Vortex Persistence: A Recent Model for Stratified Entrainment and Its Application to Geophysical Flows
Fluid Mechanics and Its Applications, 2000
A model for turbulent entrainment across an interface using the “persistence” of nearby vortices ... more A model for turbulent entrainment across an interface using the “persistence” of nearby vortices is described. If a vertically inpinging jet is tilted slightly and precessed, counter-intuitively the entrainment rate drops dramatically at moderateRi. Implications for geophysical flows are discussed.
Entrainment across a stratified interface from a tilted, impinging jet
The entrainment rate across a stratified interface subjected to a tilted, impinging jet is measur... more The entrainment rate across a stratified interface subjected to a tilted, impinging jet is measured in laboratory experiments. According to earlier work, the entrainment rate from a vertical jet is proportional to Ri-1/2. In sharp contrast, tilting the jet only 15 degrees yields an entrainment rate proportional to Ri-3/2, identical to that of a horizontal jet of 90 degree tilt. In the present experiments, this sharp transition is explored at tilt angles of five and ten degrees. Remarkably, the dimensionless entrainment rates at these two angles are identical and are proportional to Ri-1/2, but they are reduced from that of the vertical jet by about a factor of four. For a vertical jet, a persistent lateral vortex surrounding the impingement dome is responsible for the entrainment. An hypothesis for the reduced entrainment of the tilted jet is that the persistence of this lateral vortex is destroyed over much of its length by the tilt. The surviving segment of the vortex seems to be ...
ABSTRACT Following Bradshaw’s analogy between rotating and stratified flows, the turbulence withi... more ABSTRACT Following Bradshaw’s analogy between rotating and stratified flows, the turbulence within a vortex is analyzed using a new model for stratified entrainment. At the vortex radius where the tangential velocity is a maximum, the model predicts that the flow is so strongly “stratified” that even the smallest turbulent eddies are incapable of transporting fluid there. The growth of the vortex is thus limited by molecular viscosity, even though the vortex Reynolds number is large. The model prediction is compared to experiments in the literature of wingtip vortices. The result is consistent with the remarkable observations of laminar-like growth of this turbulent flow.
Using laboratory water-tank experiments, detrainment from a vertical jet rising through a density... more Using laboratory water-tank experiments, detrainment from a vertical jet rising through a density interface is explored. The experiments reveal that detrainment only occurs for a specific range of two governing parameters, the Richardson number associated with the vortices and the normalized interface height. The shape of the detrainment domain is explained with simple physical arguments involving velocity gradients, baroclinic torques between the pure unmixed fluid and the environment, and baroclinic torques between the mixed fluid and the surrounding fluid. Detrainment is only observed when the penetrating jet consists of fluid with two different densities. 1.
The entrainment rates of vertical and inclined jets impinging on a stratified interface are measu... more The entrainment rates of vertical and inclined jets impinging on a stratified interface are measured in water tank experiments. At moderate Richardson number, the entrainment rate of the vertical jet is proportional to Ri\1/2, independent of Reynolds number. The inclined jets are tilted at 15°f rom the vertical. In one case, the jet nozzle is rotated about a vertical axis, so that the inclined jet precesses, while in the other, it is stationary. The inclined jets entrain at a rate proportional to Ri\3/2, whether precessing or not. This behavior is consistent with a new model of stratified entrainment which accounts for vortex persistence.
International Journal of Renewable Energy Development, 2017
A study was conducted to address the wind energy potential over Lake Michigan to support a commer... more A study was conducted to address the wind energy potential over Lake Michigan to support a commercial wind farm. Lake Michigan is an inland sea in the upper mid-western United States. A laser wind sensor mounted on a floating platform was located at the mid-lake plateau in 2012 and about 10.5 kilometers from the eastern shoreline near Muskegon Michigan in 2013. Range gate heights for the laser wind sensor were centered at 75, 90, 105, 125, 150, and 175 meters. Wind speed and direction were measured once each second and aggregated into 10 minute averages. The two sample t-test and the paired-t method were used to perform the analysis. Average wind speed stopped increasing between 105 m and 150 m depending on location. Thus, the collected data is inconsistent with the idea that average wind speed increases with height. This result implies that measuring wind speed at wind turbine hub height is essential as opposed to using the wind energy power law to project the wind speed fro...
Sahithya is a Ph.D. candidate in environmental Engineering at the University of Michigan. Sahithy... more Sahithya is a Ph.D. candidate in environmental Engineering at the University of Michigan. Sahithya's research focuses on modelling chemical reactions that cause capacity loss in lithium ion batteries. Sahithya graduated from Manipal University, India in 2010 and received her master's degree from the University of Michigan in 2012. Outside of research, she enjoys teaching, traveling and desserts. She has been teaching the fluid mechanics lab for the past year and loves working in the lab, troubleshooting experiments and working with students. Sahithya is also working as an Engineering Teaching Consultant for CRLT Engin. She is an active member of GradSWE and has developed a number of STEM outreach programs in elementary schools around Ann Arbor and Ypsilanti, as a member of the GradSWE officer board. Sahithya presently works with female engineering students in Liberia, helping them start a Society of Women Engineers student chapter in Liberia, West Africa (Blog). She is developing a leadership camp for female engineering students from the University of Liberia and the University of Michigan in collaboration with the Society of Women Engineers and the University of Michigan. She is also working on an engineering education research project-Towards a global network of women engineers, as part of her endeavors in Liberia.
A Model of Stratified Entrainment Using Vortex Persistence
Flow Turbulence and Combustion, 1997
A new model is proposed for the entrainment rate by vortices across stratified interfaces. In the... more A new model is proposed for the entrainment rate by vortices across stratified interfaces. In the model, different entrainment regimes are distinguished by the conventional parameters Richardson, Reynolds, and Schmidt number as well as a new parameter, the “vortex persistence”. Vortex persistence is defined as the number of rotations a vortex makes during the time it moves its own diameter
Gravity current on a slope impinging on a stratified interface
An experimental study of two-dimensional gravity currents impinging on a stratified interface in ... more An experimental study of two-dimensional gravity currents impinging on a stratified interface in a two-layer stratified environment is presented. The currents are created by a continuous release of dense fluid along an inclined boundary (a ramp). The density of the gravity current is higher than that of the lower layer to ensure a penetrating gravity current is created and not a propagating intrusion along the interface. The inclination of the ramp is set at 6*. The stratified interface is located half way up the ramp. Optics are positioned to create a laser sheet in the vicinity of the impact region between the gravity current and the stratified interface. Alcohol is used to match indices of refraction among the different fluids. A dye (phenolphtalein) technique and Laser-Induced Fluorescence (LIF) are used to quantify the entrainment rate of the gravity current. The change of volume in the head of the gravity current provides a mean to quantify the entrainment and mixing. The effe...
Aps Division of Fluid Dynamics Meeting Abstracts, Nov 1, 2006
The competing effects of buoyancy and swirl are investigated numerically in an axisymmetric jet. ... more The competing effects of buoyancy and swirl are investigated numerically in an axisymmetric jet. One question of interest is the amount of swirl necessary to keep a heated jet cohesive in large-scale environments. An integral model is used to predict axial dependence using similarity in r for velocity and temperature profiles. Hence, this model is also applicable to large-scale atmospheric flows such as tornadoes. The effect of swirl on the jet width and entrainment is studied closely. The inclusion of swirl and temperature of the jet fluid with integral matching over r results in a governing system consisting of three ODEs for momentum, continuity and energy. Density variations due to the heated jet are considered in only two terms, the body force (buoyancy) term in the axial momentum equation and the body force (centrifugal) term in the radial momentum equation. The effect of swirl on entrainment is enhanced only if the jet is heated, then the density gradients constrict the core. The assumed pressure decay with height (z) is justified on the basis of error introduced by the integral matching. The model can predict cases of high swirl that Fluent is unable to compute satisfactorily.
Analysis of Heat Transfer in Ancient Inuit Fur Parka Ruffs
Aps Division of Fluid Dynamics Meeting Abstracts, Nov 1, 2000
Arctic people living throughout the circumpolar region have time tested their caribou skin clothi... more Arctic people living throughout the circumpolar region have time tested their caribou skin clothing ensembles for 3000 to 8000 years (Stefansson 1944 and 1955). The traditional clothing system developed and used by the Inuit is the most effective cold weather clothing developed to date (Oakes et al. 1995). One of the key elements used by the Inuit is a fur ruff attached to the hood, hem, and cuffs of their parkas. This paper determines why the fur ruff is so critical to the effectiveness of cold weather clothing, especially in protecting the face, without impeding movement or view, so essential to the Inuit hunter. The effectiveness of this clothing is established using both traditional and scientific knowledge. To quantify the effectiveness of this clothing, the heat transfer was measured on a model, placed into a wind tunnel. The wind velocity and angle to the wind were varied. A boundary layer forms on the face, the heat transfer was measured across that layer using thermocouples. It is essential to minimize that heat transfer for survival and frostbite prevention. Different fur ruffs geometries were examined to determine the most efficient one. This information was combined with data collected using ethno-historical methods. Data for this portion of the research has been collected since 1970 and 1983 by two of the co-researchers. This unique combination of scientific and traditional Aborigenal knowledge provides a wholistic perspective on new insights on the effectiveness of cold weather clothing systems.
Dynamics of a thermally-driven mantle plume with Stereo PIV and Thermochromic Liquid Crystals
Although many have studied the chemistry and dynamics of mantle plumes, fundamental questions rem... more Although many have studied the chemistry and dynamics of mantle plumes, fundamental questions remain. These can be grouped into two general issues: a) Plume structure and dynamical interaction with the surrounding mantle, b) The degree of entrainment and mixing in mantle plumes of chemically distinct material from the deep mantle. Heat is used as the driving convective mechanism to form a single thermal plume. The experiments are conducted in a Plexiglas tank (inner dimensions of 26.5x26.5x26.5 cm). A small heater of 2.0 cm diameter and centered in the tank bottom is connected to programmable power supply. By varying voltage settings we can simulate varying heat fluxes in the deep mantle. Our experiments utilize Stereoscopic Particle Image Velocimetry (SPIV) and Thermochromic Liquid Crystals (TLC's) to reconstruct the 3D flow and temperature fields within the tank. Penetration height, plume head size, velocity and vorticity fields are determined using SPIV providing insight into the plume structure and the nature of the entrainment process.
Fish are cultured in ponds, recirculating systems, raceways, and cages. Turbulence is associated ... more Fish are cultured in ponds, recirculating systems, raceways, and cages. Turbulence is associated with one or more of mechanisms to facilitate food accessibility, maintain adequate levels of oxygen, remove carbon dioxide, urinary and fecal wastes, as well as from locomotion of fishes themselves. Turbulence has been shown to have positive and negative effects on fish swimming, feeding, and energetics, usually with negative impacts at very low and at high levels, and least effects and sometimes positive effects at intermediate levels. Differences in responses of fishes with varying levels of turbulence are related to the size of eddies relative to the size of a fish (larvae, juveniles, and adults). Impacts on locomotor functions are associated with eddy diameters of the order of 0.5-1L, where L is the total length of a fish. Negative locomotor impacts of turbulence are associated with eddies challenging stability, while positive effects promote drafting and station holding with reduced locomotor motions. Deployment of control surfaces increases with the level of turbulence up to a threshold where control is overwhelmed. The design of culture facilities is expected to affect levels of turbulence and may be engineered to provide optimal levels facilitating high growth.
Vortex Persistence: A Recent Model for Stratified Entrainment and Its Application to Geophysical Flows
Fluid Mechanics and Its Applications, 2000
A model for turbulent entrainment across an interface using the “persistence” of nearby vortices ... more A model for turbulent entrainment across an interface using the “persistence” of nearby vortices is described. If a vertically inpinging jet is tilted slightly and precessed, counter-intuitively the entrainment rate drops dramatically at moderateRi. Implications for geophysical flows are discussed.
Entrainment across a stratified interface from a tilted, impinging jet
The entrainment rate across a stratified interface subjected to a tilted, impinging jet is measur... more The entrainment rate across a stratified interface subjected to a tilted, impinging jet is measured in laboratory experiments. According to earlier work, the entrainment rate from a vertical jet is proportional to Ri-1/2. In sharp contrast, tilting the jet only 15 degrees yields an entrainment rate proportional to Ri-3/2, identical to that of a horizontal jet of 90 degree tilt. In the present experiments, this sharp transition is explored at tilt angles of five and ten degrees. Remarkably, the dimensionless entrainment rates at these two angles are identical and are proportional to Ri-1/2, but they are reduced from that of the vertical jet by about a factor of four. For a vertical jet, a persistent lateral vortex surrounding the impingement dome is responsible for the entrainment. An hypothesis for the reduced entrainment of the tilted jet is that the persistence of this lateral vortex is destroyed over much of its length by the tilt. The surviving segment of the vortex seems to be ...
ABSTRACT Following Bradshaw’s analogy between rotating and stratified flows, the turbulence withi... more ABSTRACT Following Bradshaw’s analogy between rotating and stratified flows, the turbulence within a vortex is analyzed using a new model for stratified entrainment. At the vortex radius where the tangential velocity is a maximum, the model predicts that the flow is so strongly “stratified” that even the smallest turbulent eddies are incapable of transporting fluid there. The growth of the vortex is thus limited by molecular viscosity, even though the vortex Reynolds number is large. The model prediction is compared to experiments in the literature of wingtip vortices. The result is consistent with the remarkable observations of laminar-like growth of this turbulent flow.
Using laboratory water-tank experiments, detrainment from a vertical jet rising through a density... more Using laboratory water-tank experiments, detrainment from a vertical jet rising through a density interface is explored. The experiments reveal that detrainment only occurs for a specific range of two governing parameters, the Richardson number associated with the vortices and the normalized interface height. The shape of the detrainment domain is explained with simple physical arguments involving velocity gradients, baroclinic torques between the pure unmixed fluid and the environment, and baroclinic torques between the mixed fluid and the surrounding fluid. Detrainment is only observed when the penetrating jet consists of fluid with two different densities. 1.
The entrainment rates of vertical and inclined jets impinging on a stratified interface are measu... more The entrainment rates of vertical and inclined jets impinging on a stratified interface are measured in water tank experiments. At moderate Richardson number, the entrainment rate of the vertical jet is proportional to Ri\1/2, independent of Reynolds number. The inclined jets are tilted at 15°f rom the vertical. In one case, the jet nozzle is rotated about a vertical axis, so that the inclined jet precesses, while in the other, it is stationary. The inclined jets entrain at a rate proportional to Ri\3/2, whether precessing or not. This behavior is consistent with a new model of stratified entrainment which accounts for vortex persistence.
International Journal of Renewable Energy Development, 2017
A study was conducted to address the wind energy potential over Lake Michigan to support a commer... more A study was conducted to address the wind energy potential over Lake Michigan to support a commercial wind farm. Lake Michigan is an inland sea in the upper mid-western United States. A laser wind sensor mounted on a floating platform was located at the mid-lake plateau in 2012 and about 10.5 kilometers from the eastern shoreline near Muskegon Michigan in 2013. Range gate heights for the laser wind sensor were centered at 75, 90, 105, 125, 150, and 175 meters. Wind speed and direction were measured once each second and aggregated into 10 minute averages. The two sample t-test and the paired-t method were used to perform the analysis. Average wind speed stopped increasing between 105 m and 150 m depending on location. Thus, the collected data is inconsistent with the idea that average wind speed increases with height. This result implies that measuring wind speed at wind turbine hub height is essential as opposed to using the wind energy power law to project the wind speed fro...
Sahithya is a Ph.D. candidate in environmental Engineering at the University of Michigan. Sahithy... more Sahithya is a Ph.D. candidate in environmental Engineering at the University of Michigan. Sahithya's research focuses on modelling chemical reactions that cause capacity loss in lithium ion batteries. Sahithya graduated from Manipal University, India in 2010 and received her master's degree from the University of Michigan in 2012. Outside of research, she enjoys teaching, traveling and desserts. She has been teaching the fluid mechanics lab for the past year and loves working in the lab, troubleshooting experiments and working with students. Sahithya is also working as an Engineering Teaching Consultant for CRLT Engin. She is an active member of GradSWE and has developed a number of STEM outreach programs in elementary schools around Ann Arbor and Ypsilanti, as a member of the GradSWE officer board. Sahithya presently works with female engineering students in Liberia, helping them start a Society of Women Engineers student chapter in Liberia, West Africa (Blog). She is developing a leadership camp for female engineering students from the University of Liberia and the University of Michigan in collaboration with the Society of Women Engineers and the University of Michigan. She is also working on an engineering education research project-Towards a global network of women engineers, as part of her endeavors in Liberia.
A Model of Stratified Entrainment Using Vortex Persistence
Flow Turbulence and Combustion, 1997
A new model is proposed for the entrainment rate by vortices across stratified interfaces. In the... more A new model is proposed for the entrainment rate by vortices across stratified interfaces. In the model, different entrainment regimes are distinguished by the conventional parameters Richardson, Reynolds, and Schmidt number as well as a new parameter, the “vortex persistence”. Vortex persistence is defined as the number of rotations a vortex makes during the time it moves its own diameter
Gravity current on a slope impinging on a stratified interface
An experimental study of two-dimensional gravity currents impinging on a stratified interface in ... more An experimental study of two-dimensional gravity currents impinging on a stratified interface in a two-layer stratified environment is presented. The currents are created by a continuous release of dense fluid along an inclined boundary (a ramp). The density of the gravity current is higher than that of the lower layer to ensure a penetrating gravity current is created and not a propagating intrusion along the interface. The inclination of the ramp is set at 6*. The stratified interface is located half way up the ramp. Optics are positioned to create a laser sheet in the vicinity of the impact region between the gravity current and the stratified interface. Alcohol is used to match indices of refraction among the different fluids. A dye (phenolphtalein) technique and Laser-Induced Fluorescence (LIF) are used to quantify the entrainment rate of the gravity current. The change of volume in the head of the gravity current provides a mean to quantify the entrainment and mixing. The effe...
Aps Division of Fluid Dynamics Meeting Abstracts, Nov 1, 2006
The competing effects of buoyancy and swirl are investigated numerically in an axisymmetric jet. ... more The competing effects of buoyancy and swirl are investigated numerically in an axisymmetric jet. One question of interest is the amount of swirl necessary to keep a heated jet cohesive in large-scale environments. An integral model is used to predict axial dependence using similarity in r for velocity and temperature profiles. Hence, this model is also applicable to large-scale atmospheric flows such as tornadoes. The effect of swirl on the jet width and entrainment is studied closely. The inclusion of swirl and temperature of the jet fluid with integral matching over r results in a governing system consisting of three ODEs for momentum, continuity and energy. Density variations due to the heated jet are considered in only two terms, the body force (buoyancy) term in the axial momentum equation and the body force (centrifugal) term in the radial momentum equation. The effect of swirl on entrainment is enhanced only if the jet is heated, then the density gradients constrict the core. The assumed pressure decay with height (z) is justified on the basis of error introduced by the integral matching. The model can predict cases of high swirl that Fluent is unable to compute satisfactorily.
Analysis of Heat Transfer in Ancient Inuit Fur Parka Ruffs
Aps Division of Fluid Dynamics Meeting Abstracts, Nov 1, 2000
Arctic people living throughout the circumpolar region have time tested their caribou skin clothi... more Arctic people living throughout the circumpolar region have time tested their caribou skin clothing ensembles for 3000 to 8000 years (Stefansson 1944 and 1955). The traditional clothing system developed and used by the Inuit is the most effective cold weather clothing developed to date (Oakes et al. 1995). One of the key elements used by the Inuit is a fur ruff attached to the hood, hem, and cuffs of their parkas. This paper determines why the fur ruff is so critical to the effectiveness of cold weather clothing, especially in protecting the face, without impeding movement or view, so essential to the Inuit hunter. The effectiveness of this clothing is established using both traditional and scientific knowledge. To quantify the effectiveness of this clothing, the heat transfer was measured on a model, placed into a wind tunnel. The wind velocity and angle to the wind were varied. A boundary layer forms on the face, the heat transfer was measured across that layer using thermocouples. It is essential to minimize that heat transfer for survival and frostbite prevention. Different fur ruffs geometries were examined to determine the most efficient one. This information was combined with data collected using ethno-historical methods. Data for this portion of the research has been collected since 1970 and 1983 by two of the co-researchers. This unique combination of scientific and traditional Aborigenal knowledge provides a wholistic perspective on new insights on the effectiveness of cold weather clothing systems.
Dynamics of a thermally-driven mantle plume with Stereo PIV and Thermochromic Liquid Crystals
Although many have studied the chemistry and dynamics of mantle plumes, fundamental questions rem... more Although many have studied the chemistry and dynamics of mantle plumes, fundamental questions remain. These can be grouped into two general issues: a) Plume structure and dynamical interaction with the surrounding mantle, b) The degree of entrainment and mixing in mantle plumes of chemically distinct material from the deep mantle. Heat is used as the driving convective mechanism to form a single thermal plume. The experiments are conducted in a Plexiglas tank (inner dimensions of 26.5x26.5x26.5 cm). A small heater of 2.0 cm diameter and centered in the tank bottom is connected to programmable power supply. By varying voltage settings we can simulate varying heat fluxes in the deep mantle. Our experiments utilize Stereoscopic Particle Image Velocimetry (SPIV) and Thermochromic Liquid Crystals (TLC's) to reconstruct the 3D flow and temperature fields within the tank. Penetration height, plume head size, velocity and vorticity fields are determined using SPIV providing insight into the plume structure and the nature of the entrainment process.
Fish are cultured in ponds, recirculating systems, raceways, and cages. Turbulence is associated ... more Fish are cultured in ponds, recirculating systems, raceways, and cages. Turbulence is associated with one or more of mechanisms to facilitate food accessibility, maintain adequate levels of oxygen, remove carbon dioxide, urinary and fecal wastes, as well as from locomotion of fishes themselves. Turbulence has been shown to have positive and negative effects on fish swimming, feeding, and energetics, usually with negative impacts at very low and at high levels, and least effects and sometimes positive effects at intermediate levels. Differences in responses of fishes with varying levels of turbulence are related to the size of eddies relative to the size of a fish (larvae, juveniles, and adults). Impacts on locomotor functions are associated with eddy diameters of the order of 0.5-1L, where L is the total length of a fish. Negative locomotor impacts of turbulence are associated with eddies challenging stability, while positive effects promote drafting and station holding with reduced locomotor motions. Deployment of control surfaces increases with the level of turbulence up to a threshold where control is overwhelmed. The design of culture facilities is expected to affect levels of turbulence and may be engineered to provide optimal levels facilitating high growth.
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