# On the generation of surface waves by shear flows

@article{Miles1957OnTG, title={On the generation of surface waves by shear flows}, author={John Miles}, journal={Journal of Fluid Mechanics}, year={1957}, volume={3}, pages={185 - 204} }

A mechanism for the generation of surface waves by a parallel shear flow U(y) is developed on the basis of the inviscid Orr-Sommerfeld equation. It is found that the rate at which energy is transferred to a wave of speed c is proportional to the profile curvature -U"(y) at that elevation where U = c. The result is applied to the generation of deep-water gravity waves by wind. An approximate solution to the boundary value problem is developed for a logarithmic profile and the corresponding…

## 1,343 Citations

### On the generation of surface waves by shear flows. Part 5

- Environmental Science, PhysicsJournal of Fluid Mechanics
- 1967

Laboratory and field measurements of the generation of gravity waves by turbulent winds imply that a theoretical model based on laminar flow may be adequate on a laboratory, but not an oceanographic,…

### On the generation of surface waves by shear flows Part 3. Kelvin-Helmholtz instability

- Physics, Environmental ScienceJournal of Fluid Mechanics
- 1959

The Kelvin-Helmholtz model for the formation of surface waves at the interface between two fluids in relative motion is generalized for parallel shear flows. It is assumed that phase changes across…

### On the generation of surface waves by shear flows. Part 2

- PhysicsJournal of Fluid Mechanics
- 1959

A previous analysis for the generation of surface waves by a parallel shear flow (Miles 1957 a) is extended by: (a) presenting results based on a more accurate solution of the differential equation;…

### Surface-wave generation revisited

- Physics, Environmental ScienceJournal of Fluid Mechanics
- 1993

The quasi-laminar model for the transfer of energy to a surface wave from a turbulent shear flow (Miles 1957) is modified to incorporate the wave-induced perturbations of the Reynolds stresses, which…

### An asymptotic theory for the generation of nonlinear surface gravity waves by turbulent air flow

- Physics, Environmental ScienceJournal of Fluid Mechanics
- 1996

Based on a previous linear theory (van Duin & Janssen 1992), turbulent air flow over a surface gravity wave of finite amplitude is studied analytically by the methods of matched asymptotic expansions…

### Generation of surface waves by shear-flow instability

- PhysicsJournal of Fluid Mechanics
- 2013

Abstract We consider the linear stability of an inviscid parallel shear flow of air over water with gravity and capillarity. The velocity profile in the air is monotonically increasing upwards from…

### Growth of Stokes Waves Induced by Wind on a Viscous Liquid of Infinite Depth

- Physics, Environmental Science
- 2016

The original investigation of Lamb (1932, {\S}349) for the effect of viscosity on monochromatic surface waves is extended to account for second-order Stokes surface waves on deep water in the…

### An analytic model of the generation of surface gravity waves by turbulent air flow

- Physics, Environmental ScienceJournal of Fluid Mechanics
- 1992

Turbulent air flow over a surface gravity wave of small amplitude is studied on the basis of a family of first-order closure models, of which the eddy viscosity model and Prandtl's mixing-length…

## References

SHOWING 1-10 OF 21 REFERENCES

### On the generation of waves by turbulent wind

- Environmental Science, PhysicsJournal of Fluid Mechanics
- 1957

A theory is initiated for the generation of waves upon a water surface, originally at rest, by a random distribution of normal pressure associated with the onset of a turbulent wind. Corrlations…

### The Generation of Wind Waves on a Water Surface

- Environmental Science
- 1953

The statistical methods for treating continuous media developed elsewhere are applied to the generation of surface gravity waves. The wind stress is assumed to be everywhere normal to the disturbed…

### On the Formation of Water Waves by Wind

- Geology
- 1925

It is well known that in certain circumstances a type of instability may arise at the surface of separation of two fluids when there is a finite difference between the velocities on the two sides of…

### The growth of waves on water due to the action of the wind

- Environmental Science
- 1932

The behaviour of the surface of water over which a wind is blowing was considered mathematically by Kelvin. Assuming the air and the water to be perfect liquids moving irrotationally, he found that…

### The law of the wake in the turbulent boundary layer

- EngineeringJournal of Fluid Mechanics
- 1956

After an extensive survey of mean-velocity profile measurements in various two-dimensional incompressible turbulent boundary-layer flows, it is proposed to represent the profile by a linear…

### Wind stress on water: An hypothesis

- Environmental Science
- 1955

The form drag of wind on an irregular surface is found to equal the product of U2 (U is anemometer wind-speed) and a function of the two-dimensional spectrum of this surface. For a solid surface this…

### Hydrodynamic stability of the flow in the laminar boundary layer between parallel streams

- Engineering, Environmental ScienceMathematical Proceedings of the Cambridge Philosophical Society
- 1954

ABSTRACT A method is given for determining the stability of small sinusoidal oscillations in the steady laminar flow of a horizontal wind over the surface of a liquid at rest (with particular…

### Some observations of air flow over the sea

- Environmental Science
- 1955

Wind speeds were measured over the sea at five heights up to 8 m. Though the fetch was limited, the wind profiles obtained are considered representative of flow over the sea.
The wind speed varies…

### The theory of sound

- Engineering
- 1894

Volume 1: Preface 1. Sound due to vibrations 2. Composition of harmonic motions of like period 3. Systems with one degree of freedom 4. Generalized co-ordinates 5. Cases in which the three functions,…

### Beitrag zur Entstehung von Wasserwellen durch Wind

- Mathematics
- 1949

Die Entstehung von Wasserwellen durch Wind wird auf eine Instabilitat der ebenen Wasserflache gegenuber kleinen Storungen zuruckgefuhrt. Dabei werden laminare Grenzschichten in Wasser und Luft…