Rossby wave energy: a local Eulerian isotropic invariant
<p>Conservation laws relate the local<span>&#160; </span>time-rate-of-change of the spatial integral of a density function to the divergence of its<span>&#160; </span>flux through the boundaries of the integration domain. These provide integral constraints on the spatio-temporal development<span>&#160; </span>of a field. Here we show<span>&#160; </span>that<span>&#160; </span>a new type of conserved quantity exists, that does not require integration over a particular domain but which holds locally,<span>&#160; </span>at any point in the field.<span>&#160; </span>This is derived for the pseudo-energy density of<span>&#160; </span>nondivergent Rossby waves where<span>&#160; </span>local invariance is obtained for (1) a single plane wave, and (2) waves produced by an impulsive point-source of vorticity.<span>&#160;</span></p><p>The definition of pseudo-energy used here<span>&#160; </span>consists of a conventional kinetic part, as well as an unconventional pseudo-potential part, proposed by<span>&#160; </span>Buchwald (1973).<span>&#160;&#160;</span>The anisotropic nature of the nondivergent energy flux that appears in response to the point source further clarifies the role of the beta plane in the<span>&#160; </span>observed western intensification of ocean currents.<span>&#160;</span></p>