Grid-scale instability of convective-adjustment schemes

Through a simple illustrative example, it is shown that instantaneous convective adjustment schemes, of the type used in general circulation models to parametrize nonhydrostatic convective processes, lead to the spontaneous emergence of the smallest resolved horizontal scale: the grid mode is unstable regardless of the strength of the horizontal diffusivity. Convective adjustment vertically mixes properties at each grid-point, irrespective of the horizontal distribution of such properties. Thus, horizontal spatial gradients are amplified by convective adjustment, as long as adjustment is faster than the horizontal diffusion (or advection) time between neighboring grid-points. In the example presented here, the grid-scale instability is a global attractor and can only be “suppressed” by inaccurate time-stepping, or by the finite computational representation of numbers. This clarifies that the “grid-mode” is not a computational instability, but an intrinsic property of instantaneous convective adjustment schemes. A smooth solution, without grid-scale gradients, also exists, but it is unstable to infinitesimal perturbations for all values of the external parameters. We emphasize that the spatial average of the grid-mode differs substantially from the spatial average of the smooth (but unstable) solution

Recirculation and separation of boundary currents

An inertial multi-layer model of the recirculation gyres surrounding a separated boundary current is presented. The boundary current is defined to be separated when the upper layer thickness vanishes. The strong eastward flow found at the outcrop causes the circulation to extend to the bottom through baroclinic instability. In order to decrease the vertical shear responsible for the instability, the deep flow must also have maximum eastward velocity at the outcrop latitude. Thus the deep flow to the north of the outcrop (where no upper fluid is present) must move so as to keep velocity continuous. The eastward flowing deep water is returned in a westward flow to the south and north of the separation latitude. Thus in the upper layer we find a single anticyclonic gyre bounded by the outcrop latitude to the north, while the deep circulation is characterized by two almost antisymmetric counterrotating gyres. The recirculating gyres are defined as regions in which the flow conserves potential vorticity and Bernoulli function, and are surrounded by motionless fluid. The model predicts the location of the separation latitude and of the gyres\u27 boundaries, together with the flow inside the gyres, as functions of the potential vorticity and Bernoulli function in each layer

Laminar separation of colliding western boundary currents

A barotropic model is employed to study the dynamics of colliding jets along a western boundary. To isolate the processes at the western wall we use a regional model where two opposing jets are induced by prescribing narrow inflows at the northern and southern edges of the computational domain. The fluid is withdrawn from the domain on the eastern side

On the role of topography and of boundary forcing in the ocean circulation

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution August 1987This thesis consists of two loosely related problems, both of which analyze some consequences of the failure of Sverdrup relation. In the first part, Chapters 2 and 3, the Sverdrup relation is invalidated because substantial flow is obtained at the bottom where topography exists. The eddies play an essential role in transfering momentum vertically from the surface, where the forcing is applied, to the bottom, which is otherwise unforced. If the topography has a structure in the longitudinal direction, then the inviscid theory predicts the occurence of strong jets in the interior of the model ocean. According to the structure of the topography these internal jets can occur in both vertically homeogenous and baroclinic oceans. If the topographic slope changes sign, then one kind of jets is observed both in stratified and in homogeneous oceans. This phenomenon is robust to moderate amounts of dissipation and is not disturbed by the occurrence of recirculating gyres within the basin. If the topographic slope is constant, then another kind of internal jets is observed, and it occurs in stratified models only. I was unable to observe this kind of jets in the presence of weak dissipation. The reason for this failure is twofold: on one hand friction, especially interfacial friction, tends to make the flow more barotropic (and we believe that indeed this is one of the processes that the eddies accomplish in a stratified fluid) and therefore the phenomena that rely strongly on baroclinicity are discouraged. On the other hand, reduction of the dissipation leads to the onset of a strong recirculating, inertial gyre which, although confined in space, affects the global properties of the flow. In the second part of the thesis (Chapters 4 and 5) I developed a simple model of the recirculating, inertial gyre. Again the dynamics of this feature are far from being in Sverdrup balance. In this case inertia is responsible for the failure of Sverdrup relation, together with the eddy field which provides a mean for transfering momentum vertically and laterally into regions away from where the forcing is applied. In this model there is no direct forcing in the recirculation region, and the input of momentum is confined to the boundary currents surrounding the gyre, for example the separated Gulf Stream. One of the results of the recirculation model is the prediction of its transport. It is shown that most of the transport is depth independent, i.e. it can be calculated without detailed knowledge of the density structure of the ocean. It is also shown that the "barotropic" part of the transport increases as the cube of the meridional extent of the gyre.The thesis work has been supported by a National Foundation grant from the Office of Atmospheric Sciences

Time-dependent response to cooling in a beta-plane basin

Author Posting. © American Meteorological Society, 2006. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 36 (2006): 2185-2198, doi:10.1175/JPO2967.1.The time-dependent response of an ocean basin to the imposition of cooling (or heating) is examined in the context of a quasigeostrophic, two-layer model on the beta plane. The focus is on the structure and magnitude of the vertical motion and its response to both a switch-on forcing and a periodic forcing. The model employed is a time-dependent version of an earlier model used to discuss the intensification of sinking in the region of the western boundary current. The height of the interface of the two-layer model serves as an analog of temperature, and the vertical velocity at the interface consists of a cross-isopycnal velocity modeled in terms of a relaxation to a prescribed interface height, an adiabatic representation of eddy thickness fluxes parameterized as lateral diffusion of thickness, and the local vertical motion of the interface itself. The presence of time dependence adds additional dynamical features to the problem, in particular the emergence of low-frequency, weakly damped Rossby basin modes. If the buoyancy forcing is zonally uniform the basin responds to a switch-on of the forcing by coming into steady-state equilibrium after the passage of a single baroclinic Rossby wave. If the forcing is nonuniform in the zonal direction, a sequence of Rossby basin modes is excited and their decay is required before the basin achieves a steady state. For reasonable parameter values the boundary layers, in which both horizontal and vertical circulations are closed, are quasi-steady and respond to the instantaneous state of the interior. As in the steady problem the flow is sensitive to small nonquasigeostrophic mass fluxes across the perimeter of the basin. These fluxes generally excite basin modes as well. The basin modes will also be weakly excited if the beta-plane approximation is relaxed. The response to periodic forcing is also examined, and the sensitivity of the response to the structure of the forcing is similar to the switch-on problem.This research was supported in part by NSF Grant OCE-9901654

On the role of topography in the ocean circulation

The ideas developed by Rhines and Young (1982a,b) are used to analyze the effect of topography in simple baroclinic models. The presence of longitude-dependent topography induces strong internal jets with transports of the same magnitude as the interior flow. It is shown that the existence of these features is independent of the forcing structure at the top of the model ocean, of the topography form and of the forcing in subsurface layers as long as the latter is small. Some examples are given both for forcings which, in the absence of topography, would give circulations closed in the interior and for forcings that require a western boundary current.Topography also shifts the line of zero transport allowing for significant flow across the line of zero wind stress curl. Moreover, the lines dividing the subtropical gyre from the subpolar gyre are different in every layer, a feature absent in the flat bottom case

Recent Contributions of Theory to Our Understanding of the Atlantic Meridional Overturning Circulation

Revolutionary observational arrays, together with a new generation of ocean and climate models, have provided new and intriguing insights into the Atlantic Meridional Overturning Circulation (AMOC) over the last two decades. Theoretical models have also changed our view of the AMOC, providing a dynamical framework for understanding the new observations and the results of complex models. In this paper we review recent advances in conceptual understanding of the processes maintaining the AMOC. We discuss recent theoretical models that address issues such as the interplay between surface buoyancy and wind forcing, the extent to which the AMOC is adiabatic, the importance of mesoscale eddies, the interaction between the middepth North Atlantic Deep Water cell and the abyssal Antarctic Bottom Water cell, the role of basin geometry and bathymetry, and the importance of a three‐dimensional multiple‐basin perspective. We review new paradigms for deep water formation in the high‐latitude North Atlantic and the impact of diapycnal mixing on vertical motion in the ocean interior. And we discuss advances in our understanding of the AMOC's stability and its scaling with large‐scale meridional density gradients. Along with reviewing theories for the mean AMOC, we consider models of AMOC variability and discuss what we have learned from theory about the detection and meridional propagation of AMOC anomalies. Simple theoretical models remain a vital and powerful tool for articulating our understanding of the AMOC and identifying the processes that are most critical to represent accurately in the next generation of numerical ocean and climate models

Dissipative dynamics of western boundary currents

We investigate the steady barotropic circulation patterns driven by inflow-outflow boundary conditions on a rectangular β-plane domain. An inertial jet enters the domain in the southwest corner and a broad eastward outflow is prescribed at the eastern boundary. On the western wall there is no mass flux and no slip.With weak viscosity, ν the western boundary jet ?overshoots? northward, beyond the latitude band of the eastern outflow. As the viscosity is reduced the length of this overshoot increases as ν−2/3, before the jet gradually peels away from the western wall, plunges southward and eventually turns eastward. Away from the wall the current forms a damped stationary Rossby wave, as described by Moore in 1963.The initial northward overshoot and southward plunge is a distinct dynamical regime, and not merely the first and largest undulation of the Rossby wave. For instance the zonal length scale of the overshoot is just the Munk scale, (ν/β)1/3 and inertia, planetary vorticity and viscosity are all important at leading order in the dynamical balance as ν → 0. All of the streamlines pass through this dissipative region and most of the Lagrangian potential vorticity alterations occur here, rather than in the Rossby wave.The preceeding scenario applies only when the northern boundary is distant, so that the overshoot peels away from the western wall before striking the northwest corner of the domain. If the jet reaches the northern boundary it drives an inertial recirculating gyre in the corner

The effects of pressed sugar beet pulp silage (PBPS) and dairy whey on heavy pig production

The effects of pressed beet pulp silage (PBPS) replacing barley for 10% and 20% (DM basis) were studied on heavy pigs (60 Hypor pigs from 28 kg) fed dairy whey-diluted diets