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 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.

A Quasi-three-dimensional Finite-volume Shallow Water Model for Green Water on Deck

2013 ◽  
Vol 57 (03) ◽  
pp. 125-140
Author(s):  
Daniel A. Liut ◽  
Kenneth M. Weems ◽  
Tin-Guen Yen
Keyword(s):  
Shallow Water ◽  
Finite Volume ◽  
Time Domain ◽  
Degrees Of Freedom ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Green Water ◽  
Water Model ◽  
Ship Motions ◽  
Shallow Water Model

A quasi-three-dimensional hydrodynamic model is presented to simulate shallow water phenomena. The method is based on a finite-volume approach designed to solve shallow water equations in the time domain. The nonlinearities of the governing equations are considered. The methodology can be used to compute green water effects on a variety of platforms with six-degrees-of-freedom motions. Different boundary and initial conditions can be applied for multiple types of moving platforms, like a ship's deck, tanks, etc. Comparisons with experimental data are discussed. The shallow water model has been integrated with the Large Amplitude Motions Program to compute the effects of green water flow over decks within a time-domain simulation of ship motions in waves. Results associated to this implementation are presented.

scholarly journals Improved moist-convective rotating shallow water model and its application to instabilities of hurricane-like vortices

2018 ◽  
Author(s):  
LMD
Keyword(s):  
Tropical Cyclone ◽  
Shallow Water ◽  
Water Vapour ◽  
Large Scale ◽  
Precipitable Water ◽  
Water Model ◽  
Moist Convection ◽  
Shallow Water Model ◽  
Atmospheric Motions ◽  
Rotating Shallow Water

We show how the two-layer moist-convective rotating shallow water model (mcRSW), which proved to be a simple and robust tool for studying effects of moist convection on large-scale atmospheric motions, can be improved by including, in addition to the water vapour, precipitable water, and the effects of vaporisation, entrainment, and precipitation. Thus improved mcRSW becomes cloud-resolving. It is applied, as an illustration, to model the development of instabilities of tropical cyclone-like vortices.

scholarly journals A Shallow Water Model for Convective Self-Aggregation

2020 ◽  
Author(s):  
Da Yang
Keyword(s):  
Shallow Water ◽  
Gravity Waves ◽  
Large Scale ◽  
Wave Pattern ◽  
Water Model ◽  
Shallow Water Model ◽  
Modeling Framework ◽  
Convective Storms ◽  
Wide Range ◽  
Self Aggregation

AbstractRandomly distributed convective storms can self-aggregate in the absence of large-scale forcings. Here we present a 1D shallow water model to study the convective self-aggregation. This model simulates the dynamics of the planetary boundary layer and represents convection as a triggered process. Once triggered, convection lasts for finite time and occupies finite length. We show that the model can successfully simulate self-aggregation, and that the results are robust to a wide range of parameter values. In the simulations, convection excites gravity waves. The gravity waves then form a standing wave pattern, separating the domain into convectively active and inactive regions. We analyze the available potential energy (APE) budget and show that convection generates APE, providing energy for self-aggregation. By performing dimensional analysis, we develop a scaling theory for the size of convective aggregation, which is set by the gravity wave speed, damping timescale, and number density of convective storms. This paper provides a simple modeling framework to further study convective self-aggregation.

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 Triggered Convection, Gravity Waves, and the MJO: A Shallow-Water Model

2013 ◽  
Vol 70 (8) ◽  
pp. 2476-2486 ◽  
Author(s):  
Da Yang ◽  
Andrew P. Ingersoll
Keyword(s):  
Shallow Water ◽  
Large Scale ◽  
Low Frequency ◽  
Propagation Speed ◽  
Water Model ◽  
Shallow Water Model ◽  
Horizontal Scale ◽  
Frequency Wave ◽  
Large Scale Structures ◽  
Scale Structures

Abstract The Madden–Julian oscillation (MJO) is the dominant mode of intraseasonal variability in the tropics. Despite its primary importance, a generally accepted theory that accounts for fundamental features of the MJO, including its propagation speed, planetary horizontal scale, multiscale features, and quadrupole structures, remains elusive. In this study, the authors use a shallow-water model to simulate the MJO. In this model, convection is parameterized as a short-duration localized mass source and is triggered when the layer thickness falls below a critical value. Radiation is parameterized as a steady uniform mass sink. The following MJO-like signals are observed in the simulations: 1) slow eastward-propagating large-scale disturbances, which show up as low-frequency, low-wavenumber features with eastward propagation in the spectral domain, 2) multiscale structures in the time–longitude (Hovmöller) domain, and 3) quadrupole vortex structures in the longitude–latitude (map view) domain. The authors propose that the simulated MJO signal is an interference pattern of westward and eastward inertia–gravity (WIG and EIG) waves. Its propagation speed is half of the speed difference between the WIG and EIG waves. The horizontal scale of its large-scale envelope is determined by the bandwidth of the excited waves, and the bandwidth is controlled by the number density of convection events. In this model, convection events trigger other convection events, thereby aggregating into large-scale structures, but there is no feedback of the large-scale structures onto the convection events. The results suggest that the MJO is not so much a low-frequency wave, in which convection acts as a quasi-equilibrium adjustment, but is more a pattern of high-frequency waves that interact directly with the convection.

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