scholarly journals Dynamics of the Upper Oceanic Layers in Terms of Surface Quasigeostrophy Theory

2006 ◽  
Vol 36 (2) ◽  
pp. 165-176 ◽  
Author(s):  
G. Lapeyre ◽  
P. Klein
Keyword(s):  
Potential Vorticity ◽  
Surface Density ◽  
Three Dimensional ◽  
Surface Boundary ◽  
Strongly Correlated ◽  
Basin Scale ◽  
Surface Boundary Condition ◽  
Balanced Flow ◽  
Circumpolar Current ◽  
Quasigeostrophic Model

Abstract In this study, the relation between the interior and the surface dynamics for nonlinear baroclinically unstable flows is examined using the concepts of potential vorticity. First, it is demonstrated that baroclinic unstable flows present the property that the potential vorticity mesoscale and submesoscale anomalies in the ocean interior are strongly correlated to the surface density anomalies. Then, using the invertibility of potential vorticity, the dynamics are decomposed in terms of a solution forced by the three-dimensional (3D) potential vorticity and a solution forced by the surface boundary condition in density. It is found that, in the upper oceanic layers, the balanced flow induced only by potential vorticity is strongly anticorrelated with that induced only by the surface density with a dominance of the latter. The major consequence is that the 3D balanced motions can be determined from only the surface density and the characteristics of the basin-scale stratification by solving an elliptic equation. These properties allow for the possibility to reconstruct the 3D balanced velocity field of the upper layers from just the knowledge of the surface density by using a simpler model, that is, an “effective” surface quasigeostrophic model. All these results are validated through the examination of a primitive equation simulation reproducing the dynamics of the Antarctic Circumpolar Current.

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.

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.

Potential Vorticity Diagnosis of a Simulated Hurricane. Part I: Formulation and Quasi-Balanced Flow

2003 ◽  
Vol 60 (13) ◽  
pp. 1593-1607 ◽  
Author(s):  
Xingbao Wang ◽  
Da-Lin Zhang
Keyword(s):  
Boundary Layer ◽  
Potential Vorticity ◽  
Diabatic Heating ◽  
Inner Core ◽  
Three Dimensional ◽  
Hurricane Andrew ◽  
High Resolution Data ◽  
Balanced Flow ◽  
Upper Level ◽  
Balanced Dynamics

Abstract Because of the lack of three-dimensional (3D) high-resolution data and the existence of highly nonelliptic flows, few studies have been conducted to investigate the inner-core quasi-balanced characteristics of hurricanes. In this study, a potential vorticity (PV) inversion system is developed, which includes the nonconservative processes of friction, diabatic heating, and water loading. It requires hurricane flows to be statically and inertially stable but allows for the presence of small negative PV. To facilitate the PV inversion with the nonlinear balance (NLB) equation, hurricane flows are decomposed into an axisymmetric, gradient-balanced reference state and asymmetric perturbations. Meanwhile, the nonellipticity of the NLB equation is circumvented by multiplying a small parameter ɛ and combining it with the PV equation, which effectively reduces the influence of anticyclonic vorticity. A quasi-balanced ω equation in pseudoheight coordinates is derived, which includes the effects of friction and diabatic heating as well as differential vorticity advection and the Laplacians of thermal advection by both nondivergent and divergent winds. This quasi-balanced PV–ω inversion system is tested with an explicit simulation of Hurricane Andrew (1992) with the finest grid size of 6 km. It is shown that (a) the PV–ω inversion system could recover almost all typical features in a hurricane, and (b) a sizeable portion of the 3D hurricane flows are quasi-balanced, such as the intense rotational winds, organized eyewall updrafts and subsidence in the eye, cyclonic inflow in the boundary layer, and upper-level anticyclonic outflow. It is found, however, that the boundary layer cyclonic inflow and upper-level anticyclonic outflow also contain significant unbalanced components. In particular, a low-level outflow jet near the top of the boundary layer is found to be highly unbalanced (and supergradient). These findings are supported by both locally calculated momentum budgets and globally inverted winds. The results indicate that this PV inversion system could be utilized as a tool to separate the unbalanced from quasi-balanced flows for studies of balanced dynamics and propagating inertial gravity waves in hurricane vortices.

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.

Theory of Blade Design for Large Deflections: Part I—Two-Dimensional Cascade

1984 ◽  
Vol 106 (2) ◽  
pp. 346-353 ◽  
Author(s):  
W. R. Hawthorne ◽  
C. Wang ◽  
C. S. Tan ◽  
J. E. McCune
Keyword(s):  
Three Dimensional ◽  
Tangential Velocity ◽  
Mean Value ◽  
Three Dimensions ◽  
Surface Boundary ◽  
Large Deflections ◽  
Two Dimensional ◽  
Axial Compressors ◽  
A Value ◽  
Surface Boundary Condition

As a step in the development of an analytical method for designing highly loaded, three-dimensional blade profiles for axial compressors and turbines, a simple two-dimensional method was first investigated. The fluid is assumed to be incompressible and inviscid, the blades of negligible thickness, and the mean tangential velocity is prescribed. The blades are represented by a distributed bound vorticity whose strength is determined by the prescribed tangential velocity. The velocity induced by the bound vortices is obtained by a conventional Biot-Savart method assuming a first approximation to the blade profile. Using the blade surface boundary condition, the profile is then obtained by iteration. It is shown that this procedure is successful even for large pitch-chord ratios and large deflections. In order to develop a method for use in three dimensions, the velocity is divided into a pitchwise mean value and a value varying periodically in the pitchwise direction. By using generalized functions to represent the bound vorticity and a Clebsch formulation for the periodic velocity, series expressions are obtained which can be adapted to three-dimensional problems. Several numerical results were obtained using both approaches.

scholarly journals Nonlinear effects of locally heterogeneous hydraulic conductivity fields on regional stream–aquifer exchanges

2015 ◽  
Vol 19 (11) ◽  
pp. 4531-4545 ◽  
Author(s):  
J. Zhu ◽  
C. L. Winter ◽  
Z. Wang
Keyword(s):  
Groundwater Flow ◽  
Effective Conductivity ◽  
Model Simulation ◽  
Three Dimensional ◽  
Small Scale ◽  
Heihe River ◽  
Effective Parameters ◽  
Aquifer Systems ◽  
Basin Scale ◽  
Local Grid

Abstract. Computational experiments are performed to evaluate the effects of locally heterogeneous conductivity fields on regional exchanges of water between stream and aquifer systems in the Middle Heihe River basin (MHRB) of northwestern China. The effects are found to be nonlinear in the sense that simulated discharges from aquifers to streams are systematically lower than discharges produced by a base model parameterized with relatively coarse effective conductivity. A similar, but weaker, effect is observed for stream leakage. The study is organized around three hypotheses: (H1) small-scale spatial variations of conductivity significantly affect regional exchanges of water between streams and aquifers in river basins, (H2) aggregating small-scale heterogeneities into regional effective parameters systematically biases estimates of stream–aquifer exchanges, and (H3) the biases result from slow paths in groundwater flow that emerge due to small-scale heterogeneities. The hypotheses are evaluated by comparing stream–aquifer fluxes produced by the base model to fluxes simulated using realizations of the MHRB characterized by local (grid-scale) heterogeneity. Levels of local heterogeneity are manipulated as control variables by adjusting coefficients of variation. All models are implemented using the MODFLOW (Modular Three-dimensional Finite-difference Groundwater Flow Model) simulation environment, and the PEST (parameter estimation) tool is used to calibrate effective conductivities defined over 16 zones within the MHRB. The effective parameters are also used as expected values to develop lognormally distributed conductivity (K) fields on local grid scales. Stream–aquifer exchanges are simulated with K fields at both scales and then compared. Results show that the effects of small-scale heterogeneities significantly influence exchanges with simulations based on local-scale heterogeneities always producing discharges that are less than those produced by the base model. Although aquifer heterogeneities are uncorrelated at local scales, they appear to induce coherent slow paths in groundwater fluxes that in turn reduce aquifer–stream exchanges. Since surface water–groundwater exchanges are critical hydrologic processes in basin-scale water budgets, these results also have implications for water resources management.

Sign in / Sign up

Export Citation Format

Share Document