 Two-dimensional viscous shearing wave

ID: two-dimensional-viscous-shearing-wave

For

k_{z} = v_{z} = 0

and

k_{y} \neq = 0

Z = i (k_{x} v_{y} - k_{y} v_{x})

. Uniform rotation does not enter its evolution:

\dot{Z} = - ν k^{2} Z

v_{x} = i k_{y} Z / k^{2}

and

v_{y} = - i k_{x} Z / k^{2}

. With

T = k_{x} / k_{y}

and

Re = A / (ν k_{y}^{2})

E (T) / E (T_{0}) = [(1 + T_{0}^{2}) / (1 + T^{2})] exp [- (T + T^{3} /3 - T_{0} - T_{0}^{3} /3) / Re]

. Leading waves can gain energy as shear reduces their wavevector magnitude, before viscosity and subsequent winding damp them.

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