Herein, we derive the fractional Laplacian operator as a means to represent the mean friction for... more Herein, we derive the fractional Laplacian operator as a means to represent the mean friction force arising in a turbulent flow: $ \rho \frac{D\bar{\bf u}}{Dt} = -\nabla p + \mu_\alpha \nabla^2\bar{\bf u} + \rho C_\alpha \iiint_{\!-\infty}^\infty \frac{ \bar{\bf u}{\scriptstyle(t,{\bf x}')} - \bar{\bf u}{\scriptstyle(t,{\bf x})} }{|{\bf x}'-{\bf x}|^{\alpha+3}} \,d{\bf x}' $, where $\bar{\bf u}{\scriptstyle(t,{\bf x})}$ is the ensemble-averaged velocity field, $\mu_\alpha$ is an enhanced molecular viscosity, and $C_\alpha$ is a turbulent mixing coefficient (with units (length)$^\alpha$/(time)). The derivation is grounded in Boltzmann kinetic theory, which presumes an equilibrium probability distribution $f_\alpha^{eq}(t,{\bf x},{\bf u})$ of particle speeds. While historically $f_\alpha^{eq}$ has been assumed to be the Maxwell-Boltzmann distribution, we show that any member of the family of L\'evy $\alpha$-stable distributions is a suitable alternative. If $\alpha=2$,...
ObjectiveProcedure-intense specialties, such as surgery or endoscopy, are a major contributor to ... more ObjectiveProcedure-intense specialties, such as surgery or endoscopy, are a major contributor to the impact of the healthcare sector on the environment. We aimed to measure the amount of waste generated during endoscopic procedures and to understand the impact on waste of changing from reusable to single use endoscopes in the USA.DesignWe conducted a 5-day audit (cross-sectional study) of all endoscopies performed at two US academic medical centres with low and a high endoscopy volume (2000 and 13 000 procedures annually, respectively). We calculated the average disposable waste (excluding waste from reprocessing) generated during one endoscopic procedure to estimate waste of all endoscopic procedures generated in the USA annually (18 million). We further estimated the impact of changing from reusable to single-use endoscopes taking reprocessing waste into account.Results278 endoscopies were performed for 243 patients. Each endoscopy generated 2.1 kg of disposable waste (46 L volume...
It is well known that the Navier-Stokes equations can be derived from the Boltzmann Equation, whi... more It is well known that the Navier-Stokes equations can be derived from the Boltzmann Equation, which governs the kinetic theory of gases, upon (i) assuming the Bhatnagar-Gross-Krook collision formulation (a simple relaxation toward an equilibrium distribution), (ii) assuming the Maxwell-Boltzmann form of this equilibrium distribution, and (iii) performing the so-called Chapman-Enskog perturbation expansion under the assumption of a short relaxation time. Herein, we demonstrate that there is an alternate path from Boltzmann to Navier-Stokes (in lieu of the Chapman-Enskog expansion) and that the particular form of the equilibrium distribution is inconsequential, as long as it meets some basic properties such as isotropy in velocity space and integrability of several moments. The essential ingredients are the relaxation formulation of the collision term and the assumption of a short relaxation time. This analysis provides new insights into the connections between kinetic theory and cont...
ABSTRACT Extending the study of geostrophic turbulence to scales beyond the radius of deformation... more ABSTRACT Extending the study of geostrophic turbulence to scales beyond the radius of deformation and to finite vertical displacements is made possible by the derivation of a generalized geostrophic equation. First, some earlier versions of this equation, the various regimes it contains and the invariants are discussed. Then, preliminar3I numerical results are presented, which reveal that the energy cascade toward larger scales can halt at a statistical equilibrium beyond the radius of deformation. This state is characterized by the ...
This chapter presents internal gravity waves, which exist in the presence of vertical stratificat... more This chapter presents internal gravity waves, which exist in the presence of vertical stratification. After the derivation of the dispersion relation and examination of wave properties, the chapter briefly considers mountain waves and nonlinear effects. Vertical-mode decomposition is introduced and treated numerically as an eigenvalue problem
Abstract At timescales longer than about a day, geophysical flows are ordinarily in a nearly geos... more Abstract At timescales longer than about a day, geophysical flows are ordinarily in a nearly geostrophic state, and it is advantageous to capitalize on this property to obtain a simplified dynamical formalism. Here, we derive the traditional quasi-geostrophic dynamics and present some applications in both linear and nonlinear regimes. The central component of quasi-geostrophic models, namely advection of vorticity, requires particular attention in numerical models, for which the Arakawa Jacobian is presented
Herein, we derive the fractional Laplacian operator as a means to represent the mean friction for... more Herein, we derive the fractional Laplacian operator as a means to represent the mean friction force arising in a turbulent flow: $ \rho \frac{D\bar{\bf u}}{Dt} = -\nabla p + \mu_\alpha \nabla^2\bar{\bf u} + \rho C_\alpha \iiint_{\!-\infty}^\infty \frac{ \bar{\bf u}{\scriptstyle(t,{\bf x}')} - \bar{\bf u}{\scriptstyle(t,{\bf x})} }{|{\bf x}'-{\bf x}|^{\alpha+3}} \,d{\bf x}' $, where $\bar{\bf u}{\scriptstyle(t,{\bf x})}$ is the ensemble-averaged velocity field, $\mu_\alpha$ is an enhanced molecular viscosity, and $C_\alpha$ is a turbulent mixing coefficient (with units (length)$^\alpha$/(time)). The derivation is grounded in Boltzmann kinetic theory, which presumes an equilibrium probability distribution $f_\alpha^{eq}(t,{\bf x},{\bf u})$ of particle speeds. While historically $f_\alpha^{eq}$ has been assumed to be the Maxwell-Boltzmann distribution, we show that any member of the family of L\'evy $\alpha$-stable distributions is a suitable alternative. If $\alpha=2$,...
ObjectiveProcedure-intense specialties, such as surgery or endoscopy, are a major contributor to ... more ObjectiveProcedure-intense specialties, such as surgery or endoscopy, are a major contributor to the impact of the healthcare sector on the environment. We aimed to measure the amount of waste generated during endoscopic procedures and to understand the impact on waste of changing from reusable to single use endoscopes in the USA.DesignWe conducted a 5-day audit (cross-sectional study) of all endoscopies performed at two US academic medical centres with low and a high endoscopy volume (2000 and 13 000 procedures annually, respectively). We calculated the average disposable waste (excluding waste from reprocessing) generated during one endoscopic procedure to estimate waste of all endoscopic procedures generated in the USA annually (18 million). We further estimated the impact of changing from reusable to single-use endoscopes taking reprocessing waste into account.Results278 endoscopies were performed for 243 patients. Each endoscopy generated 2.1 kg of disposable waste (46 L volume...
It is well known that the Navier-Stokes equations can be derived from the Boltzmann Equation, whi... more It is well known that the Navier-Stokes equations can be derived from the Boltzmann Equation, which governs the kinetic theory of gases, upon (i) assuming the Bhatnagar-Gross-Krook collision formulation (a simple relaxation toward an equilibrium distribution), (ii) assuming the Maxwell-Boltzmann form of this equilibrium distribution, and (iii) performing the so-called Chapman-Enskog perturbation expansion under the assumption of a short relaxation time. Herein, we demonstrate that there is an alternate path from Boltzmann to Navier-Stokes (in lieu of the Chapman-Enskog expansion) and that the particular form of the equilibrium distribution is inconsequential, as long as it meets some basic properties such as isotropy in velocity space and integrability of several moments. The essential ingredients are the relaxation formulation of the collision term and the assumption of a short relaxation time. This analysis provides new insights into the connections between kinetic theory and cont...
ABSTRACT Extending the study of geostrophic turbulence to scales beyond the radius of deformation... more ABSTRACT Extending the study of geostrophic turbulence to scales beyond the radius of deformation and to finite vertical displacements is made possible by the derivation of a generalized geostrophic equation. First, some earlier versions of this equation, the various regimes it contains and the invariants are discussed. Then, preliminar3I numerical results are presented, which reveal that the energy cascade toward larger scales can halt at a statistical equilibrium beyond the radius of deformation. This state is characterized by the ...
This chapter presents internal gravity waves, which exist in the presence of vertical stratificat... more This chapter presents internal gravity waves, which exist in the presence of vertical stratification. After the derivation of the dispersion relation and examination of wave properties, the chapter briefly considers mountain waves and nonlinear effects. Vertical-mode decomposition is introduced and treated numerically as an eigenvalue problem
Abstract At timescales longer than about a day, geophysical flows are ordinarily in a nearly geos... more Abstract At timescales longer than about a day, geophysical flows are ordinarily in a nearly geostrophic state, and it is advantageous to capitalize on this property to obtain a simplified dynamical formalism. Here, we derive the traditional quasi-geostrophic dynamics and present some applications in both linear and nonlinear regimes. The central component of quasi-geostrophic models, namely advection of vorticity, requires particular attention in numerical models, for which the Arakawa Jacobian is presented
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Papers by Benoit Cushman-roisin