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Register a new userDissipative models of swell propagation across the Pacific
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Ocean swell plays an important role in the transport of energy across the ocean, yet its evolution is still not well understood. In the late 1960s, the nonlinear Schr{o}dinger (NLS) equation was derived as a model for the propagation of ocean swell over large distances. More recently, a number of dissipative generalizations of the NLS equation based on a simple dissipation assumption have been proposed. These models have been shown to accurately model wave evolution in the laboratory setting, but their validity in modeling ocean swell has not previously been examined. We study the efficacy of the NLS equation and four of its generalizations in modeling the evolution of swell in the ocean. The dissipative generalizations perform significantly better than conservative models and are overall reasonable models for swell amplitudes, indicating dissipation is an important physical effect in ocean swell evolution. The nonlinear models did not out-perform their linearizations, indicating linear models may be sufficient in modeling ocean swell evolution.
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In this paper we describe the construction of an efficient probabilistic parameterization that could be used in a coarse-resolution numerical model in which the variation of moisture is not properly resolved. An Eulerian model using a coarse-grained field on a grid cannot properly resolve regions of saturation---in which condensation occurs---that are smaller than the grid boxes. Thus, in the absence of a parameterization scheme, either the grid box must become saturated or condensation will be underestimated. On the other hand, in a stochastic Lagrangian model of moisture transport, trajectories of parcels tagged with humidity variables are tracked and small-scale moisture variability can be retained; however, explicitly implementing such a scheme in a global model would be computationally prohibitive. One way to introduce subgrid-scale saturation into an Eulerian model is to assume the humidity within a grid box has a probability distribution. To close the problem, this distribution is conventionally determined by relating the required subgrid-scale properties of the flow to the grid-scale properties using a turbulence closure. Here, instead, we determine an assumed probability distribution by using the statistical moments from a stochastic Lagrangian version of the system. The stochastic system is governed by a Fokker--Planck equation and we use that, rather than explicitly following the moisture parcels, to determine the parameters of the assumed distribution. We are thus able to parameterize subgrid-scale condensation in an Eulerian model in a computationally efficient and theoretically well-founded way. In two idealized advection--condensation problems we show that a coarse Eulerian model with the subgrid parameterization is well able to mimic its Lagrangian counterpart.
Calculations of entropy fluxes and production rate have been evaluated with some success to study atmospheric processes. However, recurring questions arise as to how best to take into account entropy flux due to radiation, for example. This article raises another kind of question: how to define the entropy of the atmosphere itself, which is composed of variable proportions of dry air (nitrogen, oxygen, argon, etc.) and water (vapour, liquid, ice). The specific values of the entropy for such a variable composition system depend on the reference values of its components. Most of the current definitions are based on entropies set at zero for dry air and liquid water at zero degrees Celsius. Differently, the third law of thermodynamics assumes that the entropy of all species cancels out for the more stable solid state at the zero of absolute temperatures. In this paper, we analyze the possible consequences of this absolute definition of entropy of moist air on the calculation of entropy fluxes. The impacts of moisture are significant and these new calculation methods seem to be able to modify the budgets of atmospheric entropy, with possible impacts on the nature of the equilibrium of the atmosphere resulting from entropic imbalances induced by radiations.
A careful reading of old articles puts Olivier Pauluis criticisms concerning the definition of isentropic processes in terms of a potential temperature closely associated with the entropy of moist air, together with the third principle of thermodynamics, into perspective.
It is important to be able to calculate the moist-air entropy of the atmosphere with precision. A potential temperature has already been defined from the third law of thermodynamics for this purpose. However, a doubt remains as to whether this entropy potential temperature can be represented with simple but accurate first- or second-order approximate formulas. These approximations are rigorously defined in this paper using mathematical arguments and numerical adjustments to some datasets. The differentials of these approximations lead to simple but accurate formulations for tendencies, gradients and turbulent fluxes of the moist-air entropy. Several physical consequences based on these approximations are described and can serve to better understand moist-air processes (like turbulence or diabatic forcing) or properties of certain moist-air quantities (like the static energies).
A framework is introduced to compare moist `potential temperatures. The equivalent potential temperature, $theta_e,$ the liquid water potential temperature, $theta_ell,$ and the entropy potential temperature, $theta_s$ are all shown to be potential temperatures in the sense that they measure the temperature moist-air, in some specified state, must have to have the same entropy as the air-parcel that they characterize. They only differ in the choice of reference state composition: $theta_ell$ describes the temperature a condensate-free state, $theta_e$ a vapor-free state, and $theta_s$ a water-free state would require to have the same entropy as the given state. Although in this sense $theta_e,$ $theta_ell,$ and $theta_s$ are all different flavors of the same thing, only $theta_ell$ satisfies the stricter definition of a `potential temperature, as corresponding to a reference temperature accessible by an isentropic and closed transformation of a system in equilibrium; only $theta_e$ approximately measures the ability of moist-air to do work; and only $theta_s$ measures air-parcel entropy. None mix linearly, but all do so approximately, and all reduce to the dry potential temperature, $theta$ in the limit as the water mass fraction goes to zero. As is well known, $theta$ does mix linearly and inherits all the favorable (entropic, enthalpic, and potential temperature) properties of its various -- but descriptively less rich -- moist counterparts. All, involve quite complex expressions, but admit relatively simple and useful approximations. Of the three moist `potential temperatures, $theta_s$ is the least familiar, but the most well mixed in the broader tropics, a property that merits further study as a basis for constraining mixing processes.
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