Instability of a tidal mixing front in the presence of realistic tides and mixing

Instability and lateral eddy fluxes associated with a tidal mixing front are studied using idealized primitive equation numerical model runs. The front itself develops as a result of turbulence associated with imposed tidal currents over a sloping bottom. Thus, the model includes realistic levels of turbulence and time-dependence in the base-state conditions. In all of the 21 configurations considered, the front is unstable to fluctuations that usually draw energy primarily from the potential energy pool. Scalings are developed to parameterize a) the location of the tidal mixing front; b) the eddy kinetic energy; and c) the lateral eddy coefficients. In all cases, baroclinic instability enhances the lateral mixing relative to the two-dimensional case, but the extent of enhancement varies with the input parameters. Preliminary model runs that include a simple nutrient-phytoplankton-zooplankton-detritus biological model do not suggest any substantial ecological effect of the baroclinic instabilities. The lack of a strong biological effect, despite the enhanced eddy transports, occurs because of the near cancelation of oppositely directed cross-isobath eddy fluxes in the upper and lower parts of the water column. Similarly, shallow and deep cross-frontal eddy heat fluxes also nearly balance: this cancelation appears to help explain how the classical one-dimensional potential energy criterion for frontal location can work so well in a complex ocean

Baroclinic instability of an idealized tidal mixing front

Tidal mixing fronts separate vertically homogenized waters from stratified ambient waters. The linear and nonlinear baroclinic stability of an idealized tidal mixing front is treated here in the parameter range that is stable with regard to symmetric instabilities and that has no bottom friction. All model configurations considered are unstable, and the dependence on bottom slope, stratification and other parameters is similar to that suggested by models (such as that of Blumsack and Gierasch, 1972) with much simpler configurations. The finite-amplitude evolution of the instabilities is treated using a primitive equation numerical model. The initial length scale and growth rate of the instabilities are well predicted by the linear calculations. As the system evolves, gravitational potential energy is transferred to eddy kinetic energy, which peaks at about the time that potential energy stops decreasing. The peak eddy kinetic energy depends strongly on the bottom slope, with the greatest values occurring when the bottom and near-bottom isopycnals slope in the same direction. As the fields continue to evolve, eddy kinetic energy decreases, mean kinetic energy increases, and the eddies become larger and more barotropic. The horizontal eddy mixing coefficient is estimated at the time of maximum lateral heat flux and is found to be sensitive to the magnitude of the bottom slope but not its sign. Overall, the instability and the related eddy mixing are strong enough to encourage the idea that these instabilities might be effective at a more realistic tidal mixing front

Time-dependent motions and the nonlinear bottom Ekman layer

The laminar bottom Ekman layer beneath a flow with finite relative vorticity is studied. First, the case with only a steady interior shear flow is reviewed, and then a case with a spatially uniform oscillating flow is superimposed. In both cases, the problem can be reduced to solving ordinary differential equations. The competition of two effects governs the results. The interior vorticity effectively modifies the rotation rate, but advection (especially vertically, due to Ekman pumping) tends to counteract the vorticity modification. Vertical advection keeps the time-dependent boundary layer well behaved for negative interior vorticities, but a boundary layer singularity can still exist at a single superinertial frequency when interior relative vorticity is positive

Three-body model calculations for 16C nucleus

We apply a three-body model consisting of two valence neutrons and the core nucleus $^{14}$C in order to investigate the ground state properties and the electronic quadrupole transition of the $^{16}$C nucleus. The discretized continuum spectrum within a large box is taken into account by using a single-particle basis obtained from a Woods-Saxon potential. The calculated B(E2) value from the first 2$^+$ state to the ground state shows good agreement with the observed data with the core polarization charge which reproduces the experimental B(E2) value for $^{15}$C. We also show that the present calculation well accounts for the longitudinal momentum distribution of $^{15}$C fragment from the breakup of $^{16}$C nucleus. We point out that the dominant ($d_{5/2})^2$ configuration in the ground state of $^{16}$C plays a crucial role for these agreement.Comment: 5 pages, 3 figures, 3 table

Counterterms in Gravity in the Light-Front Formulation and a D=2 Conformal-like Symmetry in Gravity

In this paper we discuss gravity in the light-front formulation (light-cone gauge) and show how possible counterterms arise. We find that Poincare invariance is not enough to find the three-point counterterms uniquely. Higher-spin fields can intrude and mimic three-point higher derivative gravity terms. To select the correct term we have to use the remaining reparametrization invariance that exists after the gauge choice. We finally sketch how the corresponding programme for N=8 Supergravity should work.Comment: 26 pages, references added, published versio

George Veronis: An appreciation

George Veronis was born in New Brunswick, New Jersey on June 3, 1926, one of six accomplished children of a Greek immigrant couple. He grew up in Easton, Pennsylvania, where his talent for mathematics was recognized early on. World War II interrupted his education, however, and he enlisted in the U.S. Navy where he served aboard submarines in the Pacific Ocean. With the end of the global conflict, George entered college on the G.I. Bill and graduated with a B.S. in Mathematics from nearby Lafayette College in 1950..

The efficiency of education in generating literacy: a stochastic frontier approach

The growing importance attached to education as a key factor to improve economic performance coupled with the persistent scarcity of resources for education makes it important that skills and literacy are produced efficiently. This paper provides an international comparison of the efficiency of literacy production. We find substantial differences between countries in levels of literacy, differences in literacy between education levels and differences in the efficiency of literacy production. There are some notable differences between more Anglo-Saxon countries and the Continental European countries. The findings suggest that in almost all countries the scope for efficiency improvements in education is large. So even without major increases in (public) funding, improvements in educational outcomes are achievable. We can get better value for the money we spend on education.

Comments on ‘‘The non-wavelike response of a continental shelf to wind’’ by G. T. Csanady

Csanady (1998) presents solutions for time-dependent wind-driven flow in a barotropic coastal ocean. We disagree with two of his three boundary condition options and wish to clarify the origin of the non-wavelike aspect of the flow

Buoyancy arrest and shelf–ocean exchange

Author Posting. © American Meteorological Society, 2012. 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 42 (2012): 644–658, doi:10.1175/JPO-D-11-0143.1.When steady flow in a stratified ocean passes between the continental slope and open ocean, its ability to cross isobaths is potentially limited by buoyancy arrest. If the bottom Ekman transport vanishes and there are no interior stresses, then steady linear flow on an f plane must be geostrophic and follow isobaths exactly. The influence of arrest on cross-shelf transport is investigated here to establish 1) whether there are substantial penetration asymmetries between cases with upwelling and downwelling in the bottom boundary layer; 2) over what spatial scales, hence in what parameter regime, buoyancy arrest is important; and 3) the effects of depth-dependent interior flow. The problem is approached using scalings and idealized numerical models. The results show that there is little or no asymmetry introduced by bottom boundary layer behavior. Further, if the stratification is weak or moderate, as measured by a slope Burger number s = αN/f (where α is the bottom slope, N is buoyancy frequency, and f is the Coriolis parameter), buoyancy arrest does not exert a strong constraint on cross-isobath exchange.This research was supported by the National Science Foundation Physical Oceanography program through Grant OCE-0849498.2012-10-0

Continuous Spin Representations of the Poincar\'e and Super-Poincar\'e Groups

We construct Wigner's continuous spin representations of the Poincar\'e algebra for massless particles in higher dimensions. The states are labeled both by the length of a space-like translation vector and the Dynkin indices of the {\it short little group} $SO(d-3)$, where $d$ is the space-time dimension. Continuous spin representations are in one-to-one correspondence with representations of the short little group. We also demonstrate how combinations of the bosonic and fermionic representations form supermultiplets of the super-Poincar\'e algebra. If the light-cone translations are nilpotent, these representations become finite dimensional, but contain zero or negative norm states, and their supersymmetry algebra contains a central charge in four dimensions.Comment: 19 page