Showing papers by "David C. Fritts published in 1998"

Vorticity dynamics in a breaking internal gravity wave. Part 1. Initial instability evolution

Abstract: A three-dimensional simulation of a breaking internal gravity wave in a stratified, compressible, sheared fluid is used to examine the vorticity dynamics accompanying the transition from laminar to turbulent flow. Our results show that baroclinic sources contribute preferentially to eddy vorticity generation during the initial convective instability of the wave field; the resulting counter-rotating vortices are aligned with the external shear flow. These vortices enhance the spanwise vorticity of the shear flow via stretching and distort the spanwise vorticity via advective tilting. The resulting vortex sheets undergo a dynamical (Kelvin–Helmholtz) instability which rolls the vortex sheets into tubes. These vortex tubes link with the original streamwise convective rolls to produce a collection of intertwined vortex loops. A companion paper (Part 2) describes the subsequent interactions among and the perturbations to these vortices that drive the evolution toward turbulence and smaller scales of motion.

Vorticity dynamics in a breaking internal gravity wave. Part 2. Vortex interactions and transition to turbulence

Abstract: A companion paper (Part 1) employed a three-dimensional numerical simulation to examine the vorticity dynamics of the initial instabilities of a breaking internal gravity wave in a stratified, sheared, compressible fluid. The present paper describes the vorticity dynamics that drive this flow to smaller-scale, increasingly isotropic motions at later times. Following the initial formation of discrete and intertwined vortex loops, the most important interactions are the self-interactions of single vortex tubes and the mutual interactions of multiple vortex tubes in close proximity. The initial formation of vortex tubes from the roll-up of localized vortex sheets gives the vortex tubes axial variations with both axisymmetric and azimuthal-wavenumber-2 components. The axisymmetric variations excite axisymmetric twist waves or Kelvin vortex waves which propagate along the tubes, drive axial flows, deplete the tubes' cores, and fragment the tubes. The azimuthal-wavenumber-2 variations excite m = 2 twist waves on the vortex tubes, which undergo strong amplification and unravel single vortex tubes into pairs of intertwined helical tubes; the vortex tubes then burst or fragment. Reconnection often occurs among the remnants of such vortex fragmentation. A common mutual interaction is that of orthogonal vortex tubes, which causes mutual stretching and leads to long-lived structures. Such an interaction also sometimes creates an m = 1 twist wave having an approximately steady helical form as well as a preferred sense of helicity. Interactions among parallel vortex tubes are less common, but include vortex pairing. Finally, the intensification and roll-up of weaker vortex sheets into new tubes occurs throughout the evolution. All of these vortex interactions result in a rapid cascade of energy and enstrophy toward smaller scales of motion.

Recent results with an MF radar at McMurdo, Antarctica : Characteristics and variability of motions near 12-hour period in the mesosphere

Abstract: We present an analysis of the first wind measurements obtained with an MF (medium frequency) radar installed at McMurdo Station, Antarctica in January 1996. The largest amplitude motions are the quasi-12-hr motions, with additional periodicities at 24 hr, ∼10 hr and 2 to 10 days. The quasi-12-hr motions occur at discrete periods distinct from 12 hr and exhibit pronounced amplitude and vertical wavenumber modulations at planetary wave periodicities. During the months analyzed in this report (mid-January through April 1996) the 12-hr wave is by far the dominant motion the mesosphere. The source of this wave is unknown, but our results provide additional support for the suggestion that such motions arise through nonlinear interactions involving the migrating semidiurnal tide and low-frequency planetary wave motions.

Dynamics of counter-rotating vortex pairs in stratified and sheared environments

Abstract: The evolution of a vertically propagating vortex pair in stratified and sheared environments is studied with a two-dimensional numerical model. We consider a range of Froude (Fr) and Richardson (Ri) numbers, and a limited number of Reynolds numbers (Re). We find that stratification causes the formation of counter-sign vorticity around each of the original vortices through baroclinic production. At higher Fr, this wake vorticity advects the primary vortices closer together, decreasing their separation distance and increasing their vertical propagation speed, as predicted by Crow (1974) and Scorer & Davenport (1970). For these higher values of Fr, the wake vorticity also participates in an instability of the primary vortex pair, with the direction of propagation of the pair oscillating about the vertical. We term this instability the vortex head instability to distinguish it from the jet instabilities to which the wake itself is also susceptible. At lower Fr, internal gravity wave radiation dominates, and the intensity and spatial coherence of each vortex is rapidly reduced.When a mean horizontal flow having constant shear is present in an unstratified fluid, we find that the vortices eventually rotate about one another with the same rotational sense as the background shear flow, as predicted in Lissaman et al. (1973). When stratification is also present, we find that the distribution of baroclinically generated wake vorticity is asymmetric, which sometimes leads to the emergence of a solitary vortex with the same sign as the background shear vorticity (depending on the values of Fr, Ri, and Re). Our limited survey of parameter space indicates that a solitary vortex emerges more rapidly for smaller values of Ri, smaller values of Fr, and/or larger values of Re.

HRDI observations of mean meridional winds at solstice

Abstract: High Resolution Doppler Imager (HRDI) measurements of daytime and nighttime winds at 95 km are used to deduce seasonally averaged Eulerian mean meridional winds during six solstice periods. These estimates are compared with seasonally averaged radar meridional winds and with results from dynamical and empirical wind models. HRDI mean meridional winds are directed from the summer pole toward the winter pole over much of the globe. Peak equatorward winds of about 15 m s−1 are usually observed in the summer hemisphere near 30°. A local minimum in the equatorward winds is often observed poleward of this latitude, with winds approaching zero or reversing direction. A similar structure is seen in contemporaneous radar winds. This behavior differs from residual meridional wind patterns predicted by models. The discrepancies may be related to gravity wave paramaterizations or a consequence of planetary wave influences.

Gravity wave excitation and momentum transport in the solar interior: implications for a residual circulation and lithium depletion

Abstract: We present a conceptual model for the excitation, filtering, and anisotropic propagation of gravity waves in the stratified solar interior at and below the base of the convection zone. Excitation occurs via penetrative convection into the strat- ified and sheared interior, where gravity waves (or g-modes) are excited on spatial and temporal scales imposed by convection and the zonal shearing due to differential rotation. The resulting wave spectrum propagates into the solar interior with increas- ing anisotropy in the horizontal azimuth of propagation with increasing depth. This is due both to the preferential excitation of waves propagating against the mean flow in shear and to the filtering of the spectrum by the mean shear below the source depth. Anisotropic propagation into the solar interior induces momentum transports and accompanying body forces where the waves undergo dissipation. Because the radial shear of the zonal motion reverses sign at 37 o , these momentum fluxes and their associated body forces are prograde at lower latitudes and retrograde at high latitudes with respect to the nearly solid- body rotation of the core. The implications of this forcing in the absence of thermal diffusion on the large scale motions are an induced residual circulation providing Coriolis torques that balance the body forces and a systematic overturning at outer radii of the solar radiative interior. For plausible estimates of the relevant spatial scales and magnitudes of gravity wave forc- ing, we find that the induced circulation penetrates to depths at which Lithium is destroyed and occurs on time scales that are consistent with its observed depletion and the age of the Sun. Using the same estimates, we also find that these processes can- not contribute significantly to Beryllium depletion on the same time scales.

The instability of a vortex tube in a weak external shear and strain

Abstract: We investigate the stability of a straight vortex tube of constant vorticity in the presence of external shearing and straining flows orthogonal to the axis of the vortex tube. We find that the tube is unstable at degenerate wavenumbers (i.e., wavenumbers at which two Kelvin wavemodes have the same frequency). The maximum growth rate of the instability is weighted by the sum of the shear magnitude and the strain magnitude. The presence of the shear also shifts the wavenumber of the instability.