One Bold Experiment

A monthly exchange of letters from 165 seventh graders in an arts school in Charleston, South Carolina to similar classrooms in 16 countries around the world proved to be the writing project that captured every state writing standard all at once -- brainstorming, writing, collaboration, analysis, proofreading, and re-writing. This one activity was the highlight of the year for each student as letters and gifts poured in from every continent September to June. This was truly a teacher\u27s dream come true

Instability in Geophysical Flows

An Open Access overview of physical processes that generate instability in geophysical systems. It covers classical analytical approaches together with numerical methods for quick prediction of stability in a system. Including exercises and MATLAB® coding examples, it can be used for self-study or advanced courses in the environmental sciences

Dissipation-range geometry and scalar specta in sheared stratified turbulence

Direct numerical simulations of turbulence resulting from Kelvin{Helmholtz instability in stratified shear flow are used to examine the geometry of the dissipation range in a variety of flow regimes. As the buoyancy and shear Reynolds numbers that quantify the degree of isotropy in the dissipation range increase, alignment statistics evolve from those characteristic of parallel shear flow to those found previously in studies of stationary, isotropic, homogeneous turbulence (e.g. Ashurst et al. 1987; She et al. 1991; Tsinober et al. 1992). The analysis yields a limiting value for the mean compression rate of scalar gradients that is expected to be characteristic of all turbulent flows at sufficiently high Reynolds number. My main focus is the value of the constant q that appears in both the Batchelor (1959) and Kraichnan (1968) theoretical forms for the passive scalar spectrum. Taking account of the effects of time-dependent strain, I propose a revised estimate of q, denoted qe, which appears to agree with spectral shapes derived from simulations and observations better than do previous theoretical estimates. The revised estimate is qe = 7.3±0.4, and is expected to be valid whenever the buoyancy Reynolds number exceeds O(10²). The Kraichnan (1968) spectral form, in which effects of intermittency are accounted for, provides a better fit to the DNS results than does the Batchelor (1959) form

Kelvin-Helmholtz billow evolution from a localized source

The envelope function for Kelvin–Helmholtz billows growing from a point disturbance is derived on the basis of linear perturbation theory. The result describes an elliptical patch of billows that expands linearly in time as the billows grow. An analytical model of the dispersion relation is used to derive quantitative expressions for the spreading rate and ellipticity of the patch as functions of the bulk Richardson number. The theoretical results are verified using a combination of two- and three-dimensional nonlinear simulations, and are compared with visual observations of billow patches in the atmosphere.Keywords: Turbulence, Stratified shear flow, Instabilit

Secondary Kelvin-Helmholtz instability in weakly stratified shear flow

The growth of secondary vortices on the braids separating Kelvin–Helmholtz billows is investigated via numerical simulations. The similarity theory of Corcos & Sherman (1976) is extended to include mixing processes with Prandtl number greater than unity, and is shown to provide a useful description of the physics of the braid regions just prior to the onset of secondary instability. The numerical study of Staquet (1995) is extended to include a wider range of Prandtl numbers and bulk Richardson numbers. Length and time scales of the secondary instability are compared with predictions based on normal-mode stability analysis of the braids. The onset of instability is shown to be accompanied by a dramatic increase in mixing efficiency in the braid region, emphasizing the potential importance of preturbulent Kelvin–Helmholtz billows for mixing stratified fluids

Secondary circulations in Holmboe waves

A sequence of direct simulations is used to study mechanisms for the growth of secondary circulations and turbulence in stratified shear flows. Five cases are examined, of which four deliver Holmboe waves as the primary instability and the fifth generates Kelvin-Helmholtz billows. Secondary circulations range in strength from weak, laminar motions to turbulence that destroys the parent wave. Processes that drive disturbance growth include shear production via the Orr mechanism, sheared convection in overturned regions, and sloping convection in stably stratified wave crests. Results are compared with previous predictions based on normal mode stability analysis

Effects of Ambient Turbulence on Interleaving at a Baroclinic Front

In this paper the authors investigate the action of ambient turbulence on thermohaline interleaving using both theory and numerical calculations in combination with observations from Meddy Sharon and the Faroe Front. The highly simplified models of ambient turbulence used previously are improved upon by allowing turbulent diffusivities of momentum, heat, and salt to depend on background gradients and to evolve as the instability grows. Previous studies have shown that ambient turbulence, at typical ocean levels, can quench the thermohaline interleaving instability on baroclinic fronts. These findings conflict with the observation that interleaving is common in baroclinic frontal zones despite ambient turbulence. Another challenge to the existing theory comes from numerical experiments showing that the Schmidt number for sheared salt fingers is much smaller than previously assumed. Use of the revised value in an interleaving calculation results in interleaving layers that are both weaker and thinner than those observed. This study aims to resolve those paradoxes. The authors show that, when turbulence has a Prandtl number greater than unity, turbulent momentum fluxes can compensate for the reduced Schmidt number of salt fingering. Thus, ambient turbulence determines the vertical scale of interleaving. In typical oceanic interleaving structures, the observed property gradients are insufficient to predict interleaving growth at an observable level, even when improved turbulence models are used. The deficiency is small, though: gradients sharper by a few tens of percent are sufficient to support instability. The authors suggest that this is due to the efficiency of interleaving in erasing those property gradients. A new class of mechanisms for interleaving, driven by flow-dependent fluctuations in turbulent diffusivities, is identified. The underlying mechanism is similar to the well-known Phillips layering instability; however, because of Coriolis effects, it has a well-defined vertical scale and also a tilt angle opposite to that of finger-driven interleaving

Efficiency of Mixing Forced by Unsteady Shear Flow

The dependence of mixing efficiency on time-varying forcing is studied by direct numerical simulation (DNS) of Kelvin–Helmholtz (KH) instability. Time-dependent forcing fields are designed to reproduce a wavelike oscillation by solving the equations of motion in a tilted coordinate frame and allowing the tilt angle to vary in time. Mixing efficiency Γ is defined as the ratio of potential energy gain to dissipation, both averaged over one forcing cycle and first examined via parameters characterizing waves: the minimum Richardson number Riₘᵢₙ and the normalized frequency of the forcing ω/N. The effect of Reynolds number Re₀ and the initial random disturbance amplitude b are also examined. In the experiments presented, Γ varies between 0.21 and 0.36 and is controlled by the timing of two events: the emergence of KH billows and the arrival of the deceleration of the mean shear by the wavelike forcing. Here, Γ is higher than a canonical value of 0.2 when the deceleration phase of the forcing suppresses the less efficient turbulence after breakdown of KH billows. However, when Riₘᵢₙ and ω/N are small, KH billows start to develop before Riₘᵢₙ is achieved. Therefore, the forcing accelerates the mean shear and thereby sustains turbulence after the breakdown of KH billows. The canonical value is then reproduced in the DNS. Although larger values of Re₀ and b intensify the development of KH billows and modify Γ, this effect is less significant when forcing fields act to sustain turbulence. The time-averaged Thorpe scale and Ozmidov scale are also used to see how mixing is modified by forcing fields and compared with past microstructure measurements. It is found that DNS also corresponds to past observations if the forcing accelerates the mean shear to sustain turbulence

Instability and Diapycnal Momentum Transport in a Double-Diffusive, Stratified Shear Layer

The linear stability of a double-diffusively stratified, inflectional shear flow is investigated. Double-diffusive stratification has little effect on shear instability except when the density ratio R[subscript]ρ is close to unity. Double-diffusive instabilities have significant growth rates and can represent the fastest-growing mode even in the presence of inflectionally unstable shear with a low Richardson number. In the linear regime, background shear has no effect on double-diffusive modes except to select the orientation of the wave vector. The converse is not true: double-diffusive modes modify the mean shear via momentum fluxes. The momentum flux driven by salt sheets is parameterized in terms of a Schmidt number (ratio of eddy viscosity to saline diffusivity) Sc[subscript]s. In the oceanic parameter regime, Sc[subscript]s is less than unity and can be approximated as Sc[subscript]s = 0.08 ln[R[subscript]ρ/(R[subscript]ρ − 1)]. Enhanced molecular dissipation by unstable motions is quantified in terms of the dissipation ratio Γ, and the results are compared with observations. Corresponding results are given for diffusive convection in an inflectional shear flow, though linear theory is expected to give a less accurate description of this mechanism.Keywords: Transport, Ocean models, Diffusio