield a classification scheme that shows how different types of flows are possible depending on the relative sizes of a parameter J , which we define as fQ ( Nhv ) -1 , E (the Ekman number fh 2 v -1 ), and Pr .
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withdrawal of a Stratified Fluid from a rotating channel
Journal of Fluid Mechanics, 1992Co-Authors: Robb N Mcdonald, Jörg ImbergerAbstract:The flow of a Stratified Fluid toward a line sink in a rotating channel of finite width and depth is studied. The withdrawal flow is shown to be established by a set of Kelvin shear waves trapped within a distance of Nh/fn from the right-hand side wall ( f > 0) looking in the direction of propagation, where n = 1, 2,… is the vertical mode number. In addition there are a set of waves (Poincare modes) which propagate away from the sink with a cross-channel modal structure. The withdrawal flow has a boundary-layer structure: far from the right-hand wall the flow resembles that of McDonald & Imberger (1991), whereas close to the right-hand wall the development of the vertical structure of the withdrawal flow resembles that of the non-rotating case due to the presence of Kelvin shear waves. In a narrow channel Kelvin shear waves dominate the establishment of the withdrawal flow. The withdrawal flow is investigated for large times compared to the inertial period, where it is shown that the width of the boundary layer is of the same order as the distance downstream from the sink. The flow within the boundary layer is unsteady as the withdrawal layer thickness δ continues to collapse indefinitely, while outside the boundary layer it is steady with δ ∼ fL / N , L being the horizontal lengthscale downstream from the sink. A scaling analysis is developed for the narrow channel case in which the cross-channel velocity can be ignored. The results are applied to actual field data, where it is shown that the effect of rotation may explain why previous non-rotating theories have been inaccurate in predicting withdrawal layer thickness.
Hiroyasu Yoshikawa - One of the best experts on this subject based on the ideXlab platform.
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numerical simulation of jets generated by a sphere moving vertically in a Stratified Fluid
Journal of Fluid Mechanics, 2015Co-Authors: Hideshi Hanazaki, S Nakamura, Hiroyasu YoshikawaAbstract:The flow past a sphere moving vertically at constant speeds in a salt-Stratified Fluid is investigated numerically at moderate Reynolds numbers . Time development of the flow shows that the violation of density conservation is the key process for the generation of the buoyant jet observed in the experiments. For example, if the sphere moves downward, isopycnal surfaces are simply deformed and dragged down by the sphere while the density is conserved along the flow. (The flow pattern is inverted if the sphere moves upward. Some explanations are given in the introduction.) Then, the flow will never become steady. As density diffusion becomes effective around the sphere surface and generates a horizontal hole in the isopycnal surface, Fluid with non-conserved density is detached from the isopycnal surface and moves upward to generate a buoyant jet. These processes will constitute a steady state near the sphere. With lengths scaled by the sphere diameter and velocities by the downward sphere velocity, the duration of density conservation at the rear/upper stagnation point, or the maximum distance that the isopycnal surface is dragged downward, is proportional to the Froude number , and estimated well by for and , corresponding to a constant potential energy. The radius of a jet defined by the density and velocity distributions, which would have correlations with the density and velocity boundary layers on the sphere, is estimated well by and respectively for , where is the Schmidt number. Numerical results agree well with the previous experiments, and the origin of the conspicuous bell-shaped structure observed by the shadowgraph method is identified as an internal wave.
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numerical simulation of jets generated by a sphere moving vertically in a Stratified Fluid
Journal of Fluid Mechanics, 2015Co-Authors: Hideshi Hanazaki, S Nakamura, Hiroyasu YoshikawaAbstract:The flow past a sphere moving vertically at constant speeds in a salt-Stratified Fluid is investigated numerically at moderate Reynolds numbers $\mathit{Re}$ . Time development of the flow shows that the violation of density conservation is the key process for the generation of the buoyant jet observed in the experiments. For example, if the sphere moves downward, isopycnal surfaces are simply deformed and dragged down by the sphere while the density is conserved along the flow. (The flow pattern is inverted if the sphere moves upward. Some explanations are given in the introduction.) Then, the flow will never become steady. As density diffusion becomes effective around the sphere surface and generates a horizontal hole in the isopycnal surface, Fluid with non-conserved density is detached from the isopycnal surface and moves upward to generate a buoyant jet. These processes will constitute a steady state near the sphere. With lengths scaled by the sphere diameter and velocities by the downward sphere velocity, the duration of density conservation at the rear/upper stagnation point, or the maximum distance that the isopycnal surface is dragged downward, is proportional to the Froude number $\mathit{Fr}$ , and estimated well by ${\rm\pi}\mathit{Fr}$ for $\mathit{Fr}\gtrsim 1$ and $\mathit{Re}\gtrsim 200$ , corresponding to a constant potential energy. The radius of a jet defined by the density and velocity distributions, which would have correlations with the density and velocity boundary layers on the sphere, is estimated well by $\sqrt{\mathit{Fr }/2\mathit{Re }\mathit{ Sc}}$ and $\sqrt{\mathit{Fr }/2\mathit{Re}}$ respectively for $\mathit{Fr}\lesssim 1$ , where $\mathit{Sc}$ is the Schmidt number. Numerical results agree well with the previous experiments, and the origin of the conspicuous bell-shaped structure observed by the shadowgraph method is identified as an internal wave.
Roger Grimshaw - One of the best experts on this subject based on the ideXlab platform.
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coupled ostrovsky equations for internal waves in a shear flow
Physics of Fluids, 2014Co-Authors: Roger Grimshaw, A Alias, K R KhusnutdinovaAbstract:In the context of Fluid flows, the coupled Ostrovsky equations arise when two distinct linear long wave modes have nearly coincident phase speeds in the presence of background rotation. In this paper, nonlinear waves in a Stratified Fluid in the presence of shear flow are investigated both analytically, using techniques from asymptotic perturbation theory, and through numerical simulations. The dispersion relation of the system, based on a three-layer model of a Stratified shear flow, reveals various dynamical behaviours, including the existence of unsteady and steady envelope wave packets.
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steady transcritical flow over a hole parametric map of solutions of the forced korteweg de vries equation
Physics of Fluids, 2010Co-Authors: Roger Grimshaw, Daohua Zhang, K W ChowAbstract:Transcritical flow of a Stratified Fluid over an obstacle, or through a contraction, can be modeled by the forced Korteweg–de Vries equation, which describes a balance among weak nonlinearity, weak dispersion, and small forcing effects. Here we seek steady solutions with constant but different amplitudes upstream and downstream of the forcing region. Our interest is in the case when the forcing has negative polarity, which represents a hole. The effects of the width of the hole and the amplitude of the hole on these steady solutions are investigated.
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transcritical flow of a Stratified Fluid the forced extended korteweg de vries model
Physics of Fluids, 2002Co-Authors: Roger Grimshaw, K.h. Chan, K W ChowAbstract:Transcritical, or resonant, flow of a Stratified Fluid over an obstacle is studied using a forced extended Korteweg–de Vries model. This model is particularly relevant for a two-layer Fluid when the layer depths are near critical, but can also be useful in other similar circumstances. Both quadratic and cubic nonlinearities are present and they are balanced by third-order dispersion. We consider both possible signs for the cubic nonlinear term but emphasize the less-studied case when the cubic nonlinear term and the dispersion term have the same-signed coefficients. In this case, our numerical computations show that two kinds of solitary waves are found in certain parameter regimes. One kind is similar to those of the well-known forced Korteweg–de Vries model and occurs when the cubic nonlinear term is rather small, while the other kind is irregularly generated waves of variable amplitude, which may continually interact. To explain this phenomenon, we develop a hydraulic theory in which the dispersion ter...
K W Chow - One of the best experts on this subject based on the ideXlab platform.
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steady transcritical flow over a hole parametric map of solutions of the forced korteweg de vries equation
Physics of Fluids, 2010Co-Authors: Roger Grimshaw, Daohua Zhang, K W ChowAbstract:Transcritical flow of a Stratified Fluid over an obstacle, or through a contraction, can be modeled by the forced Korteweg–de Vries equation, which describes a balance among weak nonlinearity, weak dispersion, and small forcing effects. Here we seek steady solutions with constant but different amplitudes upstream and downstream of the forcing region. Our interest is in the case when the forcing has negative polarity, which represents a hole. The effects of the width of the hole and the amplitude of the hole on these steady solutions are investigated.
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transcritical flow of a Stratified Fluid the forced extended korteweg de vries model
Physics of Fluids, 2002Co-Authors: Roger Grimshaw, K.h. Chan, K W ChowAbstract:Transcritical, or resonant, flow of a Stratified Fluid over an obstacle is studied using a forced extended Korteweg–de Vries model. This model is particularly relevant for a two-layer Fluid when the layer depths are near critical, but can also be useful in other similar circumstances. Both quadratic and cubic nonlinearities are present and they are balanced by third-order dispersion. We consider both possible signs for the cubic nonlinear term but emphasize the less-studied case when the cubic nonlinear term and the dispersion term have the same-signed coefficients. In this case, our numerical computations show that two kinds of solitary waves are found in certain parameter regimes. One kind is similar to those of the well-known forced Korteweg–de Vries model and occurs when the cubic nonlinear term is rather small, while the other kind is irregularly generated waves of variable amplitude, which may continually interact. To explain this phenomenon, we develop a hydraulic theory in which the dispersion ter...
