The counter-propagating Rossby-wave perspective on baroclinic instability. Part III: Primitive-equation disturbances on the sphere

Baroclinic instability of perturbations described by the linearized primitive quations, growing on steady zonal jets on the sphere, can be understood in terms of the interaction of pairs of counter-propagating Rossby waves (CRWs). The CRWs can be viewed as the basic components of the dynamical system where the Hamiltonian is the pseudoenergy and each CRW has a zonal coordinate and pseudomomentum. The theory holds for adiabatic frictionless flow to the extent that truncated forms of pseudomomentum and pseudoenergy are globally conserved. These forms focus attention on Rossby wave activity. Normal mode (NM) dispersion relations for realistic jets are explained in terms of the two CRWs associated with each unstable NM pair. Although derived from the NMs, CRWs have the conceptual advantage that their structure is zonally untilted, and can be anticipated given only the basic state. Moreover, their zonal propagation, phase-locking and mutual interaction can all be understood by ‘PV-thinking’ applied at only two ‘home-bases’—potential vorticity (PV) anomalies at one home-base induce circulation anomalies, both locally and at the other home-base, which in turn can advect the PV gradient and modify PV anomalies there. At short wavelengths the upper CRW is focused in the mid-troposphere just above the steering level of the NM, but at longer wavelengths the upper CRW has a second wave-activity maximum at the tropopause. In the absence of meridional shear, CRW behaviour is very similar to that of Charney modes, while shear results in a meridional slant with height of the air-parcel displacement-structures of CRWs in sympathy with basic-state zonal angular-velocity surfaces. A consequence of this slant is that baroclinically growing eddies (on jets broader than the Rossby radius) must tilt downshear in the horizontal, giving rise to up-gradient momentum fluxes that tend to accelerate the barotropic component of the jet.

Protochordate Zic genes define primitive somite compartments and highlight molecular changes underlying neural crest evolution

The vertebrate Zic gene family encodes C2H2 zinc finger transcription factors closely related to the Gli proteins. Zic genes are expressed in multiple areas of developing vertebrate embryos, including the dorsal neural tube where they act as potent neural crest inducers. Here we describe the characterization of a Zic ortholog from the amphioxus Branchiostoma floridae and further describe the expression of a Zic ortholog from the ascidian Ciona intestinalis. Molecular phylogenetic analysis and sequence comparisons suggest the gene duplications that formed the vertebrate Zic family were specific to the vertebrate lineage. In Ciona maternal CiZic/Ci-macho1 transcripts are localized during cleavage stages by asymmetric cell division, whereas zygotic expression by neural plate cells commences during neurulation. The amphioxus Zic ortholog AmphiZic is expressed in dorsal mesoderm and ectoderm during gastrulation, before being eliminated first from midline cells and then from all neurectoderm during neurulation. After neurulation, expression is reactivated in the dorsal neural tube and dorsolateral somite. Comparison of CiZic and AmphiZic expression with vertebrate Zic expression leads to two main conclusions. First, Zic expression allows us to define homologous compartments between vertebrate and amphioxus somites, showing primitive subdivision of vertebrate segmented mesoderm. Second, we show that neural Zic expression is a chordate synapomorphy, whereas the precise pattern of neural expression has evolved differently on the different chordate lineages. Based on these observations we suggest that a change in Zic regulation, specifically the evolution of a dorsal neural expression domain in vertebrate neurulae, was an important step in the evolution of the neural crest.

Riemann solvers with primitive parameter vectors for two-dimensional compressible flows of a real gas

An analysis of averaging procedures is presented for an approximate Riemann solver for the equations governing the compressible flow of a real gas. This study extends earlier work for the Euler equations with ideal gases.