Achim Wirth

Hyperviscosity, Galerkin truncation and bottlenecks in turbulence

It is shown that the use of a high power alpha of the Laplacian in the dissipative term of hydrodynamical equations leads asymptotically to truncated inviscid conservative dynamics with a finite range of spatial Fourier modes. Those at large wave numbers thermalize, whereas modes at small wave numbers obey ordinary viscous dynamics [C. Cichowlas et al., Phys. Rev. Lett. 95, 264502 (2005)10.1103/Phys. Rev. Lett. 95.264502]. The energy bottleneck observed for finite alpha may be interpreted as incomplete thermalization. Artifacts arising from models with alpha>1 are discussed.

Variability of the Great Whirl from Observations and Models

Observations from cruises in the Arabian Sea and data from satellites are interpreted using different realizations of a multi-level primitive equation model and an eddy-permitting reduced-gravity shallow water model of the Indian Ocean. The focus is on the interannual circulation variability of the Arabian Sea, and especially of the meridional location of the Great Whirl (GW). The results suggest that the variability in the western Arabian Sea is not only due to the interannual variability in the wind field, but that a substantial part is caused by the chaotic nature of the ocean dynamics. Decreasing the friction coefficient from 1000 to 500m2s-1 in a 19o numerical reduced-gravity model, the variance of the GW location increases dramatically, and the mean position moves southward by one degree. In the eddy-permitting experiments analyzed, both mechanisms appear to determine the GW location at the onset of the GW dynamics in late summer.

Large-scale dynamo produced by negative magnetic eddy diffusivities

Abstract The existence of incompressible flow producing negative magnetic eddy diffusivities is demonstrated. This provides for a dynamo mechanism, alternative to α-type effects, requiring neither the presence of mean heliciiy nor the breaking of parity invariance. In the kinematic dynamo phase, the magnetic field grows exponentially with a growth rate proportional to the square of the wavenumber. The concrete example, analyzed by means of multiscale techniques, is a parity-invariant flow of the Taylor-Green type.

Eddy viscosity of three-dimensional flow

Theoretical and numerical results are presented for the eddy viscosity of three-dimensional spatially periodic incompressible flow.

Mean Circulation and Structures of Tilted Ocean Deep Convection

Abstract Convection in a homogeneous ocean is investigated by numerically integrating the three-dimensional Boussinesq equations in a tilted, rotating frame ( f–F plane) subject to a negative buoyancy flux (cooling) at the surface. The study focuses on determining the influence of the angle (tilt) between the axis of rotation and gravity on the convection process. To this end the following two essential parameters are varied: (i) the magnitude of the surface heat flux, and (ii) the angle (tilt) between the axis of rotation and gravity. The range of the parameters investigated is a subset of typical open-ocean deep convection events. It is demonstrated that when gravity and rotation vector are tilted with respect to each other (i) the Taylor–Proudman–Poincare theorem leaves an imprint in the convective structures, (ii) a horizontal mean circulation is established, and (iii) the second-order moments involving horizontal velocity components are considerably increased. Tilted rotation thus leaves a substantia...

A box model for the paleoceanography of the Black Sea

The evolution of the Black Seas salinity after the opening of the Bosporus about 7500 years ago is investigated using a simple two-box model. The model consists of watermass and salt conservation equations, and allows for changes in halocline depth. The paleoceanographic box model is forced by present-day Mediterranean inflow and outflow, and atmospheric forcings. Analytic solutions for the evolution of the box volumes are given. Model salinities reach 90% of their the present-day values in both boxes about 2,500 years after the opening of the Bosporus. The evolution of the salinities is shown to be almost independent of the evolution of the box volumes, and the results are compared with the existing paleoceanographic proxy records.

Error evolution in the dynamics of an ocean general circulation model

The problem of error propagation is considered for spatially uncorrelated errors of the barotropic stream function in an oceanic general circulation model (OGCM). Such errors typically occur when altimetric data from satellites are assimilated into ocean models. It is shown that the error decays at first due to the dissipation of the smallest scales in the error field. The error then grows exponentially before it saturates at the value corresponding to the difference between independent realizations. A simple analytic formula for the error behavior is derived; it matches the numerical results documented for the present primitive-equation ocean model, and other models in the literature.

A Drag-Induced Barotropic Instability in Air–Sea Interaction

Abstract A new mechanism that induces barotropic instability in the ocean is discussed. It is due to the air–sea interaction with a quadratic drag law and horizontal viscous dissipation in the atmosphere. The authors show that the instability spreads to the atmosphere. The preferred spatial scale of the instability is that of the oceanic baroclinic Rossby radius of deformation. It can only be represented in numerical models, when the dynamics at this scale is resolved in the atmosphere and ocean. The dynamics are studied using two superposed shallow water layers: one for the ocean and one for the atmosphere. The interaction is due to the shear between the two layers. The shear applied to the ocean is calculated using the velocity difference between the ocean and the atmosphere and the quadratic drag law. In one-way interaction, the shear applied to the atmosphere neglects the ocean dynamics; it is calculated using the atmospheric wind only. In two-way interaction, it is opposite to the shear applied to th...

Complex eddy-viscosity: a three-dimensional effect

Abstract It is shown that the response of spatially periodic three-dimensional flow to weak large-scale momentum perturbation may involve a complex eddy-viscosity. This is in contrast to the eddy-diffusivity which is always positive and to the eddy-viscosity of two-dimensional flow which is real (but not necessarily positive). A simple “two-and-a-half dimensional” flow with a complex eddy-viscosity is (sin(x + y - z), 0, sin(x + y - z) + (1/ √3) sin x).

Estimation of friction parameters in gravity currents by data assimilation in a model hierarchy

Abstract. This paper is the last in a series of three investigating the friction laws and their parametrisation in idealised gravity currents in a rotating frame. Results on the dynamics of a gravity current (Wirth, 2009) and on the estimation of friction laws by data assimilation (Wirth and Verron, 2008) are combined to estimate the friction parameters and discriminate between friction laws in non-hydrostatic numerical simulations of gravity current dynamics, using data assimilation and a reduced gravity shallow water model. I demonstrate, that friction parameters and laws in gravity currents can be estimated using data assimilation. The results clearly show that friction follows a linear Rayleigh law for small Reynolds numbers and the estimated value agrees well with the analytical value obtained for non-accelerating Ekman layers. A significant and sudden departure towards a quadratic drag law at an Ekman layer based Reynolds number of around 800 is shown, in agreement with classical laboratory experiments. The drag coefficient obtained compares well to friction values over smooth surfaces. I show that data assimilation can be used to determine friction parameters and discriminate between friction laws and that it is a powerful tool in systematically connecting models within a model hierarchy.