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Paul M. Tag

Abstract

The diagnosis and conservation of energy during condensation is examined. It is shown that the latent enthalpy, when defined in conjunction with the individual enthalpies of water vapor and liquid water, cannot be a function of the latent heat of condensation L but a modified value (L′) which is ∼30% larger than L. The additional energy represented in L′ can be thought of as a necessary absorption by the liquid water to bring the post-condensation air-vapor-liquid system into thermal equilibrium. The difference between L′ and L is a function of the difference in specific heats of water vaper and liquid water. If we assume that (C pdC pr is constant, as is required in our energy conservation derivation, L′ is shown to vary by only 0.59% when computed over the range −50 to +60°C; a representative value for L' is 3.142×106 J Kg−1

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Paul M. Tag

Abstract

Abstract not available.

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Paul M. Tag and Thomas E. Rosmound

Abstract

Accuracy and energy conservation are examined in a three-dimensional (3D) anelastic model. For both dry and moist (noncondensing) atmospheres, we prescribe analytic solutions of momentum, potential temperature and mixing ratio for both periodic and closed boundaries. Accuracy is assessed by comparing amplitudes and phase speeds from both the numerical and analytic solutions. Kinetic and potential energies and enthalpy (including air, vapor, liquid and latent) are calculated for both the mean

and perturbation states. To assess the energetics involved in phase changes, we examine a separate cloud simulation. Two-dimensional (2D) and hydrostatic experiments are also conducted using the cloud simulation.

For the linear analytic wave solutions, phase speeds as a function of time step for our semi-implicit model are compared to both implicit and explicit linear stability generated speeds. We show that an explicit scheme enhances the phase speed up to the CFL cutoff while an implicit scheme retards the phase speed. For the quasi-Lagrangian method of moisture advection, we find that a water conservation algorithm is necessary to maintain conservation of total perturbation energy. Similarly. the correct inclusion of moisture in the computation of density is most critical to energy conservation. In comparing a 2D forced cloud to the 3D simulation, only 17% of the perturbation energy which changes form in the 3D case does so in the 2D experiment-in direct relation to the larger cloud in the 3D simulation. And finally, comparing experiments both with and without the hydrostatic assumption, we verify earlier 2D findings that the magnitude of the vertical motion is larger in a hydrostatic model.

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Paul M. Tag and Steven W. Payne

Abstract

Cloud top entrainment instability, as a mechanism for the breakup of marine stratus, is examined with a three-dimensional, planetary boundary layer (PBL) model. Specifically, we examine the criterion developed by Randall and Deardorff; this criterion states that stratus will break up if the equivalent potential temperature gradient at cloud top becomes less than a critical value. To examine this hypothesis, we simulate a horizontally uniform stratus layer which is excited from above by small random temperature perturbations. The buoyancy instability ratio (BIR), defined as Δθe(Δθe)crit and computed at cloud top, is calculated locally across the domain and also averaged to define a mean value. Six cases, involving different wind speeds and above-cloud soundings, produce different initial BIRs and different breakup sequences. In general, we find that a mean BIR greater that one is a necessary condition for stratus breakup; however, we also find that the timing of breakup following achievement of the critical ratio is different from run to run. The low wind speed cases, initially most stable at cloud top, are the first to break up, while the higher wind speed (most unstable) cases require longer time to break up. We conclude that an additional mechanism is necessary to stimulate vertical motion in order to take advantage of the cloud-top entrainment instability. In our simulations, that additional stimulation comes from vertical motions generated by Rayleigh-type instability in the PBL.

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