Lectures on Geophysical Fluid Dynamics

Samelson, R. M.

doi:10.1029/98eo00402

Cited by 197 publications

(382 citation statements)

References 0 publications

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“…In each plot the points from the dipole region lie very close to a curve whose tangent has a negative slope at each of its points. This confirms the dominance of the inertial and β terms in the dynamic balance of the recirculation zone and the fact that the flow in this region is well approximated by a free mode, with a one-to-one relationship PV = F(ψ) (Stern, 1975;Larichev and Reznik, 1976;Salmon, 1998). As shown in greater detail in Fig.…”

Section: Spatio-temporal Variability Of the Solutions I Empirical Ortsupporting

confidence: 56%

Spatio‐temporal variability in a mid‐latitude ocean basin subject to periodic wind forcing

2007

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The mid-latitude ocean's response to time-dependent zonal wind-stress forcing is studied using a reduced-gravity, 1.5-layer, shallow-water IntroductionThe wind-driven, basin-scale circulation in the mid-latitude upper ocean exhibits variability on different time scales. This variability could be due to changes in the external atmospheric forcing or to the system's intrinsic instability and nonlinearity. The latter explanation was first put forward by Veronis (1963Veronis ( , 1966, but the former has enjoyed greater popularity in the oceanographic community until fairly recently. A systematic application of the methods of dynamical systems theory to the wind-driven circulation problem has yielded several physical mechanisms for the observed lowfrequency variability, on the time scale of several months to several years . This circulation has been studied in the last decade with a hierarchy of models that include rectangular-basin, as well as more realistic configurations. Pedlosky (1996) reviewed work that used time-independent, single-gyre forcing. Single-gyre results of particular interest since then include Berloff's (1997a, 1997b) work that emphasizes the role of basin size in this problem, and Sheremet et al.'s (1997) classification of instabilities for the single gyre. Chang et al. (2001) reviewed double-gyre results and compared the physical mechanisms for intrinsic variability found in this case with those obtained in the single-gyre problem. We only review here, therefore, the results that are most relevant to the present work. These emphasize the double-gyre problem. Jiang et al. (1995; JJG hereafter) studied the double-gyre wind-driven circulation in a mid-latitude rectangular basin on a β-plane using a 1.5-layer, reduced-gravity, shallow-water (SW) model. They used a time-constant zonal-wind profile, symmetric about the basin's mid-latitude axis. Their results showed that when non-linear processes come into play, multiple steady state solutions satisfying identical boundary conditions can arise for sufficiently strong wind-stress forcing. Two stable solutions were found to co-exist over a certain range of parameters. One had a stronger subpolar gyre and the other a stronger subtropical gyre, with overshooting of the western boundary currents to the north and south of the symmetry axis, respectively. Their periodic solutions had periods of several years and several weeks. Following JJG, Speich et al. (1995) analyzed the dependence of the stationary solutions on the SW model's nondimensional parameters such as the amplitude of the forcing, the Ekman number, the Rossby number, the non-dimensional β parameter, and the bottom drag coefficient. Using pseudo-

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Section: Spatio-temporal Variability Of the Solutions I Empirical Ortsupporting

confidence: 56%

Spatio‐temporal variability in a mid‐latitude ocean basin subject to periodic wind forcing

2007

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“…Now we simplify the above conditional mean tendency equation for purely Gaussian EOF modes. The pdfs of EOFs of GCM data are nearly Gaussian (Hsu & Zwiers 2001;Franzke et al 2005;Franzke & Majda 2006;Majda et al 2006a;Berner & Branstator 2007) and there are many geophysical models without damping and forcing that exactly satisfy these assumptions such as barotropic flow on the sphere with topography (Carnevale & Frederiksen 1987;Salmon 1998;Majda & Wang 2006); thus, it is reasonable as a starting point to assume that the pdf is exactly Gaussian. Thus, in the EOF basis, the pdf factors like…”

Section: (B ) Idealized Models For Stochastic Mode Reductionmentioning

confidence: 99%

An applied mathematics perspective on stochastic modelling for climate

Majda

Franzke

Khouider

2008

Phil. Trans. R. Soc. A.

129

159

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Systematic strategies from applied mathematics for stochastic modelling in climate are reviewed here. One of the topics discussed is the stochastic modelling of mid-latitude low-frequency variability through a few teleconnection patterns, including the central role and physical mechanisms responsible for multiplicative noise. A new lowdimensional stochastic model is developed here, which mimics key features of atmospheric general circulation models, to test the fidelity of stochastic mode reduction procedures. The second topic discussed here is the systematic design of stochastic lattice models to capture irregular and highly intermittent features that are not resolved by a deterministic parametrization. A recent applied mathematics design principle for stochastic column modelling with intermittency is illustrated in an idealized setting for deep tropical convection; the practical effect of this stochastic model in both slowing down convectively coupled waves and increasing their fluctuations is presented here.

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“…To alleviate this problem and extend the modelling capability of these stochastic models into the surf zone, Herbers et al (2003) proposed a heuristic, dissipation-controlled closure approximation, with a relaxation to Gaussian statistics on the scale of the surf zone width. This approach is similar to the relaxation of the quasiGaussian closure used in turbulence models (e.g., Salmon, 1998). Generally good agreement between observations and model simulations is found, even at locations well within the surf zone.…”

Section: Stochastic Modelsmentioning

confidence: 59%

Wave modelling – The state of the art

Cavaleri¹,

Alves²,

Ardhuin³

et al. 2007

Progress in Oceanography

453

177

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This paper is the product of the wave modelling community and it tries to make a picture of the present situation in this branch of science, exploring the previous and the most recent results and looking ahead towards the solution of the problems we presently face. Both theory and applications are considered.The many faces of the subject imply separate discussions. This is reflected into the single sections, seven of them, each dealing with a specific topic, the whole providing a broad and solid overview of the present state of the art. After an introduction framing the problem and the approach we followed, we deal in sequence with the following subjects: (Section) 2, generation by wind; 3, non-linear interactions in deep water; 4, white-capping dissipation; 5, non-linear interactions in shallow water; 6, dissipation at the sea bottom; 7, wave propagation; 8, numerics. The two final sections, 9 and 10, summarize the present situation from a general point of view and try to look at the future developments. Keywords

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Lectures on Geophysical Fluid Dynamics

Cited by 197 publications

References 0 publications

Spatio‐temporal variability in a mid‐latitude ocean basin subject to periodic wind forcing

Spatio‐temporal variability in a mid‐latitude ocean basin subject to periodic wind forcing

An applied mathematics perspective on stochastic modelling for climate

Wave modelling – The state of the art

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