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Gerardo Hernandez-Duenas, Leslie M. Smith, and Samuel N. Stechmann

Abstract

A linear stability analysis is presented for fluid dynamics with water vapor and precipitation, where the precipitation falls relative to the fluid at speed V T. The aim is to bridge two extreme cases by considering the full range of V T values: (i) V T = 0, (ii) finite V T, and (iii) infinitely fast V T. In each case, a saturated precipitating atmosphere is considered, and the sufficient conditions for stability and instability are identified. Furthermore, each condition is linked to a thermodynamic variable: either a variable θ s, which denotes the saturated potential temperature, or the equivalent potential temperature θ e. When V T is finite, separate sufficient conditions are identified for stability versus instability: e/dz > 0 versus s/dz < 0, respectively. When V T = 0, the criterion s/dz = 0 is the single boundary that separates the stable and unstable conditions; and when V T is infinitely fast, the criterion e/dz = 0 is the single boundary. Asymptotics are used to analytically characterize the infinitely fast V T case, in addition to numerical results. Also, the small-V T limit is identified as a singular limit; that is, the cases of V T = 0 and small V T are fundamentally different. An energy principle is also presented for each case of V T, and the form of the energy identifies the stability parameter: either s/dz or e/dz. Results for finite V T have some resemblance to the notion of conditional instability: separate sufficient conditions exist for stability versus instability, with an intermediate range of environmental states where stability or instability is not definitive.

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Gerardo Hernández-Dueñas, M.-Pascale Lelong, and Leslie M. Smith

Abstract

Submesoscale lateral transport of Lagrangian particles in pycnocline conditions is investigated by means of idealized numerical simulations with reduced-interaction models. Using a projection technique, the models are formulated in terms of wave-mode and vortical-mode nonlinear interactions, and they range in complexity from full Boussinesq to waves-only and vortical-modes-only (QG) models. We find that, on these scales, most of the dispersion is done by vortical motions, but waves cannot be discounted because they play an important, albeit indirect, role. In particular, we show that waves are instrumental in filling out the spectra of vortical-mode energy at smaller scales through nonresonant vortex–wave–wave triad interactions. We demonstrate that a richer spectrum of vortical modes in the presence of waves enhances the effective lateral diffusivity, relative to QG. Waves also transfer energy upscale to vertically sheared horizontal flows that are a key ingredient for internal-wave shear dispersion. In the waves-only model, the dispersion rate is an order of magnitude smaller and is attributed entirely to internal-wave shear dispersion.

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