Greg Holloway

The equilibrium statistical mechanics of simple quasi-geostrophic models

We have applied the methods of classical statistical mechanics to derive the inviscid equilibrium states for one- and two-layer nonlinear quasi-geostrophic flows, with and without bottom topography and variable rotation rate. In the one-layer case without topography we recover the equilibrium energy spectrum given by Kraichnan (1967). In the two-layer case, we find that the internal radius of deformation constitutes an important dividing scale: at scales of motion larger than the radius of deformation the equilibrium flow is nearly barotropic, while at smaller scales the stream functions in the two layers are statistically uncorrelated. The equilibrium lower-layer flow is positively correlated with bottom topography (anticyclonic flow over seamounts) and the correlation extends to the upper layer at scales larger than the radius of deformation. We suggest that some of the statistical trends observed in non-equilibrium flows may be looked on as manifestations of the tendency for turbulent interactions to maximize the entropy of the system.

Representing Topographic Stress for Large-Scale Ocean Models

Abstract Interaction of eddies with seafloor topography can exert enormous, systematic forces on the ocean circulation. This interaction has been considered previously under idealized circumstances. Theoretical results are here simplified and extended toward practical application in large-scale ocean circulation models. Among the suggestions is that coarse resolution models can “correct” a depth-independent part of the velocity field toward a velocity given by −z × ∇fLH, where z is the vertical unit vector, f is Coriolis form, L is a length scale O(10 km), and H is the total depth. Absence of this tendency may be implicated in a number of systematic defects that appear in present ocean models.

Has Arctic Sea Ice Rapidly Thinned

Abstract Reports based on submarine sonar data have suggested Arctic sea ice has thinned nearly by half in recent decades. Such rapid thinning is a concern for detection of global change and for Arctic regional impacts. Including atmospheric time series, ocean currents and river runoff into an ocean–ice–snow model show that the inferred rapid thinning was unlikely. The problem stems from undersampling. Varying winds that readily redistribute Arctic ice create a recurring pattern whereby ice shifts between the central Arctic and peripheral regions, especially in the Canadian sector. Timing and tracks of the submarine surveys missed this dominant mode of variability. Although model-derived overall thinning from the 1960s to the 1990s was less than hitherto supposed, there is also indication of accelerated thinning during the early–mid-1990s.

Stochastic closure for nonlinear Rossby waves

An extension of the turbulence ‘test-field model’ (Kraichnan 1971 a) is given for twodimensional flow with Rossby-wave propagation. Such a unified treatment of waves and turbulence is necessary for flows in which the relative strength of nonlinear terms depends upon the length scale considered. We treat the geophysically interesting case in which long, fast Rossby waves propagate substantially without interaction while short Rossby waves are thoroughly dominated by advection. We recover the observations of Rhines (1975) that the tendency of two-dimensional flow to organize energy into larger scales of motion is inhibited by Rossby waves and that an initially isotropic flow develops anisotropy preferring zonal motion. The anisotropy evolves to an equilibrium functional dependence on the isotropic part of the flow spectrum. Theoretical results are found to be in quantitative agreement with numerical flow simulations.

Sensitivity of the GFDL Ocean General Circulation Model to a Parameterization of Vertical Diffusion

Abstract A coarse resolution, primitive equation general circulation model with idealized geometry and forcing is used to explore sensitivity to the assumption that vertical diffusion depends upon local stability. A case with constant diffusivity is compared with a case in which the diffusivity is inversely proportional to the local Brunt-V frequency. The stability-dependent parameterization of vertical diffusivity yields a poleward heat flux similar to that of a small, constant diffusivity. However, this parameterization increases the mean temperature in the deep ocean by about 0.8°C and the strength of the meridional circulation by over 40%. In addition, the stability-dependent diffusivity is found to increase the stratification in the deep ocean. The experiments suggest that it may be possible to calibrate the rate of deep-water formation of general circulation models, without affecting the poleward heat transport, by varying the magnitude of the vertical diffusivity below the thermocline. The explicit...

Dynamics of circulation of the Japan Sea

Including mean flow forcing due to eddy-topography interaction in a numerical model of the Japan Sea appears to improve defects identified in previous modelling studies. Characteristic western boundary current overshoot (by the East Korea Warm Current) is reduced or eliminated while a southward undercurrent brings colder, fresher water along the Korean coast. Cyclonic circulation in the north includes a strengthened Liman Current. A more nearly continuous Nearshore Branch follows the Honshu shelf break with northward-flowing undercurrent. Interannual variability persists under fixed (seasonally repeating or annual mean) external forcing.

Oceanic Internal Waves Are Not Weak Waves

Abstract It is shown that the oceanic internal wave field is too energetic by roughly two orders of magnitude to be treated theoretically as an assemblage of weakly interacting waves. This may be seen both from recent weak wave theoretical calculations which contradict their premises and also from inspection of magnitudes of advection and wave propagation terms. Thus, much recent discussion of results of implications of weak wave theory should be questioned critically. Scaling arguments based on buoyant turbulence are reviewed briefly. The role of vertical mass flux as distinguishing weak wave interactions from stronger turbulence is discussed. Possible progress by renormalization of wave interaction equations is considered.

A Global Ocean Model with Double-Diffusive Mixing

Abstract A global ocean model is described in which parameterizations of diapycnal mixing by double-diffusive fingering and layering are added to a stability-dependent background turbulent diffusivity. Model runs with and without double-diffusive mixing are compared for annual-mean and seasonally varying surface forcing. Sensitivity to different double-diffusive mixing parameterizations is considered. In all cases, the locales and extent of salt fingering (as diagnosed from buoyancy ratio Rρ) are grossly comparable to climatology, although fingering in the models tends to be less intense than observed. Double-diffusive mixing leads to relatively minor changes in circulation but exerts significant regional influences on temperature and salinity.

Arctic Ocean Study: Synthesis of Model Results and Observations

Model development and simulations represent a comprehensive synthesis of observations with advances in numerous disciplines (physics; mathematics; and atmospheric, oceanic, cryospheric, and related sciences), enabling hypothesis testing via numerical experiments. For the Arctic Ocean, modeling has become one of the major instruments for understanding past conditions and explaining recently observed changes. In this context, the international Arctic Ocean Model Intercomparison Project (AOMiphttp://fish.cims.nyu.edu/project_aomip/overview. html) has investigated various aspects of ocean and sea ice changes for the time period 1948 to present. Among the major AOMIP themes are investigations of the origin and variability of Atlantic water (AW) circulation, mechanisms of accumulation and release of fresh water (FW), causes of sea level rise, and the role of tides in shaping climate.

Effect of topographic stress on circulation in the western Mediterranean

The interaction of eddies with seafloor topography can exert large systematic forces on ocean circulation. Using a statistical mechanics approach it is possible to obtain a parametrization of this effect (the Neptune effect) for application in large-scale ocean circulation models. Circulation of the western Mediterranean has been observed to follow a definite cyclonic path. Numerical models usually show good qualitative agreement for the large-scale circulation but show systematic deficiencies at a subbasin scale. We have tested the importance of the Neptune effect on the circulation of the western Mediterranean Sea. To perform this test, different numerical experiments on western Mediterranean circulation were done with and without eddy-topography interaction. As a first step we analyze the influence of the Neptune effect in an ideal western Mediterranean with closed straits. After these experiments the more realistic case of open straits is studied. All the experiments show that the Neptune effect may be a significant factor in the basin and subbasin scale circulation in the western Mediterranean Sea.