Implementation of the LANS-alpha turbulence model in a primitive equation ocean model

This paper presents the first numerical implementation and tests of the Lagrangian-averaged Navier-Stokes-alpha (LANS-alpha) turbulence model in a primitive equation ocean model. The ocean model in which we work is the Los Alamos Parallel Ocean Program (POP); we refer to POP and our implementation of LANS-alpha as POP-alpha. Two versions of POP-alpha are presented: the full POP-alpha algorithm is derived from the LANS-alpha primitive equations, but requires a nested iteration that makes it too slow for practical simulations; a reduced POP-alpha algorithm is proposed, which lacks the nested iteration and is two to three times faster than the full algorithm. The reduced algorithm does not follow from a formal derivation of the LANS-alpha model equations. Despite this, simulations of the reduced algorithm are nearly identical to the full algorithm, as judged by globally averaged temperature and kinetic energy, and snapshots of temperature and velocity fields. Both POP-alpha algorithms can run stably with longer timesteps than standard POP. Comparison of implementations of full and reduced POP-alpha algorithms are made within an idealized test problem that captures some aspects of the Antarctic Circumpolar Current, a problem in which baroclinic instability is prominent. Both POP-alpha algorithms produce statistics that resemble higher-resolution simulations of standard POP. A linear stability analysis shows that both the full and reduced POP-alpha algorithms benefit from the way the LANS-alpha equations take into account the effects of the small scales on the large. Both algorithms (1) are stable; (2) make the Rossby Radius effectively larger; and (3) slow down Rossby and gravity waves.Comment: Submitted to J. Computational Physics March 21, 200

A simplified general circulation model for a baroclinic ocean with topography. Part I: Theory, waves and wind-driven circulations

A new type of ocean circulation model is described and tested for various simplewind-driven circulation problems. The model resides on the vorticity balance ofthe depth averaged velocity and a hierarchy of balance equations for thevertical moments of baroclinic velocity and density, the lowest density momentbeing the baroclinic potential energy. The latter is the most importantdynamical link between the barotropic and the baroclinic motion in the presenceof a sloping topography. We derive a coupled hierarchy of tendency equations forthe potential energy and higher order density moments which, together withmoments for the baroclinic velocities and an appropriate truncation and thebarotropic vorticity balance yields in a simplified set of vertical integratedequations describing the BARotropic-Baroclinic-Interaction (BARBI) of motions inthe ocean. Using a numerical implementation of BARBI, idealized companionexperiments with a full primitive equation model (MOM) show that wavepropagation properties and baroclinic adjustments are correctly represented inBARBI in mid latitudes as well as in equatorial latitudes. Furthermore, a set ofexperiments with a realistic application to the Atlantic/Southern Ocean systemreadily reveals important aspects which have been previously reported by studiesof gyre circulations and circumpolar currents using full primitive equationmodels

A simplified model of the Martian atmosphere - Part 1: a diagnostic analysis

In this paper we derive a reduced-order approximation to the vertical and horizontal structure of a simplified model of the baroclinically unstable Martian atmosphere. The original model uses the full hydrostatic primitive equations on a sphere, but has only highly simplified schemes to represent the detailed physics of the Martian atmosphere, e.g. forcing towards a plausible zonal mean temperature state using Newtonian cooling. Three different norms are used to monitor energy conversion processes in the model and are then compared. When four vertical modes (the barotropic and first three baroclinic modes) are retained in the reduced-order approximation, the correlation norm captures approximately 90% of the variance, while the kinetic energy and total energy norms capture approximately 83% and 78% of the kinetic and total energy respectively. We show that the leading order Proper Orthogonal Decomposition (POD) modes represent the dominant travelling waves in the baroclinically-unstable, winter hemisphere. In part 2 of our study we will develop a hierarchy of truncated POD-Galerkin expansions of the model equations using up to four vertical modes

Recent Advances Concerning Certain Class of Geophysical Flows

This paper is devoted to reviewing several recent developments concerning certain class of geophysical models, including the primitive equations (PEs) of atmospheric and oceanic dynamics and a tropical atmosphere model. The PEs for large-scale oceanic and atmospheric dynamics are derived from the Navier-Stokes equations coupled to the heat convection by adopting the Boussinesq and hydrostatic approximations, while the tropical atmosphere model considered here is a nonlinear interaction system between the barotropic mode and the first baroclinic mode of the tropical atmosphere with moisture. We are mainly concerned with the global well-posedness of strong solutions to these systems, with full or partial viscosity, as well as certain singular perturbation small parameter limits related to these systems, including the small aspect ratio limit from the Navier-Stokes equations to the PEs, and a small relaxation-parameter in the tropical atmosphere model. These limits provide a rigorous justification to the hydrostatic balance in the PEs, and to the relaxation limit of the tropical atmosphere model, respectively. Some conditional uniqueness of weak solutions, and the global well-posedness of weak solutions with certain class of discontinuous initial data, to the PEs are also presented.Comment: arXiv admin note: text overlap with arXiv:1507.0523

On open boundary conditions for three dimensional primitive equation ocean circulation models

An open boundary condition is constructed for three dimensional primitive equation ocean circulation models. The boundary condition utilises dominant balances in the governing equations to assist calculations of variables at the boundary. The boundary condition can be used in two forms. Firstly as a passive one in which there is no forcing at the boundary and phenomena generated within the domain of interest can propagate outwards without distorting the interior. Secondly as an active condition where a model is forced by the boundary condition. Three simple idealised tests are performed to verify the open boundary condition, (1) a passive condition to test the outflow of free Kelvin waves, (2) an active condition during the spin up phase of an ocean, (3) finally an example of the use of the condition in a tropical ocean

Multilayer primitive equations model with velocity shear and stratification

The purpose of this paper is to present a multilayer primitive equations model for ocean dynamics in which the velocity and buoyancy fields within each layer are not only allowed to vary arbitrarily with horizontal position and time, but also with depth--linearly at most. The model is a generalization of Ripa's inhomogeneous one-layer model to an arbitrary number of layers. Unlike models with homogeneous layers, the present model is able to represent thermodynamics processes. Unlike models with slab layers, i.e. those in which the layer velocity and buoyancy fields are depth-independent, the present model can represent explicitly the thermal-wind balance within each layer which dominates at low frequency. In the absence of external forcing and dissipation, energy, volume, mass, and buoyancy variance constrain the dynamics; conservation of total zonal momentum requires in addition the usual zonal symmetry of the topography and horizontal domain. The model further possesses a singular Hamiltonian structure. Unlike the single-layer counterpart, however, no steady solution has been possible to prove formally (or Arnold) stable using the above invariants. It is shown here that a model with only two layers provides an excellent representation of the exact gravest baroclinic mode phase speed. This suggests that configurations with only a small number of layers will be needed to tackle a large variety of problems with enough realism