Thermodynamics is the study of energy and its transformations. Traditionally, thermodynamics has been used to understand the transfer of “heat” and the mechanical work that can be realized from it. Mechanical heat engines became important to society during the Industrial Revolution, but natural heat engines exist, too, although we do not often speak of thunderstorms and hurricanes in such terms. All such “engines” ultimately derive their organized, macroscopic motions from the random motions of the molecules making up the systems.

Thermodynamics is useful because it applies to many phenomena in the Universe. At the same time, the discipline can become abstract, especially when one is not sure exactly what part of the Universe is being considered. It is therefore important to define the components and variables of the system carefully. Traditionally, the “system” is the part of the universe we are interested in for a particular application. Any system is separated from the rest of the Universe by a “control surface” situated between it and its “surroundings” or “environment”. The “system” plus “surroundings” together make up the “universe”. The “state” of the system at any given time is specified by the magnitudes of all relevant macro-scopic variables, such as temperature, pressure, and volume of the system. In atmospheric physics, a commonly used system is a parcel of air, an amount of gas that is small enough to have uniform properties, but large enough to contain many molecules.

Importance of clouds

What would our world be like without clouds? Unimaginable – quite literally – for clouds are essential for our lives on earth. Humans, and for that matter most other land-dwelling species, would simply not exist, let alone thrive in the absence of the fresh water that clouds supply. The favorable climate we have enjoyed for thousands of years might also not exist in the absence of atmospheric water and clouds. A world without clouds would be different indeed.

Clouds contribute to the environment in many ways. Clouds, through a variety of physical processes acting over many spatial scales, provide both liquid and solid forms of precipitation and nature's only significant source of fresh water. Under extreme circumstances, however, clouds and precipitation may not form at all, leading to prolonged droughts in some regions. At other times and places, too much rain or snow falls, giving rise to devastating floods or blizzards. Liquid rain drops bring usable water directly to the surface, while simultaneously carrying many trace chemicals out of the atmosphere and into the ecosystems of the Earth. Chemical wet deposition thereby supplies nutrients (and sometimes toxic compounds) to both terrestrial and aquatic lifeforms, as well as the weak acids responsible for the weathering of the Earth's crust. The solid forms of precipitation contribute in additional ways to the world as we know it. Snow, for instance, forms the winter snowpacks that dramatically affect the radiation balance and climate of high latitudes on a seasonal basis.

The naming of cloud types began in the early 1800s. Jean Babtiste Lamarck, a French naturalist, proposed a naming scheme in about 1802, but his nomenclature did not catch on, perhaps because of the cumbersome French terms he used. Lamarck is, however, credited with proposing that clouds be identified with the level (high, middle, or low) at which they appear in the atmosphere. Then, within a year or so, Luke Howard, an English chemist/pharmacist, suggested that clouds could be grouped into four main categories: Cirrus (Latin for hair curl), Cumulus (heap), Stratus (layer), and Nimbus (rain). The simple Latin terminology likely helped Howard's categorization to be accepted more readily.

The cloud classification scheme used internationally today thus traces its roots back to the suggestions of Lamarck (for organization into three levels) and Howard (for use of Latin names). The names in Latin follow the convention used in biology: Genus species. Subspecies or varieties are often appended to distinguish one species of cloud from another. The names given to various cloud types, now as then, are all based on human observations from the surface. The modern methods of observing clouds (aircraft, radar, satellites, etc.) were not available to the early observers. The determination of cloud type is based on visual appearance only, mainly the shape/form and size of the cloud. The altitude of cloud base is difficult to judge precisely, but the form usually helps us distinguish high clouds from mid-level and low clouds.

Clouds contribute to our lives in both direct and indirect ways. Clouds are at once the most visible elements of the sky and the dominant contributors to the weather we experience every day. Less apparent, but perhaps even more important, are the roles clouds play in the global energy and water budgets that determine the climate of Earth. Through their ability to precipitate, clouds provide virtually all of the fresh water on Earth and a crucial link in the hydrologic cycle. Clouds are also the most effective agents cleansing the atmosphere, although some terrestrial and aquatic ecosystems pay the price for anthropogenic emissions of chemicals into the air. With ever-increasing importance being placed on quantifiable predictions, whether to forecast the local weather or to anticipate changes in global climate, we must learn how clouds operate in the real atmosphere, where two-way interactions with natural and anthropogenic pollutants are common.

Clouds have been the subject of observation for centuries, but serious systematic investigations began only a few decades ago. For all practical purposes, the study of clouds can be traced back to Luke Howard, the English pharmacist who began, around 1803, the system of naming cloud types that we still use today (see Appendix A). Speculation about the composition and nature of clouds persisted for many years. Direct observations from balloons and aircraft helped greatly to develop a base of empirical knowledge upon which the research community could later build testable hypotheses.

Overview

The electrification of large cumulonimbus clouds often leads to lightning, an exciting, yet sometimes frightening phenomenon of nature. The generation of electric fields of sufficient strength to cause electrical breakdown of the air involves a broad range of scales, all the way from the size of individual units of electrical charge (electrons and protons) to that of the cloud itself. Both the microphysical processes and the macroscale motions of air within thunderstorms must act in coordinated ways for charges to separate and large electric fields to develop. The subjects of charging mechanisms, electric-field evolution, and discharge events are each extensive in their own rights. The treatment here offers a basic overview to show the interconnectivity of the various scales and processes.

Electrical structure of thunderstorms and the atmosphere

Thunderstorms, by definition, produce thunder, the audible consequence of lightning. Ever since the pioneering work of Franklin and d'Alibard in the mid-1700s, it has been recognized that lightning is an electrical phenomenon resulting from excess charges in various parts of the parent cloud. Subsequent investigations by Wilson in the 1920s and many others have enabled us to develop a valid conceptual model of thunderstorm electrification.

The simplest charge structure of a thunderstorm is envisioned to be similar to that shown in Fig. 14.1. A convective storm during its mature stage of development exhibits an anvil that represents the upper outflow of cloudy air from the storm's interior.

Change occurs in nature when a system is not in equilibrium. Natural systems are frequently thrust out of balance, into a disequilibrium state that cannot persist in the long run. Sunlight shining on a puddle, for instance, heats the ground and forces the water to evaporate. Radiative transfer constitutes one way change and transformations are brought about. Atmospheric systems (e.g., clouds) routinely interact with their environments through exchanges of matter and energy, and they respond to external forces (e.g., pressure gradients). Environmental interactions shift the mechanical, thermal, and chemical balances that allowed a system to be at equilibrium in the first place, forcing the system to change, be transformed to another state. The atmosphere is never at equilibrium, so it is continually changing in one way or another. Indeed, clouds ultimately owe their existence to the disequilibrium forced by solar heating of the surface.

Deviations from equilibrium

Deviations from equilibrium drive changes in the observable properties of a system. A ladder that is kicked may suddenly topple, an example of mechanical forces that become imbalanced. A turkey placed in an oven gradually gets hot, an example of energy transfer because of a temperature difference. A mixture of air and natural gas (methane, CH4) exposed to a spark explodes, an example of one set of compounds (oxygen and methane) transforming to another (carbon dioxide and water) because of differences in the chemical potentials of the compounds involved.

Overview

Warm clouds typically form in the lower troposphere when ice is not important to the microphysics. The development of warm clouds depends on condensation to activate aerosol particles and grow liquid droplets initially. Subsequent processes include drop–drop collisions, coalescence, and disruption during the formation of rain in mature clouds. Such processes may also occur in colder, mixed-phase clouds as long as the presence of ice does not interfere significantly with any of the warm-cloud microphysical processes.

The focus of this chapter is the spectral evolution of drop populations, how small (~ 10 μm radius) cloud droplets grow to large (~ 1 mm radius) raindrops. Many of the individual processes responsible for particle formation and growth have already been treated, so we now look at how these processes work collectively to form rain.

A perspective of how liquid-phase microphysics leads to rain in a warm cloud can be obtained by viewing the different processes as discrete boxes operating simultaneously inside the cloud. As shown in Fig. 11.1, one process leads to another, from initial activation of the aerosol entering the cloud in its updraft to rain falling out through its base. Overall, rain formation requires several broad categories of spectral evolution: condensation, coalescence initiation, and continuous collection. As supersaturation develops by adiabatic cooling of the rising air, the aerosol particles grow first as haze droplets, then as cloud droplets by condensation.

Transformations, changes in the structure or composition of something, are common in our everyday world. Lakes freeze in the winter; ponds dry up on hot summer days. Salt melts ice and dissolves in water. Such examples may be classified as either physical or chemical, if you wish, but many natural phenomena represent blends of both disciplines. Of primary interest is the notion that the entity in question (here, water or salt) has undergone a change of one sort or another. Learning how transformations proceed in nature is a fundamental goal of science, so we are often concerned with “processes” and “mechanisms”, the sequence of discrete events that leads to a particular outcome. Clouds owe their existence to particular transformations: Water vapor changes into liquid droplets, and those droplets later freeze when the temperature becomes low enough. Clouds would never form (or dissipate) were water not to change, be transformed from one state to another. We simply cannot understand much about clouds without dealing with transformations in detail. In fact, it is often useful to view clouds as processes, rather than as objects or entities. This part of the book lays out the guiding principles upon which to build our deeper understanding of atmospheric processes leading to clouds.

Natural transformations take place when a system deviates in some way from its most balanced or equilibrium state.

There are two protagonists in this story: inertia and friction. One meets them first in the mechanics of particles and solids where their interplay is not very complicated: inertia tries to keep the motion while friction tries to stop it. Going from a finite to an infinite number of degrees of freedom is always a game-changer. We will see in this book how an infinitesimal viscous friction makes fluid motion infinitely more complicated than inertia alone ever could. Without friction, most incompressible flows would stay potential, i.e. essentially trivial. At solid surfaces, friction produces vorticity, which is carried away by inertia and changes the flow in the bulk. Instabilities then bring about turbulence, and statistics emerges from dynamics. Vorticity penetrating the bulk makes life interesting in ideal fluids though in a way different from superfluids and superconductors.

On the other hand, compressibility makes even potential flows non-trivial as it allows inertia to develop a finite-time singularity (shock), which friction manages to stop. It is only in a wave motion that inertia is able to have an interesting life in the absence of friction, when it is instead partnered with medium anisotropy or inhomogeneity, which cause the dispersion of waves. The soliton is a happy child of that partnership.

In this chapter, we consider systems that support small-amplitude waves whose speed depends on wavelength. This is in distinction from acoustic waves (or light in the vacuum) that all move with the same speed so that a small-amplitude one-dimensional perturbation propagates without changing its shape. When the speeds of different Fourier harmonics are different, the shape of a perturbation generally changes as it propagates. In particular, initially localized perturbation spreads. That is, dispersion of wave speed leads to packet dispersion in space. This is why such waves are called dispersive. Since different harmonics move with different speeds, then they separate with time and can subsequently be found in different places. As a result, for quite arbitrary excitation mechanisms one often finds locally sinusoidal perturbation, the property well known to everybody who has observed waves on water surface. Surface waves form the main subject of analysis in this section but the ideas and results apply equally well to numerous other dispersive waves that exist in bulk fluids, plasma and solids (where dispersion usually results from some anisotropy or inhomogeneity of the medium). We shall try to keep our description universal when we turn to a consideration of non-linear dispersive waves having finite amplitudes. We shall consider weak non-linearity, assuming amplitudes to be small, and weak dispersion, which is possible in two distinct cases: (i) when the dispersion relation is close to acoustic and (ii) when waves are excited in a narrow spectral interval.

Fluid flows can be kept steady only for very low Reynolds numbers and for velocities much less than the velocity of sound. Otherwise, either flow experiences instability and becomes turbulent or sound and shock waves are excited. Both sets of phenomena are described in this chapter.

A formal reason for instability is non-linearity of the equations of fluid mechanics. For incompressible flows, the only non-linearity is due to fluid inertia. We shall see how a perturbation of a steady flow can grow due to inertia, thus causing an instability. For large Reynolds numbers, the development of instabilities leads to a strongly fluctuating state of turbulence.

An account of compressibility, on the other hand, leads to another type of unsteady phenomena: sound waves. When density perturbation is small, velocity perturbation is much less than the speed of sound and the waves can be treated within the framework of linear acoustics. We first consider linear acoustics and discover what phenomena appear as long as one accounts for a finiteness of the speed of sound. We then consider non-linear acoustic phenomena, the creation of shocks and acoustic turbulence.

Instabilities

At large Re most of the steady solutions of the Navier–Stokes equation are unstable and generate an unsteady flow called turbulence.

Kelvin–Helmholtz instability

Apart from a uniform flow in the whole space, the simplest steady flow of an ideal fluid is a uniform flow in a semi-infinite domain with the velocity parallel to the boundary.