scholarly journals Multi-symplectic formulation of near-local Hamiltonian balanced models

2011 ◽  
Vol 467 (2136) ◽  
pp. 3424-3442 ◽  
Author(s):  
Sylvain Delahaies ◽  
Peter E. Hydon
Keyword(s):  
Potential Vorticity ◽  
Contact Structure ◽  
Fluid Motion ◽  
Local Model ◽  
Contact Transformation ◽  
Geometric Features ◽  
Coriolis Parameter ◽  
New Class

We transform near-local Hamiltonian balanced models (HBMs) describing nearly geostrophic fluid motion (with constant Coriolis parameter) into multi-symplectic (MS) systems. This allows us to determine conservation of Lagrangian momentum, energy and potential vorticity for Salmon's L 1 dynamics; a similar approach works for other near-local balanced models (such as the -model). The MS approach also enables us to determine a class of systems that have a contact structure similar to that of the semigeostrophic model. The contact structure yields a contact transformation that makes the problem of front formation tractable. The new class includes the first local model with a variable Coriolis parameter that preserves all of the most useful geometric features of the semigeostrophic model.

scholarly journals Surface signature of Mediterranean water eddies in the Northeastern Atlantic: effect of the upper ocean stratification

Ocean Science ◽  
2012 ◽  
Vol 8 (6) ◽  
pp. 931-943 ◽  
Author(s):  
I. Bashmachnikov ◽  
X. Carton
Keyword(s):  
Potential Vorticity ◽  
Initial Period ◽  
Relative Vorticity ◽  
Sea Surface ◽  
Upper Ocean ◽  
Buoyancy Frequency ◽  
Coriolis Parameter ◽  
Ocean Stratification ◽  
Surface Signature ◽  
Mediterranean Water

Abstract. Meddies, intra-thermocline eddies of Mediterranean water, can often be detected at the sea surface as positive sea-level anomalies. Here we study the surface signature of several meddies tracked with RAFOS floats and AVISO altimetry. While pushing its way through the water column, a meddy raises isopycnals above. As a consequence of potential vorticity conservation, negative relative vorticity is generated in the upper layer. During the initial period of meddy acceleration after meddy formation or after a stagnation stage, a cyclonic signal is also generated at the sea-surface, but mostly the anticyclonic surface signal follows the meddy. Based on geostrophy and potential vorticity balance, we present theoretical estimates of the intensity of the surface signature. It appears to be proportional to the meddy core radius and to the Coriolis parameter, and inversely proportional to the core depth and buoyancy frequency. This indicates that surface signature of a meddy may be strongly reduced by the upper ocean stratification. Using climatic distribution of the stratification intensity, we claim that the southernmost limit for detection in altimetry of small meddies (with radii on the order of 10–15 km) should lie in the subtropics (35–45° N), while large meddies (with radii of 25–30 km) could be detected as far south as the northern tropics (25–35° N). Those results agree with observations.

scholarly journals Destruction of Potential Vorticity by Winds

2005 ◽  
Vol 35 (12) ◽  
pp. 2457-2466 ◽  
Author(s):  
Leif N. Thomas
Keyword(s):  
Boundary Layer ◽  
Wind Stress ◽  
Potential Vorticity ◽  
Ekman Layer ◽  
Buoyancy Flux ◽  
Coriolis Parameter ◽  
Mode Water ◽  
Ocean Fronts ◽  
Secondary Circulations ◽  
Frictional Forces

Abstract The destruction of potential vorticity (PV) at ocean fronts by wind stress–driven frictional forces is examined using PV flux formalism and numerical simulations. When a front is forced by “downfront” winds, that is, winds blowing in the direction of the frontal jet, a nonadvective frictional PV flux that is upward at the sea surface is induced. The flux extracts PV out of the ocean, leading to the formation of a boundary layer thicker than the Ekman layer, with nearly zero PV and nonzero stratification. The PV reduction is not only active in the Ekman layer but is transmitted through the boundary layer via secondary circulations that exchange low PV from the Ekman layer with high PV from the pycnocline. Extraction of PV from the pycnocline by the secondary circulations results in an upward advective PV flux at the base of the boundary layer that scales with the surface, nonadvective, frictional PV flux and that leads to the deepening of the layer. At fronts forced by both downfront winds and a destabilizing atmospheric buoyancy flux FBatm, the critical parameter that determines whether the wind or the buoyancy flux is the dominant cause for PV destruction is (H/δe)(FBwind/FBatm), where H and δe are the mixed layer and Ekman layer depths, FBwind = S2τo/(ρof ), S2 is the magnitude of the lateral buoyancy gradient of the front, τo is the downfront component of the wind stress, ρo is a reference density, and f is the Coriolis parameter. When this parameter is greater than 1, PV destruction by winds dominates and may play an important role in the formation of mode water.

scholarly journals On the stability of ocean overflows

2008 ◽  
Vol 602 ◽  
pp. 241-266 ◽  
Author(s):  
LARRY J. PRATT ◽  
KARL R. HELFRICH ◽  
DAVID LEEN
Keyword(s):  
Potential Vorticity ◽  
Growth Rates ◽  
Deep Ocean ◽  
Basic Flow ◽  
Necessary Condition ◽  
Zero Energy ◽  
Coriolis Parameter ◽  
Hydraulic Behaviour ◽  
Zero Potential ◽  
The Stability

The stability of a hydraulically driven sill flow in a rotating channel with smoothly varying cross-section is considered. The smooth topography forces the thickness of the moving layer to vanish at its two edges. The basic flow is assumed to have zero potential vorticity, as is the case in elementary models of the hydraulic behaviour of deep ocean straits. Such flows are found to always satisfy Ripa's necessary condition for instability. Direct calculation of the linear growth rates and numerical simulation of finite-amplitude behaviour suggests that the flows are, in fact, always unstable. The growth rates and nonlinear evolution depend largely on the dimensionless channel curvature κ=2αg′/f2, where 2α is the dimensional curvature, g′ is the reduced gravity, and f is the Coriolis parameter. Very small positive (or negative) values of κ correspond to dynamically wide channels and are associated with strong instability and the breakup of the basic flow into a train of eddies. For moderate or large values of κ, the instability widens the flow and increases its potential vorticity but does not destroy its character as a coherent stream. Ripa's condition for stability suggests a theory for the final width and potential vorticity that works moderately well. The observed and predicted growth in these quantities are minimal for κ≥1, suggesting that the zero-potential-vorticity approximation holds when the channel is narrower than a Rossby radius based on the initial maximum depth. The instability results from a resonant interaction between two waves trapped on opposite edges of the stream. Interactions can occur between two Kelvin-like frontal waves, between two inertia–gravity waves, or between one wave of each type. The growing disturbance has zero energy and extracts zero energy from the mean. At the same time, there is an overall conversion of kinetic energy to potential energy for κ>0, with the reverse occurring for κ<0. When it acts on a hydraulically controlled basic state, the instability tends to eliminate the band of counterflow that is predicted by hydraulic theory and that confounds hydraulic-based estimates of volume fluxes in the field. Eddy generation downstream of the controlling sill occurs if the downstream value of κ is sufficiently small.

A Balanced Approximation of the One-Layer Shallow-Water Equations on a Sphere

2009 ◽  
Vol 66 (6) ◽  
pp. 1735-1748 ◽  
Author(s):  
W. T. M. Verkley
Keyword(s):  
Shallow Water ◽  
Potential Vorticity ◽  
Shallow Water Equations ◽  
Rossby Waves ◽  
Coriolis Parameter ◽  
Beta Plane ◽  
Propagating Waves ◽  
Barotropic Vorticity Equation ◽  
Barotropic Vorticity ◽  
The One

Abstract A global version of the equivalent barotropic vorticity equation is derived for the one-layer shallow-water equations on a sphere. The equation has the same form as the corresponding beta plane version, but with one important difference: the stretching (Cressman) term in the expression of the potential vorticity retains its full dependence on f 2, where f is the Coriolis parameter. As a check of the resulting system, the dynamics of linear Rossby waves are considered. It is shown that these waves are rather accurate approximations of the westward-propagating waves of the second class of the original shallow-water equations. It is also concluded that for Rossby waves with short meridional wavelengths the factor f 2 in the stretching term can be replaced by the constant value f02, where f0 is the Coriolis parameter at ±45° latitude.

Barotropic flow over finite isolated topography: steady solutions on the beta-plane and the initial value problem

1993 ◽  
Vol 250 ◽  
pp. 553-586 ◽  
Author(s):  
Luanne Thompson ◽  
Glenn R. Flierl
Keyword(s):  
Rossby Wave ◽  
Potential Vorticity ◽  
Initial Value Problem ◽  
Wave Drag ◽  
Combined Effects ◽  
Initial Value ◽  
Coriolis Parameter ◽  
Finite Height ◽  
Barotropic Flow ◽  
Steady Solutions

Solutions for inviscid rotating flow over a right circular cylinder of finite height are studied, and comparisons are made to quasi-geostrophic solutions. To study the combined effects of finite topography and the variation of the Coriolis parameter with latitude a steady inviscid model is used. The analytical solution consists of one part which is similar to the quasi-geostrophic solution that is driven by the potential vorticity anomaly over the topography, and another, similar to the solution of potential flow around a cylinder, that is driven by the matching conditions on the edge of the topography. When the characteristic Rossby wave speed is much larger than the background flow velocity, the transport over the topography is enhanced as the streamlines follow lines of constant background potential vorticity. For eastward flow, the Rossby wave drag can be very much larger than that predicted by quasi-geostrophic theory. The combined effects of finite height topography and time-dependence are studied in the inviscid initial value problem on the f-plane using the method of contour dynamics. The method is modified to handle finite topography. When the topography takes up most of the layer depth, a stable oscillation exists with all of the fluid which originates over the topography rotating around the topography. When the Rossby number is order one, a steady trapped vortex solution similar to the one described by Johnson (1978) may be reached.

Dynamic Tuning of Optical Waveguides with Electrowetting Pumps

2002 ◽  
Vol 741 ◽  
Author(s):  
Francesco Cattaneo ◽  
Peter Mach ◽  
Jennifer Hsieh ◽  
Tom Krupenkin ◽  
Shu Yang ◽  
...  
Keyword(s):  
Contact Angle ◽  
Optical Fiber ◽  
Optical Waveguides ◽  
Fluid Motion ◽  
Microfluidic Channels ◽  
New Class ◽  
Dynamic Tuning ◽  
Optical Fiber Devices ◽  
Long Period Gratings ◽  
Fiber Devices

ABSTRACTThis paper reviews some of our recent work on a new class of photonic component that uses electrowetting pumps and microfluidic channels for dynamic tuning of the characteristics of optical waveguides. These pumps exploit the ability to alter the contact angle of conductive liquids situated on top of a dielectric layer with appropriately patterned underlying electrodes. By applying different voltages to opposite sides of a conductive fluid plug, the contact angle imbalance created between the ends of the liquid drives fluid motion toward the higher field regions [1]. In our design, this electrically controlled, fully reversible motion of fluids contained within recirculating channels is used to alter the effective indices of waveguide modes of three different types of optical fiber structures: fiber Bragg and long period gratings and etched or tapered fiber. Our systems operate non-mechanically and have excellent optical performance, including low insertion and polarization-dependent losses. These characteristics suggest a promising potential for electrowetting-based microfluidic tuning of optical fiber devices and other photonic components.

scholarly journals Space time manifolds and contact structures

1990 ◽  
Vol 13 (3) ◽  
pp. 545-553 ◽  
Author(s):  
K. L. Duggal
Keyword(s):  
Contact Structure ◽  
Contact Manifold ◽  
Contact Structures ◽  
Timelike Vector ◽  
Contact Manifolds ◽  
New Class ◽  
Dimensional Spacetime ◽  
Globally Hyperbolic Spacetimes ◽  
Hyperbolic Spacetimes ◽  
Regular Contact

A new class of contact manifolds (carring a global non-vanishing timelike vector field) is introduced to establish a relation between spacetime manifolds and contact structures. We show that odd dimensional strongly causal (in particular, globally hyperbolic) spacetimes can carry a regular contact structure. As examples, we present a causal spacetime with a non regular contact structure and a physical model [Gödel Universe] of Homogeneous contact manifold. Finally, we construct a model of 4-dimensional spacetime of general relativity as a contact CR-submanifold.

scholarly journals Potential Vorticity Dynamics of Tropical Instability Vortices

2014 ◽  
Vol 44 (3) ◽  
pp. 995-1011 ◽  
Author(s):  
Ryan M. Holmes ◽  
Leif N. Thomas ◽  
LuAnne Thompson ◽  
David Darr
Keyword(s):  
Potential Vorticity ◽  
Relative Vorticity ◽  
Equatorial Region ◽  
Equatorial Pacific ◽  
Vertical Shear ◽  
Coriolis Parameter ◽  
Equatorial Undercurrent ◽  
North Equatorial Counter Current ◽  
Lateral Mixing ◽  
Counter Current

Abstract Tropical instability vortices (TIVs) in the equatorial Pacific exhibit energetic horizontal and vertical circulation characterized by regions of high Rossby number and low Richardson number. Their strong anticyclonic vorticity and vertical shear can influence the broader-scale circulation by driving lateral mixing and vertical exchange between the ocean surface and interior. The authors use a set of nested high-resolution simulations of the equatorial Pacific, with a finest grid size of 3 km, to examine the vortex dynamics associated with TIV core water formation. TIV cores are characterized by low values of the Ertel potential vorticity (PV) as the relative vorticity is anticyclonic with magnitude comparable to the local Coriolis parameter. A study of the variation of PV and other scalars along Lagrangian fluid parcel tracks entering the TIVs shows that the low-PV water in their cores is a mix of Equatorial Undercurrent (EUC) water and North Equatorial Counter Current (NECC) water. The EUC water is characterized by strong horizontal vorticity, and thus, the baroclinic component of the PV is nonnegligible and acts as a source for the anticyclonic vorticity of TIVs. This horizontal vorticity is tilted by an ageostrophic secondary circulation associated with strain-induced frontogenesis that tends to form along the path of the EUC water that enters the vortex. Frontogenesis disrupts the cyclogeostrophic balance of the frontal flow and drives differential vertical motions across the front. These results emphasize the role of submesoscale physics in the equatorial region, which are active when both the Rossby and Richardson numbers are O(1).

A variational derivation of the geostrophic momentum approximation

2014 ◽  
Vol 751 ◽  
Author(s):  
Marcel Oliver
Keyword(s):  
Shallow Water ◽  
Potential Vorticity ◽  
Point Of View ◽  
Order Operator ◽  
Coriolis Parameter ◽  
First Order ◽  
Slow Part ◽  
Momentum Approximation ◽  
Balanced Dynamics ◽  
Spatially Varying

AbstractThis paper demonstrates that the shallow water semigeostrophic equations arise from a degenerate second-order Hamilton principle of very special structure. The associated Euler–Lagrange operator factors into a fast and a slow first-order operator; restricting to the slow part yields the geostrophic momentum approximation as balanced dynamics. While semigeostrophic theory has been considered variationally before, this structure appears to be new. It leads to a straightforward derivation of the geostrophic momentum approximation and its associated potential vorticity law. Our observations further affirm, from a different point of view, the known difficulty in generalizing the semigeostrophic equations to the case of a spatially varying Coriolis parameter.

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