50 research outputs found
Global regularity criterion for the 3D Navier-Stokes equations involving one entry of the velocity gradient tensor
In this paper we provide a sufficient condition, in terms of only one of the
nine entries of the gradient tensor, i.e., the Jacobian matrix of the velocity
vector field, for the global regularity of strong solutions to the
three-dimensional Navier-Stokes equations in the whole space, as well as for
the case of periodic boundary conditions
When Does Eddy Viscosity Damp Subfilter Scales Sufficiently?
Large eddy simulation (LES) seeks to predict the dynamics of spatially filtered turbulent flows. The very essence is that the LES-solution contains only scales of size â„Î, where Î denotes some user-chosen length scale. This property enables us to perform a LES when it is not feasible to compute the full, turbulent solution of the Navier-Stokes equations. Therefore, in case the large eddy simulation is based on an eddy viscosity model we determine the eddy viscosity such that any scales of size <Î are dynamically insignificant. In this paper, we address the following two questions: how much eddy diffusion is needed to (a) balance the production of scales of size smaller than Î; and (b) damp any disturbances having a scale of size smaller than Î initially. From this we deduce that the eddy viscosity Îœe has to depend on the invariants q = Âœtr(S^2) and r =ââ
tr(S^3) of the (filtered) strain rate tensor S. The simplest model is then given by Îœe = 3/2(Î/Ï)^2|r|/q. This model is successfully tested for a turbulent channel flow (ReÏ = 590).
Decay of weak solutions to the 2D dissipative quasi-geostrophic equation
We address the decay of the norm of weak solutions to the 2D dissipative
quasi-geostrophic equation. When the initial data is in only, we prove
that the norm tends to zero but with no uniform rate, that is, there are
solutions with arbitrarily slow decay. For the initial data in ,
with , we are able to obtain a uniform decay rate in . We
also prove that when the norm of the initial data
is small enough, the norms, for have uniform
decay rates. This result allows us to prove decay for the norms, for , when the initial data is in .Comment: A paragraph describing work by Carrillo and Ferreira proving results
directly related to the ones in this paper is added in the Introduction. Rest
of the article remains unchange
Stochastic attractors for shell phenomenological models of turbulence
Recently, it has been proposed that the Navier-Stokes equations and a
relevant linear advection model have the same long-time statistical properties,
in particular, they have the same scaling exponents of their structure
functions. This assertion has been investigate rigorously in the context of
certain nonlinear deterministic phenomenological shell model, the Sabra shell
model, of turbulence and its corresponding linear advection counterpart model.
This relationship has been established through a "homotopy-like" coefficient
which bridges continuously between the two systems. That is, for
one obtains the full nonlinear model, and the corresponding linear
advection model is achieved for . In this paper, we investigate the
validity of this assertion for certain stochastic phenomenological shell models
of turbulence driven by an additive noise. We prove the continuous dependence
of the solutions with respect to the parameter . Moreover, we show the
existence of a finite-dimensional random attractor for each value of
and establish the upper semicontinuity property of this random attractors, with
respect to the parameter . This property is proved by a pathwise
argument. Our study aims toward the development of basic results and techniques
that may contribute to the understanding of the relation between the long-time
statistical properties of the nonlinear and linear models
Reducing the environmental impact of surgery on a global scale: systematic review and co-prioritization with healthcare workers in 132 countries
Background
Healthcare cannot achieve net-zero carbon without addressing operating theatres. The aim of this study was to prioritize feasible interventions to reduce the environmental impact of operating theatres.
Methods
This study adopted a four-phase Delphi consensus co-prioritization methodology. In phase 1, a systematic review of published interventions and global consultation of perioperative healthcare professionals were used to longlist interventions. In phase 2, iterative thematic analysis consolidated comparable interventions into a shortlist. In phase 3, the shortlist was co-prioritized based on patient and clinician views on acceptability, feasibility, and safety. In phase 4, ranked lists of interventions were presented by their relevance to high-income countries and lowâmiddle-income countries.
Results
In phase 1, 43 interventions were identified, which had low uptake in practice according to 3042 professionals globally. In phase 2, a shortlist of 15 intervention domains was generated. In phase 3, interventions were deemed acceptable for more than 90 per cent of patients except for reducing general anaesthesia (84 per cent) and re-sterilization of âsingle-useâ consumables (86 per cent). In phase 4, the top three shortlisted interventions for high-income countries were: introducing recycling; reducing use of anaesthetic gases; and appropriate clinical waste processing. In phase 4, the top three shortlisted interventions for lowâmiddle-income countries were: introducing reusable surgical devices; reducing use of consumables; and reducing the use of general anaesthesia.
Conclusion
This is a step toward environmentally sustainable operating environments with actionable interventions applicable to both highâ and lowâmiddleâincome countries
Vanishing viscosity limits and long-time behavior for 2D quasi-geostrophic equations
We study the 2D surface quasi-geostrophic equation for thermal active scalars, that is an equation arising in the study of fast rotating ïŹuids. This equation is a model problem
for the 3D Euler equation. We consider the problem of convergence of solutions of the viscous problem to the ones of the inviscid problem. We also consider the long time behavior and we discuss the various kind of attractors that make sense for the quasi-geostrophic equation
Sufficient conditions for the regularity of the solutions of the Navier-Stokes equations
Some results on the Navier-Stokes equations with Navier boundary conditions
A b s t r a c t . I make an overview of some results concerning the Stokes and Navier-
Stokes equations, supplemented with the Navier's type slip boundary conditions. I
try to explain the interest for this problem, the main analytical results, and also the
differences between the flat case and more general cases. Some recent results
concerning the vanishing viscosity limits are also announced