scholarly journals On the time to tracer equilibrium in the global ocean

Ocean Science ◽  
2009 ◽  
Vol 5 (1) ◽  
pp. 13-28 ◽  
Author(s):  
F. Primeau ◽  
E. Deleersnijder
Keyword(s):  
Boundary Condition ◽  
Ocean Circulation ◽  
Deep Sea ◽  
Neumann Boundary Condition ◽  
Three Dimensional ◽  
Neumann Boundary ◽  
Sea Surface ◽  
Global Ocean ◽  
Surface Boundary ◽  
Surface Boundary Condition

Abstract. An important issue for the interpretation of data from deep-sea cores is the time for tracers to be transported from the sea surface to the deep ocean. Global ocean circulation models can help shed light on the timescales over which a tracer comes to equilibrium in different regions of the ocean. In this note, we discuss how the most slowly decaying eigenmode of a model can be used to obtain a relevant timescale for a tracer that enters through the sea surface to become well mixed in the ocean interior. We show how this timescale depends critically on the choice between a Neumann surface boundary condition in which the flux of tracer is prescribed, a Robin surface boundary condition in which a combination of the flux and tracer concentration is prescribed or a Dirichlet surface boundary condition in which the concentration is prescribed. Explicit calculations with a 3-box model and a three-dimensional ocean circulation model show that the Dirichlet boundary condition when applied to only part of the surface ocean greatly overestimate the time needed to reach equilibrium. As a result regional-"injection" calculations which prescribe the surface concentration instead of the surface flux are not relevant for interpreting the regional disequilibrium between the Atlantic and Pacific found in paleo-tracer records from deep-sea cores. For tracers that enter the ocean through air-sea gas exchange a prescribed concentration boundary condition can be used to infer relevant timescales if the air-sea gas exchange rate is sufficiently fast, but the boundary condition must be applied over the entire ocean surface and not only to a patch of limited area. For tracers with a slow air-sea exchange rate such as 14C a Robin-type boundary condition is more relevant and for tracers such as δ18O that enter the ocean from melt water, a Neumann boundary condition is presumably more relevant. Our three-dimensional model results based on a steady-state modern circulation suggest that the relative disequilibrium between the deep Atlantic and Pacific is on the order of "only" 1200 years or less for a Neumann boundary condition and does not depend on the size and location of the patch where the tracer is injected.

scholarly journals On the time to tracer equilibrium in the global ocean

2008 ◽  
Vol 5 (3) ◽  
pp. 471-506
Author(s):  
F. Primeau ◽  
E. Deleersnijder
Keyword(s):  
Boundary Condition ◽  
Ocean Circulation ◽  
Dirichlet Boundary Condition ◽  
Deep Sea ◽  
Dirichlet Boundary ◽  
Three Dimensional ◽  
Sea Surface ◽  
Global Ocean ◽  
Surface Boundary ◽  
Surface Boundary Condition

Abstract. An important issue for the interpretation of data from deep-sea cores is the time for tracers to be transported from the sea surface to the deep ocean. Global ocean circulation models can help shed light on the timescales over which a tracer comes to equilibrium in different regions of the ocean. In this note, we discuss how the most slowly decaying eigenmode of a model can be used to obtain a relevant timescale for a tracer that enters through the sea surface to become well mixed in the ocean interior. We show how this timescale depends critically on the choice between a Neumann surface boundary condition in which the flux of tracer is prescribed or a Dirichlet surface boundary condition in which the concentration is prescribed. Explicit calculations with a 3-box model and a three-dimensional ocean circulation model show that the Dirichlet boundary condition when applied to only part of the surface ocean greatly overestimate the time needed to reach equilibrium. As a result regional-"injection" calculations which prescribe the surface concentration instead of the surface flux are not relevant for interpreting the regional disequilibrium between the Atlantic and Pacific found in paleo-tracer records from deep-sea cores. For tracers such as δ18O that enter the ocean from melt water, a Neumann boundary condition is more relevant. For tracers that enter the ocean through air-sea gas exchange such as 14C, a prescribed concentration boundary condition can be used to infer relevant timescales, but the Dirichlet Boundary condition must be applied over the entire ocean surface and not only to a patch of limited area. Our three-dimensional model results based on a steady-state modern circulation suggest that the relative disequilibrium between the deep Atlantic and Pacific is on the order of "only" 1200 years or less and does not depend on the size and location of the patch where the tracer is injected.

A Simplified Theory of Oscillating Aerofoils in Transonic Flow: Review and Extension

1980 ◽  
Vol 31 (4) ◽  
pp. 252-284
Author(s):  
E.H. Dowell
Keyword(s):  
Boundary Condition ◽  
Unsteady Flow ◽  
Flow Separation ◽  
Transonic Flow ◽  
Three Dimensional ◽  
Surface Boundary ◽  
Two Dimensional ◽  
Bernoulli’S Equation ◽  
Surface Boundary Condition

SummarySignificant new results are presented to show to what extent a simplified theory for transonic flow may be used. Solutions are obtained by classical techniques and compared with experiment. Results are given for two-dimensional and three-dimensional, steady and unsteady flow. The effects of flow separation and improvements in Bernoulli’s equation and the surface boundary condition are also briefly discussed.

Inverse spectral problem of an anharmonic oscillator on a half-axis with the Neumann boundary condition

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Agil K. Khanmamedov ◽  
Nigar F. Gafarova
Keyword(s):  
Boundary Condition ◽  
Neumann Boundary Condition ◽  
Inverse Spectral Problem ◽  
Anharmonic Oscillator ◽  
Neumann Boundary ◽  
Effective Algorithm ◽  
Inverse Spectral Problems ◽  
Main Equation ◽  
Inverse Spectral ◽  
Half Axis

AbstractAn anharmonic oscillator {T(q)=-\frac{d^{2}}{dx^{2}}+x^{2}+q(x)} on the half-axis {0\leq x<\infty} with the Neumann boundary condition is considered. By means of transformation operators, the direct and inverse spectral problems are studied. We obtain the main integral equations of the inverse problem and prove that the main equation is uniquely solvable. An effective algorithm for reconstruction of perturbed potential is indicated.

scholarly journals Blow-Up Analysis for a Quasilinear Parabolic Equation with Inner Absorption and Nonlinear Neumann Boundary Condition

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Zhong Bo Fang ◽  
Yan Chai
Keyword(s):  
Boundary Condition ◽  
Parabolic Equation ◽  
Neumann Boundary Condition ◽  
Blow Up ◽  
Quasilinear Parabolic Equation ◽  
Neumann Boundary ◽  
Initial Boundary ◽  
Blow Up Analysis ◽  
Inner Absorption ◽  
Quasilinear Parabolic

We investigate an initial-boundary value problem for a quasilinear parabolic equation with inner absorption and nonlinear Neumann boundary condition. We establish, respectively, the conditions on nonlinearity to guarantee thatu(x,t)exists globally or blows up at some finite timet*. Moreover, an upper bound fort*is derived. Under somewhat more restrictive conditions, a lower bound fort*is also obtained.

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