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M. Wolstencroft - One of the best experts on this subject based on the ideXlab platform.
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nusselt Rayleigh Number scaling for spherical shell earth mantle simulation up to a Rayleigh Number of 109
Physics of the Earth and Planetary Interiors, 2009Co-Authors: M. Wolstencroft, J.h. Davies, David DaviesAbstract:Abstract An investigation of the power law relationship between Nusselt Number (Nu) and Rayleigh Number (Ra) for Earth’s convecting mantle is presented. The Nu(Ra) relationship was calculated from the results of a model with three dimensional spherical geometry and free slip boundary conditions. Both basally and internally heated convection has been examined. For Nu ( Ra ) = a Ra β , β was found to be 0.294 ± 0.004 for basally heated systems, which is lower than the value of 1/3 suggested by conventional boundary layer theory. The exponent β = 0.337 ± 0.009 for internally heated systems, when the internally heated Ra is converted to a basally heated equivalent for comparison. The influence of the method used to calculate β was also considered, with particular attention paid to high Ra. As an example of the significance of β = 0.29 rather than 1/3, a Ra of 1 0 9 results in a surface heat flux which is ≈ 32% lower. Within the range of Ra used in this study, there is no evidence that β changes at high Ra. Therefore, that mechanism cannot be used to moderate mantle temperature when projecting back to early Earth conditions. The differing planform of basally and internally heated models was shown to result in different scaling relationships between root mean square surface velocity and Ra for the two modes of heating, in particular, a much lower surface velocity for internally heated cases relative to equivalent Ra basally heated cases.
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Nusselt-Rayleigh Number scaling for spherical shell Earth mantle simulation up to a Rayleigh Number of 10
Physics of the Earth and Planetary Interiors, 2009Co-Authors: M. Wolstencroft, J.h. Davies, D.r. DaviesAbstract:An investigation of the power law relationship between Nusselt Number (Nu) and Rayleigh Number (Ra) for Earth's convecting mantle is presented. The Nu(Ra) relationship was calculated from the results of a model with three dimensional spherical geometry and free slip boundary conditions. Both basally and internally heated convection has been examined. For ()=, was found to be 0.294±0.004 for basally heated systems, which is lower than the value of 1/3 suggested by conventional boundary layer theory. The exponent =0.337±0.009 for internally heated systems, when the internally heated Ra is converted to a basally heated equivalent for comparison. The influence of the method used to calculate was also considered, with particular attention paid to high Ra. As an example of the significance of =0.29 rather than 1/3, a Ra of 10 results in a surface heat flux which is ≈ 32% lower. Within the range of Ra used in this study, there is no evidence that changes at high Ra. Therefore, that mechanism cannot be used to moderate mantle temperature when projecting back to early Earth conditions. The differing planform of basally and internally heated models was shown to result in different scaling relationships between root mean square surface velocity and Ra for the two modes of heating, in particular, a much lower surface velocity for internally heated cases relative to equivalent Ra basally heated cases.
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Nusselt–Rayleigh Number scaling for spherical shell Earth mantle simulation up to a Rayleigh Number of 109
Physics of the Earth and Planetary Interiors, 2009Co-Authors: M. Wolstencroft, J.h. Davies, David DaviesAbstract:Abstract An investigation of the power law relationship between Nusselt Number (Nu) and Rayleigh Number (Ra) for Earth’s convecting mantle is presented. The Nu(Ra) relationship was calculated from the results of a model with three dimensional spherical geometry and free slip boundary conditions. Both basally and internally heated convection has been examined. For Nu ( Ra ) = a Ra β , β was found to be 0.294 ± 0.004 for basally heated systems, which is lower than the value of 1/3 suggested by conventional boundary layer theory. The exponent β = 0.337 ± 0.009 for internally heated systems, when the internally heated Ra is converted to a basally heated equivalent for comparison. The influence of the method used to calculate β was also considered, with particular attention paid to high Ra. As an example of the significance of β = 0.29 rather than 1/3, a Ra of 1 0 9 results in a surface heat flux which is ≈ 32% lower. Within the range of Ra used in this study, there is no evidence that β changes at high Ra. Therefore, that mechanism cannot be used to moderate mantle temperature when projecting back to early Earth conditions. The differing planform of basally and internally heated models was shown to result in different scaling relationships between root mean square surface velocity and Ra for the two modes of heating, in particular, a much lower surface velocity for internally heated cases relative to equivalent Ra basally heated cases.
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Nusselt–Rayleigh Number scaling for spherical shell Earth mantle simulation up to a Rayleigh Number of
Physics of the Earth and Planetary Interiors, 2009Co-Authors: M. Wolstencroft, J.h. Davies, D.r. DaviesAbstract:International audienceAn investigation of the power law relationship between Nusselt Number (Nu) and Rayleigh Number (Ra) for Earth's convecting mantle is presented. The Nu(Ra) relationship was calculated from the results of a model with three dimensional spherical geometry and free slip boundary conditions. Both basally and internally heated convection has been examined. For ()=, was found to be 0.294±0.004 for basally heated systems, which is lower than the value of 1/3 suggested by conventional boundary layer theory. The exponent =0.337±0.009 for internally heated systems, when the internally heated Ra is converted to a basally heated equivalent for comparison. The influence of the method used to calculate was also considered, with particular attention paid to high Ra. As an example of the significance of =0.29 rather than 1/3, a Ra of 10 results in a surface heat flux which is ≈ 32% lower. Within the range of Ra used in this study, there is no evidence that changes at high Ra. Therefore, that mechanism cannot be used to moderate mantle temperature when projecting back to early Earth conditions. The differing planform of basally and internally heated models was shown to result in different scaling relationships between root mean square surface velocity and Ra for the two modes of heating, in particular, a much lower surface velocity for internally heated cases relative to equivalent Ra basally heated cases
D.r. Davies - One of the best experts on this subject based on the ideXlab platform.
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Nusselt-Rayleigh Number scaling for spherical shell Earth mantle simulation up to a Rayleigh Number of 10
Physics of the Earth and Planetary Interiors, 2009Co-Authors: M. Wolstencroft, J.h. Davies, D.r. DaviesAbstract:An investigation of the power law relationship between Nusselt Number (Nu) and Rayleigh Number (Ra) for Earth's convecting mantle is presented. The Nu(Ra) relationship was calculated from the results of a model with three dimensional spherical geometry and free slip boundary conditions. Both basally and internally heated convection has been examined. For ()=, was found to be 0.294±0.004 for basally heated systems, which is lower than the value of 1/3 suggested by conventional boundary layer theory. The exponent =0.337±0.009 for internally heated systems, when the internally heated Ra is converted to a basally heated equivalent for comparison. The influence of the method used to calculate was also considered, with particular attention paid to high Ra. As an example of the significance of =0.29 rather than 1/3, a Ra of 10 results in a surface heat flux which is ≈ 32% lower. Within the range of Ra used in this study, there is no evidence that changes at high Ra. Therefore, that mechanism cannot be used to moderate mantle temperature when projecting back to early Earth conditions. The differing planform of basally and internally heated models was shown to result in different scaling relationships between root mean square surface velocity and Ra for the two modes of heating, in particular, a much lower surface velocity for internally heated cases relative to equivalent Ra basally heated cases.
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Nusselt–Rayleigh Number scaling for spherical shell Earth mantle simulation up to a Rayleigh Number of
Physics of the Earth and Planetary Interiors, 2009Co-Authors: M. Wolstencroft, J.h. Davies, D.r. DaviesAbstract:International audienceAn investigation of the power law relationship between Nusselt Number (Nu) and Rayleigh Number (Ra) for Earth's convecting mantle is presented. The Nu(Ra) relationship was calculated from the results of a model with three dimensional spherical geometry and free slip boundary conditions. Both basally and internally heated convection has been examined. For ()=, was found to be 0.294±0.004 for basally heated systems, which is lower than the value of 1/3 suggested by conventional boundary layer theory. The exponent =0.337±0.009 for internally heated systems, when the internally heated Ra is converted to a basally heated equivalent for comparison. The influence of the method used to calculate was also considered, with particular attention paid to high Ra. As an example of the significance of =0.29 rather than 1/3, a Ra of 10 results in a surface heat flux which is ≈ 32% lower. Within the range of Ra used in this study, there is no evidence that changes at high Ra. Therefore, that mechanism cannot be used to moderate mantle temperature when projecting back to early Earth conditions. The differing planform of basally and internally heated models was shown to result in different scaling relationships between root mean square surface velocity and Ra for the two modes of heating, in particular, a much lower surface velocity for internally heated cases relative to equivalent Ra basally heated cases
David Davies - One of the best experts on this subject based on the ideXlab platform.
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nusselt Rayleigh Number scaling for spherical shell earth mantle simulation up to a Rayleigh Number of 109
Physics of the Earth and Planetary Interiors, 2009Co-Authors: M. Wolstencroft, J.h. Davies, David DaviesAbstract:Abstract An investigation of the power law relationship between Nusselt Number (Nu) and Rayleigh Number (Ra) for Earth’s convecting mantle is presented. The Nu(Ra) relationship was calculated from the results of a model with three dimensional spherical geometry and free slip boundary conditions. Both basally and internally heated convection has been examined. For Nu ( Ra ) = a Ra β , β was found to be 0.294 ± 0.004 for basally heated systems, which is lower than the value of 1/3 suggested by conventional boundary layer theory. The exponent β = 0.337 ± 0.009 for internally heated systems, when the internally heated Ra is converted to a basally heated equivalent for comparison. The influence of the method used to calculate β was also considered, with particular attention paid to high Ra. As an example of the significance of β = 0.29 rather than 1/3, a Ra of 1 0 9 results in a surface heat flux which is ≈ 32% lower. Within the range of Ra used in this study, there is no evidence that β changes at high Ra. Therefore, that mechanism cannot be used to moderate mantle temperature when projecting back to early Earth conditions. The differing planform of basally and internally heated models was shown to result in different scaling relationships between root mean square surface velocity and Ra for the two modes of heating, in particular, a much lower surface velocity for internally heated cases relative to equivalent Ra basally heated cases.
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Nusselt–Rayleigh Number scaling for spherical shell Earth mantle simulation up to a Rayleigh Number of 109
Physics of the Earth and Planetary Interiors, 2009Co-Authors: M. Wolstencroft, J.h. Davies, David DaviesAbstract:Abstract An investigation of the power law relationship between Nusselt Number (Nu) and Rayleigh Number (Ra) for Earth’s convecting mantle is presented. The Nu(Ra) relationship was calculated from the results of a model with three dimensional spherical geometry and free slip boundary conditions. Both basally and internally heated convection has been examined. For Nu ( Ra ) = a Ra β , β was found to be 0.294 ± 0.004 for basally heated systems, which is lower than the value of 1/3 suggested by conventional boundary layer theory. The exponent β = 0.337 ± 0.009 for internally heated systems, when the internally heated Ra is converted to a basally heated equivalent for comparison. The influence of the method used to calculate β was also considered, with particular attention paid to high Ra. As an example of the significance of β = 0.29 rather than 1/3, a Ra of 1 0 9 results in a surface heat flux which is ≈ 32% lower. Within the range of Ra used in this study, there is no evidence that β changes at high Ra. Therefore, that mechanism cannot be used to moderate mantle temperature when projecting back to early Earth conditions. The differing planform of basally and internally heated models was shown to result in different scaling relationships between root mean square surface velocity and Ra for the two modes of heating, in particular, a much lower surface velocity for internally heated cases relative to equivalent Ra basally heated cases.
J.h. Davies - One of the best experts on this subject based on the ideXlab platform.
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nusselt Rayleigh Number scaling for spherical shell earth mantle simulation up to a Rayleigh Number of 109
Physics of the Earth and Planetary Interiors, 2009Co-Authors: M. Wolstencroft, J.h. Davies, David DaviesAbstract:Abstract An investigation of the power law relationship between Nusselt Number (Nu) and Rayleigh Number (Ra) for Earth’s convecting mantle is presented. The Nu(Ra) relationship was calculated from the results of a model with three dimensional spherical geometry and free slip boundary conditions. Both basally and internally heated convection has been examined. For Nu ( Ra ) = a Ra β , β was found to be 0.294 ± 0.004 for basally heated systems, which is lower than the value of 1/3 suggested by conventional boundary layer theory. The exponent β = 0.337 ± 0.009 for internally heated systems, when the internally heated Ra is converted to a basally heated equivalent for comparison. The influence of the method used to calculate β was also considered, with particular attention paid to high Ra. As an example of the significance of β = 0.29 rather than 1/3, a Ra of 1 0 9 results in a surface heat flux which is ≈ 32% lower. Within the range of Ra used in this study, there is no evidence that β changes at high Ra. Therefore, that mechanism cannot be used to moderate mantle temperature when projecting back to early Earth conditions. The differing planform of basally and internally heated models was shown to result in different scaling relationships between root mean square surface velocity and Ra for the two modes of heating, in particular, a much lower surface velocity for internally heated cases relative to equivalent Ra basally heated cases.
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Nusselt-Rayleigh Number scaling for spherical shell Earth mantle simulation up to a Rayleigh Number of 10
Physics of the Earth and Planetary Interiors, 2009Co-Authors: M. Wolstencroft, J.h. Davies, D.r. DaviesAbstract:An investigation of the power law relationship between Nusselt Number (Nu) and Rayleigh Number (Ra) for Earth's convecting mantle is presented. The Nu(Ra) relationship was calculated from the results of a model with three dimensional spherical geometry and free slip boundary conditions. Both basally and internally heated convection has been examined. For ()=, was found to be 0.294±0.004 for basally heated systems, which is lower than the value of 1/3 suggested by conventional boundary layer theory. The exponent =0.337±0.009 for internally heated systems, when the internally heated Ra is converted to a basally heated equivalent for comparison. The influence of the method used to calculate was also considered, with particular attention paid to high Ra. As an example of the significance of =0.29 rather than 1/3, a Ra of 10 results in a surface heat flux which is ≈ 32% lower. Within the range of Ra used in this study, there is no evidence that changes at high Ra. Therefore, that mechanism cannot be used to moderate mantle temperature when projecting back to early Earth conditions. The differing planform of basally and internally heated models was shown to result in different scaling relationships between root mean square surface velocity and Ra for the two modes of heating, in particular, a much lower surface velocity for internally heated cases relative to equivalent Ra basally heated cases.
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Nusselt–Rayleigh Number scaling for spherical shell Earth mantle simulation up to a Rayleigh Number of 109
Physics of the Earth and Planetary Interiors, 2009Co-Authors: M. Wolstencroft, J.h. Davies, David DaviesAbstract:Abstract An investigation of the power law relationship between Nusselt Number (Nu) and Rayleigh Number (Ra) for Earth’s convecting mantle is presented. The Nu(Ra) relationship was calculated from the results of a model with three dimensional spherical geometry and free slip boundary conditions. Both basally and internally heated convection has been examined. For Nu ( Ra ) = a Ra β , β was found to be 0.294 ± 0.004 for basally heated systems, which is lower than the value of 1/3 suggested by conventional boundary layer theory. The exponent β = 0.337 ± 0.009 for internally heated systems, when the internally heated Ra is converted to a basally heated equivalent for comparison. The influence of the method used to calculate β was also considered, with particular attention paid to high Ra. As an example of the significance of β = 0.29 rather than 1/3, a Ra of 1 0 9 results in a surface heat flux which is ≈ 32% lower. Within the range of Ra used in this study, there is no evidence that β changes at high Ra. Therefore, that mechanism cannot be used to moderate mantle temperature when projecting back to early Earth conditions. The differing planform of basally and internally heated models was shown to result in different scaling relationships between root mean square surface velocity and Ra for the two modes of heating, in particular, a much lower surface velocity for internally heated cases relative to equivalent Ra basally heated cases.
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Nusselt–Rayleigh Number scaling for spherical shell Earth mantle simulation up to a Rayleigh Number of
Physics of the Earth and Planetary Interiors, 2009Co-Authors: M. Wolstencroft, J.h. Davies, D.r. DaviesAbstract:International audienceAn investigation of the power law relationship between Nusselt Number (Nu) and Rayleigh Number (Ra) for Earth's convecting mantle is presented. The Nu(Ra) relationship was calculated from the results of a model with three dimensional spherical geometry and free slip boundary conditions. Both basally and internally heated convection has been examined. For ()=, was found to be 0.294±0.004 for basally heated systems, which is lower than the value of 1/3 suggested by conventional boundary layer theory. The exponent =0.337±0.009 for internally heated systems, when the internally heated Ra is converted to a basally heated equivalent for comparison. The influence of the method used to calculate was also considered, with particular attention paid to high Ra. As an example of the significance of =0.29 rather than 1/3, a Ra of 10 results in a surface heat flux which is ≈ 32% lower. Within the range of Ra used in this study, there is no evidence that changes at high Ra. Therefore, that mechanism cannot be used to moderate mantle temperature when projecting back to early Earth conditions. The differing planform of basally and internally heated models was shown to result in different scaling relationships between root mean square surface velocity and Ra for the two modes of heating, in particular, a much lower surface velocity for internally heated cases relative to equivalent Ra basally heated cases
David A. Yuen - One of the best experts on this subject based on the ideXlab platform.
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High Rayleigh Number Mantle Convection on GPU
Lecture Notes in Earth System Sciences, 2013Co-Authors: David A. Sanchez, Christopher M. Gonzalez, David A. Yuen, Grady B. Wright, Gregory A. BarnettAbstract:We implemented two- and three-dimensional Rayleigh–Benard convection on Nvidia GPUs by utilizing a 2nd-order finite difference method. By exploiting the massive parallelism of GPU using both CUDA for C and optimized CUBLAS routines, we have on a single Fermi GPU run simulations of Rayleigh Number up to \(6\times 10^{10}\) (on a mesh of \(2000 \times 4000\) uniform grid points) in two dimensions and up to 10\(^{7}\) (on a mesh of \(450\times 450\times 225\) uniform grid points) for three dimensions. On Nvidia Tesla C2070 GPUs, these implementations enjoy single-precision performance of 535 GFLOP/s and 100 GFLOP/s respectively, and double-precision performance of 230 GFLOP/s and 70 GFLOP/s respectively.
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Visualization and analysis of high Rayleigh Number: 3D convection in the earth's mantle
2002Co-Authors: Gordon Erlebacher, David A. Yuen, Fabien DubuffetAbstract:Data sets from large-scale simulations (up to 501 3 grid points) of mantle convection are analyzed with volume rendering of the temperature field and a new critical point analysis of the velocity field. As the Rayleigh Number Ra is increased the thermal field develops increasingly thin plume-like structures along which heat is convected. These eventually break down and become turbulent. Visualization methods are used to distinguish between various models of heat conductivity and to develop an intuitive understanding of the structure of the flow.
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Secondary upwelling instabilities developed in high Rayleigh Number convection: Possible applications to hot spots
Visual Geosciences, 2000Co-Authors: Marylee S. Murphy, Ludek Vecsey, Erik O. D. Sevre, David A. YuenAbstract:We have conducted numerical experiments for mantle convection in an axisymmetrical spherical-shell geometry from Rayleigh Numbers ranging from three million to 10 billion for a purely basal heating configuration. We focus on the development of secondary instabilities developed from plumes and compare them with laboratory experiments by Skilbeck and Whitehead (1978) and Whitehead, (1982). For Rayleigh Numbers between around thirty million to one billion, a string of these secondary instabilities can develop from a single plume. Analysis of the spectrum of wavelength associated with the fold instabilities shows that there is a window in the Rayleigh Number between around ten million and one bilion where these secondary folding instabilities would develop. These results, when applied to the upper mantle, may explain the formation of hot-spots in a turbulently convecting upper-mantle with a Rayleigh Number greater than ten million.
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A high-order finite-difference method applied to large Rayleigh Number mantle convection
Geophysical and Astrophysical Fluid Dynamics, 1997Co-Authors: Tine B. Larsen, David A. Yuen, Jiří Moser, Bengt FornbergAbstract:Abstract A variable-grid, high-order finite difference (FD) method is applied to the modeling of mantle convection in both two- and three-dimensional geometries. The algorithm combines extreme simplicity in programming with a very high degree of accuracy. Memory requirements are low and grow almost linearly with the total Number of grid points in three dimensions, regardless of the increase in grid points in the vertical direction. Higher-order methods, such as eighth order, yield significantly better results than a second-order method for the same grid size, with only a modest increase in memory requirements. This is particularly important for high Rayleigh Number convection, where the large Number of grid points required to obtain an accurate enough solution with second-order schemes would make the computation extremely costly. The small-scale features in the hard-turbulent regime under high-Rayleigh Number situations can greatly stress low-order methods, and in these situations a high-order method is d...
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High Rayleigh Number regime of temperature‐dependent viscosity convection and the Earth's early thermal history
Geophysical Research Letters, 1993Co-Authors: Ulrich Hansen, David A. YuenAbstract:We have carried out steady-state calculations of thermal convection with strongly temperature-dependent viscosity, spanning six decades in surface Rayleigh Number (Ras). The style of convection undergoes a transition from a stagnant-lid regime to a constant-viscosity-like regime at sufficiently high Ras. For viscosity variations of 10³ this transition would occur at around Ras of O (107) with attendant Nusselt (Nu) Numbers of around 50. This transition in the style of convection with Ra suggests that there might be a change in the style of convection and surface features in the very young Earth, when the surface Rayleigh Number was much higher from greenhouse effects, which took place in the last part of the accretionary period.
