scholarly journals On the Width of the Equatorial Deep Jets

2012 ◽  
Vol 42 (10) ◽  
pp. 1729-1740 ◽  
Author(s):  
R. J. Greatbatch ◽  
P. Brandt ◽  
M. Claus ◽  
S.-H. Didwischus ◽  
Y. Fu
Keyword(s):  
Shallow Water ◽  
Normal Mode ◽  
Ocean Circulation ◽  
Time Scale ◽  
Eddy Viscosity ◽  
Water Model ◽  
Shallow Water Model ◽  
Energy Propagation ◽  
Vertical Scale ◽  
Equatorial Ocean

Abstract The equatorial deep jets (EDJ) are a striking feature of the equatorial ocean circulation. In the Atlantic Ocean, the EDJ are associated with a vertical scale of between 300 and 700 m, a time scale of roughly 4.5 years, and upward energy propagation to the surface. It has been found that the meridional width of the EDJ is roughly 1.5 times larger than expected based on their vertical scale. Here, the authors use a shallow-water model for a high-order baroclinic vertical normal mode to argue that mixing of momentum along isopycnals can explain the enhanced width. A lateral eddy viscosity of 300 m2 s−1 is found to be sufficient to account for the width implied by observations.

scholarly journals Two Different Aperiodic Phases of Wind-Driven Ocean Circulation in a Double-Gyre, Two-Layer Shallow-Water Model

2006 ◽  
Vol 36 (7) ◽  
pp. 1265-1286 ◽  
Author(s):  
Tomonori Matsuura ◽  
Mitsutaka Fujita
Keyword(s):  
Power Spectrum ◽  
Shallow Water ◽  
Metastable State ◽  
Ocean Circulation ◽  
Lower Layer ◽  
Water Model ◽  
Barotropic Instability ◽  
Shallow Water Model ◽  
Gyre Circulation ◽  
Double Gyre

Abstract A two-layer shallow-water model is used to investigate the transition of wind-driven double-gyre circulation from laminar flow to turbulence as the Reynolds number (Re) is systematically increased. Two distinctly different phases of turbulent double-gyre patterns and energy trajectories are exhibited before and after at Re = 95: deterministic and fully developed turbulent circulations. In the former phase, the inertial subgyres vary between an asymmetric solution and an antisymmetric solution and the double-gyre circulations reach the aperiodic solution mainly due to their barotropic instability. An integrated kinetic energy in the lower layer is slight and the generated mesoscale eddies are confined in the upper layer. The power spectrum of energies integrated over the whole domain at Re = 70 has peaks at the interannual periods (4–7 yr) and the interdecadal period (10–20 yr). The loops of the attractors take on one cycle at those periods and display the blue-sky catastrophe. At Re = 95, the double-gyre circulation reaches a metastable state and the attracters obtained from the three energies form a topological manifold. In the latter, as Re increases, the double-gyre varies from a metastable state to a chaotic state because of the barotropic instability of the eastward jet and the baroclinic instability of recirculation retrograde flow, and the eastward jet meanders significantly with interdecadal variability. The generated eddies cascade to the red side of the power spectrum as expected in the geostrophic turbulence. The main results in the simulation may indicate essential mechanisms for the appearance of multiple states of the Kuroshio and for low-frequency variations in the midlatitude ocean.

Potential vorticity redistribution by localised transient forcing in the shallow-water model

2018 ◽  
Vol 852 ◽  
pp. 199-225 ◽  
Author(s):  
Michael C. Haigh ◽  
Pavel S. Berloff
Keyword(s):  
Shallow Water ◽  
Ocean Circulation ◽  
Potential Vorticity ◽  
Single Layer ◽  
Current Theory ◽  
Water Model ◽  
Eddy Flux ◽  
Shallow Water Model ◽  
Background Flow ◽  
Uniform Background

This study is motivated by the need to develop stochastic parameterisations for representing the effects of mesoscale oceanic eddies in non-eddy-resolving and eddy-permitting ocean circulation models. A necessary logical step on the way to such parameterisations is the understanding of flow responses to spatially stationary and localised, time-dependent ‘plunger’ forcings intended to represent transient eddy flux divergences. Specifically, this study develops an understanding of the plunger-induced convergence of potential vorticity (PV) fluxes using the linearised single-layer shallow-water model. Time-periodic solutions are obtained and the ‘footprint’, defined as the time-mean, quasi-linear PV flux convergence, quantifies the cumulative PV redistribution induced by the plunger. Using the footprint, the equivalent eddy flux (EEF) is defined such that it succinctly quantifies the extent of the PV redistribution, and its dependencies on the forcing latitude and the background flow are examined in detail. For a uniform background flow the EEF is positive for all forcing latitudes, corresponding to net-poleward PV flux convergence, as expected by current theory of $\unicode[STIX]{x1D6FD}$-plane Rossby waves. The EEF also has a robust dependence on the direction and magnitude of a uniform background flow, which is a useful quality for the EEF to provide a basis for a parameterisation of eddy PV fluxes. We also examine the PV redistribution due to forcing on top of a Gaussian jet background flow and find that forcing proximity to the jet core is the primary factor in determining whether the jet is sharpened or broadened.

scholarly journals Successive bifurcations in a shallow-water model applied to the wind-driven ocean circulation

1995 ◽  
Vol 2 (3/4) ◽  
pp. 241-268 ◽  
Author(s):  
S. Speich ◽  
H. Dijkstra ◽  
M. Ghil
Keyword(s):  
Shallow Water ◽  
Ocean Circulation ◽  
Degrees Of Freedom ◽  
Large Scale ◽  
Steady State Solution ◽  
Stationary Solutions ◽  
Water Model ◽  
Shallow Water Model ◽  
Current Systems ◽  
Double Gyre

Abstract. Climate - the "coarse-gridded" state of the coupled ocean - atmosphere system - varies on many time and space scales. The challenge is to relate such variation to specific mechanisms and to produce verifiable quantitative explanations. In this paper, we study the oceanic component of the climate system and, in particular, the different circulation regimes of the mid-latitude win driven ocean on the interannual time scale. These circulations are dominated by two counterrotating, basis scale gyres: subtropical and subpolar. Numerical techniques of bifurcation theory are used to stud the multiplicity and stability of the steady-state solution of a wind-driven, double-gyre, reduced-gravity, shallow water model. Branches of stationary solutions and their linear stability are calculated systematically as parameter are varied. This is one of the first geophysical studies i which such techniques are applied to a dynamical system with tens of thousands of degrees of freedom. Multiple stationary solutions obtain as a result of nonlinear interactions between the two main recirculating cell (cyclonic and anticyclonic) of the large- scale double-gyre flow. These equilibria appear for realistic values of the forcing and dissipation parameters. They undergo Hop bifurcation and transition to aperiodic solutions eventually occurs. The periodic and chaotic behaviour is probably related to an increased number of vorticity cells interaction with each other. A preliminary comparison with observations of the Gulf Stream and Kuroshio Extensions suggests that the intern variability of our simulated mid-latitude ocean is a important factor in the observed interannual variability o these two current systems.

scholarly journals Available Potential Energy in Density Coordinates

2018 ◽  
Vol 48 (8) ◽  
pp. 1867-1883 ◽  
Author(s):  
Alain Colin de Verdière ◽  
Thierry Huck ◽  
Souren Pogossian ◽  
Michel Ollitrault
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Shallow Water ◽  
Ocean Circulation ◽  
World Ocean ◽  
Water Model ◽  
Shallow Water Model ◽  
Available Potential Energy ◽  
Vertical Displacements ◽  
World Ocean Atlas

AbstractThe vertically integrated potential energy of an incompressible stratified fluid formulated in density coordinates can be simply written as a weighted vertical sum of the squares of the vertical displacements of density surfaces, a general expression valid for arbitrary displacements. The sum of this form of potential energy and kinetic energy is then a conserved quantity for the multilayer shallow water model. The formulation in density coordinates is a natural one to find the Lorenz reference state of available potential energy (APE). We describe the method to compute the APE of an ocean state and provide two applications. The first is the classical double-gyre, wind-driven circulation simulated by a shallow water model at high resolution. We show that the eddy kinetic and eddy potential energies are localized in regions of large gradients of mean APE. These large gradients surround an APE minimum found between the two gyres. The second is the time-mean World Ocean Circulation reconstructed from hydrography (World Ocean Atlas) and reference velocities at 1000 db from the Argo float program to obtain an absolute circulation. The total available potential energy exceeds the total mean kinetic energy of the World Ocean by three orders of magnitude, pointing out the very small Burger number of the circulation. The Gulf Stream, the Kuroshio, the Agulhas retroflection, and the confluence regions are four examples that confirm the shallow water model results that large gradients of mean available potential energy can be used as predictors for the presence of high eddy kinetic energy (obtained here from satellite altimetry).

The instability of vertically curved fronts in a two-layer shallow water model

2020 ◽  
Vol 32 (12) ◽  
pp. 124117
Author(s):  
M. W. Harris ◽  
F. J. Poulin ◽  
K. G. Lamb
Keyword(s):  
Shallow Water ◽  
Water Model ◽  
Shallow Water Model

scholarly journals Modelling Weirs in Two-Dimensional Shallow Water Models

Water ◽  
2021 ◽  
Vol 13 (16) ◽  
pp. 2152
Author(s):  
Gonzalo García-Alén ◽  
Olalla García-Fonte ◽  
Luis Cea ◽  
Luís Pena ◽  
Jerónimo Puertas
Keyword(s):  
Experimental Data ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Water Model ◽  
Two Dimensional ◽  
Shallow Water Model ◽  
Experimental Dataset ◽  
River Hydraulics ◽  
Shallow Water Models ◽  
Water Models

2D models based on the shallow water equations are widely used in river hydraulics. However, these models can present deficiencies in those cases in which their intrinsic hypotheses are not fulfilled. One of these cases is in the presence of weirs. In this work we present an experimental dataset including 194 experiments in nine different weirs. The experimental data are compared to the numerical results obtained with a 2D shallow water model in order to quantify the discrepancies that exist due to the non-fulfillment of the hydrostatic pressure hypotheses. The experimental dataset presented can be used for the validation of other modelling approaches.

scholarly journals Development of a Practical Model for Predicting Soil Salinity in a Salt Marsh in the Arakawa River Estuary

Water ◽  
2021 ◽  
Vol 13 (15) ◽  
pp. 2054
Author(s):  
Naoki Kuroda ◽  
Katsuhide Yokoyama ◽  
Tadaharu Ishikawa
Keyword(s):  
Salt Marsh ◽  
Hydraulic Conductivity ◽  
Shallow Water ◽  
Soil Salinity ◽  
River Estuary ◽  
Flow Simulation ◽  
Design Tool ◽  
Water Model ◽  
Shallow Water Model ◽  
Practical Model

Our group has studied the spatiotemporal variation of soil and water salinity in an artificial salt marsh along the Arakawa River estuary and developed a practical model for predicting soil salinity. The salinity of the salt marsh and the water level of a nearby channel were measured once a month for 13 consecutive months. The vertical profile of the soil salinity in the salt marsh was measured once monthly over the same period. A numerical flow simulation adopting the shallow water model faithfully reproduced the salinity variation in the salt marsh. Further, we developed a soil salinity model to estimate the soil salinity in a salt marsh in Arakawa River. The vertical distribution of the soil salinity in the salt marsh was uniform and changed at almost the same time. The hydraulic conductivity of the soil, moreover, was high. The uniform distribution of salinity and high hydraulic conductivity could be explained by the vertical and horizontal transport of salinity through channels burrowed in the soil by organisms. By combining the shallow water model and the soil salinity model, the soil salinity of the salt marsh was well reproduced. The above results suggest that a stable brackish ecotone can be created in an artificial salt marsh using our numerical model as a design tool.

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