The two parts compare a stationary wave selected by a wind with a mean flow driven by…

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Waves, acoustics and compressible flow · Waves, acoustics and compressible flow

Signal Speeds in Fluids, Ch Sound in a moving, absorbing fluid: sources, refraction and loss

Problem

The two parts compare a stationary wave selected by a wind with a mean flow driven by an absorbed beam. ((a)) A hill in a steady wind

U=12\,\mathrm{m\,s^{-1}}

generates a lee wave that is stationary over the hill, with buoyancy frequency

N=0.02\,\mathrm{s^{-1}}

in the air aloft and horizontal wavelength

\lambda=5.0\,\mathrm{km}

. Using the Scorer parameter

l=N/U

and the dispersion relation for a stationary internal wave in a moving medium,

m^2=l^2-k^2

, find the vertical wavenumber

m

and the vertical wavelength of the lee wave. Then put the ground-frame frequency

\omega=0

in the rule

\omega=\omega'+\mathbf U\cdot\mathbf k

to find the lee wave's intrinsic horizontal phase speed

|\omega'|/k

, and state what the same zero-frequency condition would demand of sound in the same wind. ((b)) A

1\,\mathrm{MHz}

ultrasound beam of intensity

I=1.5\,\mathrm{W\,cm^{-2}}

travels through sea water in which the amplitude absorption coefficient is

\alpha=0.030\,\mathrm{Np\,m^{-1}}

and the sound speed is

c_0=1482\,\mathrm{m\,s^{-1}}

. Using the mean force per unit volume that an absorbed beam leaves in the fluid, find the streaming force density. State in one sentence how this differs from the Stokes drift of a surface gravity wave, as a mean effect driven by a wave.

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