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Michael T Montgomery - One of the best experts on this subject based on the ideXlab platform.
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simple kinematic models for the environmental interaction of tropical cyclones in vertical wind shear
Atmospheric Chemistry and Physics, 2011Co-Authors: Michael Riemer, Michael T MontgomeryAbstract:Abstract. A major impediment to the intensity forecast of tropical cyclones (TCs) is believed to be associated with the interaction of TCs with dry environmental air. However, the conditions under which pronounced TC-environment interaction takes place are not well understood. As a step towards improving our understanding of this problem, we analyze here the flow topology of a TC immersed in an environment of vertical wind shear in an idealized, three-dimensional, convection-permitting numerical experiment. A set of distinct Streamlines, the so-called manifolds, can be identified under the assumptions of steady and layer-wise horizontal flow. The manifolds are shown to divide the flow around the TC into distinct regions. The manifold structure in our numerical experiment is more complex than the well-known manifold structure of a non-divergent point vortex in uniform background flow. In particular, one manifold spirals inwards and ends in a limit cycle, a meso-scale Dividing Streamline encompassing the eyewall above the layer of strong inflow associated with surface friction and below the outflow layer in the upper troposphere. From the perspective of a steady and layer-wise horizontal flow model, the eyewall is well protected from the intrusion of environmental air. In order for the environmental air to intrude into the inner-core convection, time-dependent and/or vertical motions, which are prevalent in the TC inner-core, are necessary. Air with the highest values of moist-entropy resides within the limit cycle. This "moist envelope" is distorted considerably by the imposed vertical wind shear, and the shape of the moist envelope is closely related to the shape of the limit cycle. In a first approximation, the distribution of high- and low-θe air around the TC at low to mid-levels is governed by the stirring of convectively modified air by the steady, horizontal flow. Motivated by the results from the idealized numerical experiment, an analogue model based on a weakly divergent point vortex in background flow is formulated. The simple kinematic model captures the essence of many salient features of the manifold structure in the numerical experiment. A regime diagram representing realistic values of TC intensity and vertical wind shear can be constructed for the point-vortex model. The results indicate distinct scenarios of environmental interaction depending on the ratio of storm intensity and vertical-shear magnitude. Further implications of the new results derived from the manifold analysis for TCs in the real atmosphere are discussed.
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Simple kinematic models for the environmental interaction of tropical cyclones in vertical wind shear
Copernicus Publications, 2011Co-Authors: Michael Riemer, Michael T MontgomeryAbstract:A major impediment to the intensity forecast of tropical cyclones (TCs) is believed to be associated with the interaction of TCs with dry environmental air. However, the conditions under which pronounced TC-environment interaction takes place are not well understood. As a step towards improving our understanding of this problem, we analyze here the flow topology of a TC immersed in an environment of vertical wind shear in an idealized, three-dimensional, convection-permitting numerical experiment. A set of distinct Streamlines, the so-called manifolds, can be identified under the assumptions of steady and layer-wise horizontal flow. The manifolds are shown to divide the flow around the TC into distinct regions. <br></br> The manifold structure in our numerical experiment is more complex than the well-known manifold structure of a non-divergent point vortex in uniform background flow. In particular, one manifold spirals inwards and ends in a limit cycle, a meso-scale Dividing Streamline encompassing the eyewall above the layer of strong inflow associated with surface friction and below the outflow layer in the upper troposphere. From the perspective of a steady and layer-wise horizontal flow model, the eyewall is well protected from the intrusion of environmental air. In order for the environmental air to intrude into the inner-core convection, time-dependent and/or vertical motions, which are prevalent in the TC inner-core, are necessary. Air with the highest values of moist-entropy resides within the limit cycle. This "moist envelope" is distorted considerably by the imposed vertical wind shear, and the shape of the moist envelope is closely related to the shape of the limit cycle. In a first approximation, the distribution of high- and low-<i>θ</i><sub><i>e</i></sub> air around the TC at low to mid-levels is governed by the stirring of convectively modified air by the steady, horizontal flow. <br></br> Motivated by the results from the idealized numerical experiment, an analogue model based on a weakly divergent point vortex in background flow is formulated. The simple kinematic model captures the essence of many salient features of the manifold structure in the numerical experiment. A regime diagram representing realistic values of TC intensity and vertical wind shear can be constructed for the point-vortex model. The results indicate distinct scenarios of environmental interaction depending on the ratio of storm intensity and vertical-shear magnitude. Further implications of the new results derived from the manifold analysis for TCs in the real atmosphere are discussed
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tropical cyclogenesis in a tropical wave critical layer easterly waves
Atmospheric Chemistry and Physics, 2009Co-Authors: T J Dunkerton, Michael T Montgomery, Zhuo WangAbstract:Abstract. The development of tropical depressions within tropical waves over the Atlantic and eastern Pacific is usually preceded by a "surface low along the wave" as if to suggest a hybrid wave-vortex structure in which flow Streamlines not only undulate with the waves, but form a closed circulation in the lower troposphere surrounding the low. This structure, equatorward of the easterly jet axis, is identified herein as the familiar critical layer of waves in shear flow, a flow configuration which arguably provides the simplest conceptual framework for tropical cyclogenesis resulting from tropical waves, their interaction with the mean flow, and with diabatic processes associated with deep moist convection. The recirculating Kelvin cat's eye within the critical layer represents a sweet spot for tropical cyclogenesis in which a proto-vortex may form and grow within its parent wave. A common location for storm development is given by the intersection of the wave's critical latitude and trough axis at the center of the cat's eye, with analyzed vorticity centroid nearby. The wave and vortex live together for a time, and initially propagate at approximately the same speed. In most cases this coupled propagation continues for a few days after a tropical depression is identified. For easterly waves, as the name suggests, the propagation is westward. It is shown that in order to visualize optimally the associated Lagrangian motions, one should view the flow Streamlines, or stream function, in a frame of reference translating horizontally with the phase propagation of the parent wave. In this co-moving frame, Streamlines are approximately equivalent to particle trajectories. The closed circulation is quasi-stationary, and a Dividing Streamline separates air within the cat's eye from air outside. The critical layer equatorward of the easterly jet axis is important to tropical cyclogenesis because its cat's eye provides (i) a region of cyclonic vorticity and weak deformation by the resolved flow, (ii) containment of moisture entrained by the developing gyre and/or lofted by deep convection therein, (iii) confinement of mesoscale vortex aggregation, (iv) a predominantly convective type of heating profile, and (v) maintenance or enhancement of the parent wave until the vortex becomes a self-sustaining entity and emerges from the wave as a tropical depression. The entire sequence is likened to the development of a marsupial infant in its mother's pouch. These ideas are formulated in three new hypotheses describing the flow kinematics and dynamics, moist thermodynamics and wave/vortex interactions comprising the "marsupial paradigm". A survey of 55 named tropical storms in 1998–2001 reveals that actual critical layers sometimes resemble the ideal east-west train of cat's eyes, but are usually less regular, with one or more recirculation regions in the co-moving frame. It is shown that the kinematics of isolated proto-vortices carried by the wave also can be visualized in a frame of reference translating at or near the phase speed of the parent wave. The proper translation speeds for wave and vortex may vary with height owing to vertical shear and wave-vortex interaction. Some implications for entrainment/containment of vorticity and moisture in the cat's eye are discussed from this perspective, based on the observational survey.
Maria Cristina Patria - One of the best experts on this subject based on the ideXlab platform.
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MHD oblique stagnation-point flow of a Micropolar fluid
Applied Mathematical Modelling, 2012Co-Authors: Alessandra Borrelli, Giulia Giantesio, Maria Cristina PatriaAbstract:Abstract The steady two-dimensional oblique stagnation-point flow of an electrically conducting micropolar fluid in the presence of a uniform external electromagnetic field (E0, H0) is analysed and some physical situations are examined. In particular, if E0 vanishes, H0 lies in the plane of the flow, with a direction not parallel to the boundary, and the induced magnetic field is neglected, it is proved that the oblique stagnation-point flow exists if, and only if, the external magnetic field is parallel to the Dividing Streamline. In all cases it is shown that the governing nonlinear partial differential equations admit similarity solutions and the resulting ordinary differential problems are solved numerically. Finally, the behaviour of the flow near the boundary is analysed; this depends on the three dimensionless material parameters, and also on the Hartmann number if H0 is parallel to the Dividing Streamline.
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MHD oblique stagnation-point flow of a Newtonian fluid
Zeitschrift für angewandte Mathematik und Physik, 2011Co-Authors: Alessandra Borrelli, Giulia Giantesio, Maria Cristina PatriaAbstract:The steady two-dimensional oblique stagnation-point flow of an electrically conducting Newtonian fluid in the presence of a uniform external electromagnetic field (E 0, H 0) is analysed, and some physical situations are examined. In particular, if E 0 vanishes, H 0 lies in the plane of the flow, with a direction not parallel to the boundary, and the induced magnetic field is neglected, it is proved that the oblique stagnation-point flow exists if and only if the external magnetic field is parallel to the Dividing Streamline. In all cases it is shown that the governing nonlinear partial differential equations admit similarity solutions, and the resulting ordinary differential problems are solved numerically. Finally, the behaviour of the flow near the boundary is analysed; this depends on the Hartmann number if H 0 is parallel to the Dividing Streamline.
Gareth H Mckinley - One of the best experts on this subject based on the ideXlab platform.
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extensional rheology and elastic instabilities of a wormlike micellar solution in a microfluidic cross slot device
Soft Matter, 2012Co-Authors: Simon J Haward, Thomas Joseph Ober, Monica Oliveira, M A Alves, Gareth H MckinleyAbstract:Wormlike micellar surfactant solutions are encountered in a wide variety of important applications, including enhanced oil recovery and ink-jet printing, in which the fluids are subjected to high extensional strain rates. In this contribution we present an experimental investigation of the flow of a model wormlike micellar solution (cetyl pyridinium chloride and sodium salicylate in deionised water) in a well-defined stagnation point extensional flow field generated within a microfluidic cross-slot device. We use micro-particle image velocimetry (μ-PIV) and full-field birefringence microscopy coupled with macroscopic measurements of the bulk pressure drop to make a quantitative characterization of the fluid's rheological response over a wide range of deformation rates. The flow field in the micromachined cross-slot is first characterized for viscous flow of a Newtonian fluid, and μ-PIV measurements show the flow field remains symmetric and stable up to moderately high Reynolds number, Re ≈ 20, and nominal strain rate, nom ≈ 635 s−1. By contrast, in the viscoelastic micellar solution the flow field remains symmetric only for low values of the strain rate such that nom ≤ λM−1, where λM = 2.5 s is the Maxwell relaxation time of the fluid. In this stable flow regime the fluid displays a localized and elongated birefringent strand extending along the outflow Streamline from the stagnation point, and estimates of the apparent extensional viscosity can be obtained using the stress-optical rule and from the total pressure drop measured across the cross-slot channel. For moderate deformation rates (nom ≥ λM−1) the flow remains steady, but becomes increasingly asymmetric with increasing flow rate, eventually achieving a steady state of complete anti-symmetry characterized by a Dividing Streamline and birefringent strand connecting diagonally opposite corners of the cross-slot. Eventually, as the nominal imposed deformation rate is increased further, the asymmetric divided flow becomes time dependent. These purely elastic instabilities are reminiscent of those observed in cross-slot flows of polymer solutions, but seem to be strongly influenced by the effects of shear localization of the micellar fluid within the microchannels and around the re-entrant corners of the cross-slot.
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Extensional rheology and elastic instabilities of a wormlike micellar solution in a microfluidic cross-slot device
'Royal Society of Chemistry (RSC)', 2012Co-Authors: Simon J Haward, Thomas Joseph Ober, M A Alves, Mónica S. N. Oliveira, Gareth H MckinleyAbstract:Wormlike micellar surfactant solutions are encountered in a wide variety of important applications, including enhanced oil recovery and ink-jet printing, in which the fluids are subjected to high extensional strain rates. In this contribution we present an experimental investigation of the flow of a model wormlike micellar solution (cetyl pyridinium chloride and sodium salicylate in deionised water) in a well-defined stagnation point extensional flow field generated within a microfluidic cross-slot device. We use micro-particle image velocimetry (mu-PIV) and full-field birefringence microscopy coupled with macroscopic measurements of the bulk pressure drop to make a quantitative characterization of the fluid's rheological response over a wide range of deformation rates. The flow field in the micromachined cross-slot is first characterized for viscous flow of a Newtonian fluid, and mu-PIV measurements show the flow field remains symmetric and stable up to moderately high Reynolds number, Re approximate to 20, and nominal strain rate, (epsilon)over dot(nom) approximate to 635 s(-1). By contrast, in the viscoelastic micellar solution the flow field remains symmetric only for low values of the strain rate such that (epsilon)over dot(nom) = lambda(-1)(M)) the flow remains steady, but becomes increasingly asymmetric with increasing flow rate, eventually achieving a steady state of complete anti-symmetry characterized by a Dividing Streamline and birefringent strand connecting diagonally opposite corners of the cross-slot. Eventually, as the nominal imposed deformation rate is increased further, the asymmetric divided flow becomes time dependent. These purely elastic instabilities are reminiscent of those observed in crossslot flows of polymer solutions, but seem to be strongly influenced by the effects of shear localization of the micellar fluid within the microchannels and around the re-entrant corners of the cross-slot
Harindra J. S. Fernando - One of the best experts on this subject based on the ideXlab platform.
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Stratified Flow Past a Hill: Dividing Streamline Concept Revisited
Boundary-Layer Meteorology, 2016Co-Authors: Laura S. Leo, Michael Y. Thompson, Silvana Di Sabatino, Harindra J. S. FernandoAbstract:The Sheppard formula (Q J R Meteorol Soc 82:528–529, 1956 ) for the Dividing Streamline height $$H_\mathrm{s}$$ H s assumes a uniform velocity $$U_\infty $$ U ∞ and a constant buoyancy frequency N for the approach flow towards a mountain of height h , and takes the form $$H_\mathrm{s}/h=\left( {1-F} \right) $$ H s / h = 1 - F , where $$F=U_{\infty }/Nh$$ F = U ∞ / N h . We extend this solution to a logarithmic approach-velocity profile with constant N . An analytical solution is obtained for $$H_\mathrm{s}/h$$ H s / h in terms of Lambert-W functions, which also suggests alternative scaling for $$H_\mathrm{s}/h$$ H s / h . A ‘modified’ logarithmic velocity profile is proposed for stably stratified atmospheric boundary-layer flows. A field experiment designed to observe $$H_\mathrm{s}$$ H s is described, which utilized instrumentation from the spring field campaign of the Mountain Terrain Atmospheric Modeling and Observations (MATERHORN) Program. Multiple releases of smoke at $$F\approx 0.3$$ F ≈ 0.3 –0.4 support the new formulation, notwithstanding the limited success of experiments due to logistical constraints. No Dividing Streamline is discerned for $$F\approx 10$$ F ≈ 10 , since, if present, it is too close to the foothill. Flow separation and vortex shedding is observed in this case. The proposed modified logarithmic profile is in reasonable agreement with experimental observations.
Michael Riemer - One of the best experts on this subject based on the ideXlab platform.
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simple kinematic models for the environmental interaction of tropical cyclones in vertical wind shear
Atmospheric Chemistry and Physics, 2011Co-Authors: Michael Riemer, Michael T MontgomeryAbstract:Abstract. A major impediment to the intensity forecast of tropical cyclones (TCs) is believed to be associated with the interaction of TCs with dry environmental air. However, the conditions under which pronounced TC-environment interaction takes place are not well understood. As a step towards improving our understanding of this problem, we analyze here the flow topology of a TC immersed in an environment of vertical wind shear in an idealized, three-dimensional, convection-permitting numerical experiment. A set of distinct Streamlines, the so-called manifolds, can be identified under the assumptions of steady and layer-wise horizontal flow. The manifolds are shown to divide the flow around the TC into distinct regions. The manifold structure in our numerical experiment is more complex than the well-known manifold structure of a non-divergent point vortex in uniform background flow. In particular, one manifold spirals inwards and ends in a limit cycle, a meso-scale Dividing Streamline encompassing the eyewall above the layer of strong inflow associated with surface friction and below the outflow layer in the upper troposphere. From the perspective of a steady and layer-wise horizontal flow model, the eyewall is well protected from the intrusion of environmental air. In order for the environmental air to intrude into the inner-core convection, time-dependent and/or vertical motions, which are prevalent in the TC inner-core, are necessary. Air with the highest values of moist-entropy resides within the limit cycle. This "moist envelope" is distorted considerably by the imposed vertical wind shear, and the shape of the moist envelope is closely related to the shape of the limit cycle. In a first approximation, the distribution of high- and low-θe air around the TC at low to mid-levels is governed by the stirring of convectively modified air by the steady, horizontal flow. Motivated by the results from the idealized numerical experiment, an analogue model based on a weakly divergent point vortex in background flow is formulated. The simple kinematic model captures the essence of many salient features of the manifold structure in the numerical experiment. A regime diagram representing realistic values of TC intensity and vertical wind shear can be constructed for the point-vortex model. The results indicate distinct scenarios of environmental interaction depending on the ratio of storm intensity and vertical-shear magnitude. Further implications of the new results derived from the manifold analysis for TCs in the real atmosphere are discussed.
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Simple kinematic models for the environmental interaction of tropical cyclones in vertical wind shear
Copernicus Publications, 2011Co-Authors: Michael Riemer, Michael T MontgomeryAbstract:A major impediment to the intensity forecast of tropical cyclones (TCs) is believed to be associated with the interaction of TCs with dry environmental air. However, the conditions under which pronounced TC-environment interaction takes place are not well understood. As a step towards improving our understanding of this problem, we analyze here the flow topology of a TC immersed in an environment of vertical wind shear in an idealized, three-dimensional, convection-permitting numerical experiment. A set of distinct Streamlines, the so-called manifolds, can be identified under the assumptions of steady and layer-wise horizontal flow. The manifolds are shown to divide the flow around the TC into distinct regions. <br></br> The manifold structure in our numerical experiment is more complex than the well-known manifold structure of a non-divergent point vortex in uniform background flow. In particular, one manifold spirals inwards and ends in a limit cycle, a meso-scale Dividing Streamline encompassing the eyewall above the layer of strong inflow associated with surface friction and below the outflow layer in the upper troposphere. From the perspective of a steady and layer-wise horizontal flow model, the eyewall is well protected from the intrusion of environmental air. In order for the environmental air to intrude into the inner-core convection, time-dependent and/or vertical motions, which are prevalent in the TC inner-core, are necessary. Air with the highest values of moist-entropy resides within the limit cycle. This "moist envelope" is distorted considerably by the imposed vertical wind shear, and the shape of the moist envelope is closely related to the shape of the limit cycle. In a first approximation, the distribution of high- and low-<i>θ</i><sub><i>e</i></sub> air around the TC at low to mid-levels is governed by the stirring of convectively modified air by the steady, horizontal flow. <br></br> Motivated by the results from the idealized numerical experiment, an analogue model based on a weakly divergent point vortex in background flow is formulated. The simple kinematic model captures the essence of many salient features of the manifold structure in the numerical experiment. A regime diagram representing realistic values of TC intensity and vertical wind shear can be constructed for the point-vortex model. The results indicate distinct scenarios of environmental interaction depending on the ratio of storm intensity and vertical-shear magnitude. Further implications of the new results derived from the manifold analysis for TCs in the real atmosphere are discussed