A note concerning the Lighthill “sandwich model” of tropical cyclones

Abstract

The basic element of Lighthill's ''sandwich model'' of tropical cyclones is the existence of ''ocean spray,'' a layer intermediate between air and sea made up of a cloud of droplets that can be viewed as a ''third fluid.'' We propose a mathematical model of the flow in the ocean spray based on a semiempirical turbulence theory and demonstrate that the availability of the ocean spray over the waves in the ocean can explain the tremendous acceleration of the wind as a consequence of the reduction of the turbulence intensity by droplets. This explanation complements the thermodynamic arguments proposed by Lighthill.ocean spray ͉ turbulence in stratified fluids I n his posthumously published work (1), Lighthill emphasized ''the need to fill gaps in knowledge about the ocean spray at extreme wind speeds.'' Lighthill himself concentrated on the thermodynamic issues in the phenomena: the variation of the bulk flow energy due to the evaporation of droplets in the ocean spray and the subsequent cooling of the atmosphere. A recent review of the physics of tropical cyclone motion can be found in ref. 2, where, by the way, the fundamental work (1) is not referenced.Our approach is different and complements Lighthill's. We consider the modification of the balance of turbulent energy of the flow in ocean spray by the suspension of droplets. Furthermore, we demonstrate, by using the general theory of turbulent transfer of suspended heavy particles developed by A. N. Kolmogorov and G.I.B. (see pp. 301-306 in ref. 3 and the references cited there) that the presence of large water droplets in the ocean spray leads to a significant reduction of the turbulence intensity in the flow and consequently to a sharp flow acceleration. The cooling due to the evaporation of the droplets makes an additional contribution to the reduction of turbulence, to the stabilization of the flow stratification, and to the flow acceleration. Basic Mathematical ModelWe concentrate here on a single effect: flow acceleration in an ocean spray that carries large water droplets, leaving aside the influence of the Coriolis force and the cooling effects due to the evaporation of the droplets. We demonstrate that flow acceleration by droplets is very significant by itself. The effects of air cooling by evaporation and of the Coriolis force can be included easily in numerical models.Thus, we consider a steady horizontally homogeneous flow of the air-droplets mixture, so that all components of the field, including the velocity u, the volume concentration of the droplets s, etc., depend only on the vertical coordinate z.The phenomenon is sketched in Fig. 1. We average the pattern over the horizontal coordinate. The waves, whose average height is z W , form the water-air boundary. After averaging the wave crests form a horizontal line z ϭ z W . The waves break (think of the famous painting of Hokusai), and on average the jets formed at the crests break up at the height z ϭ z 0 creating droplets. We assume in our model that all droplets are identical, and the concent...

Impact of Ocean Spray on the Dynamics of the Marine Atmospheric Boundary Layer

“…However, the assumption that the flow turns into that regime by light droplets near the surface is questionable-such a regime should exist in the main core of the flow. Barenblatt et al (2005) considered a more realistic case assuming that sea droplets are rather large with ω 1. They found that the action of the buoyancy forces results in suppression of the turbulence intensity and sharp flow acceleration in a thin layer below the breaking crests where the droplets are produced.…”

Investigation of the physical scaling of sea spray spume droplet production

“…Because of their much larger sizes (and larger mass flux) spume droplets are expected to dominate the hurricane droplet flux problem. Droplets may play a large role in latent heat transfer between the ocean and atmosphere [Edson and Fairall., 1994;Andreas et al, 1995;Makin, 1998] and under extremely high winds such as found in hurricanes, may also have a large effect on the air-sea exchange of momentum [Andreas and Emanuel, 2001;Andreas, 2004;Barenblatt et al, 2005;Makin, 2005]. From a modeling perspective, there are two fundamental problems, (1) spec-ification of the sea surface droplet source strength and (2) computation (or parameterization) of the thermodynamic effects of the sea spray [Andreas, 1992;Fairall et al, 1994;Kepert et al, 1999].…”

Effect of Ocean Spray on Vertical Momentum Transport Under High-Wind Conditions

“…We also re-examined the findings reported in Barenblatt et al (2005) in which the authors argued that the presence of water spray can significantly accelerate the flow. While our investigation was inspired by this idea and fully supports it, we believe that the numerical results reported there might be affected by computational errors and an unrealistic choice of model parameters.…”

“…Various mechanical factors that contribute to the air-sea momentum exchange have been investigated in a number of recent studies: Donelan et al (2004), Makin (2004), Barenblatt et al (2005), Kudryavtsev (2006), Vakhguelt (2007), Babanin and Makin (2008) to name a few. Several approaches have been proposed to estimate the effect of sea spray on the wind stress (Makin 2004;Barenblatt et al 2005;Kudryavtsev 2006).…”

“…Several approaches have been proposed to estimate the effect of sea spray on the wind stress (Makin 2004;Barenblatt et al 2005;Kudryavtsev 2006). Makin (2004) assumed a limiting saturation in a thin region adjacent to the sea surface as described previously by Barenblatt and Golitsyn (1974) for high flow speeds: the air in this layer absorbs the maximum possible amount of droplets given the unrestricted production of ocean spray.…”