Relation of Fourth to Second Moments in Stationary Homogeneous Hydromagnetic Tur
Relation of Fourth to Second Moments in Stationary Homogeneous Hydromagnetic Tur
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In our eReader you can find the full English version of the book. Read Relation of Fourth to Second Moments in Stationary Homogeneous Hydromagnetic Tur Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Relation of Fourth to Second Moments in Stationary Homogeneous Hydromagnetic Tur
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U. Consequences of the quasi-normality hypothesis It may be seen very simply that the quasi-normality hypothesis (3. 11) is incon- sistent with the conservation properties of the nonlinear interaction. Consider any three modes q, q^, q such that f, f„, f vanish. They could be magnetic modes or velocity modes in the inertial or dissipation ranges. Substituting the integral expression (2. 20) for q in (3. 7), one finds for the mean rate of transfer of energy to mode q through the three-mode inter...action with a y V * 9 - (U. L) -/I ^ - 2 A - y; a, f e "^ T . „ ('D)d^ 'o Y^ 11, X anX J '0 If the hypothesis (3. 11) is asserted, (U. L) may be rewritten*^" where the relations (2. 18), (3. 9) have been used.
It may now be noted that the integrals on the right side of (U. 2) are all positive quantities. This follows from the fact that the spectrum of e is everywhere positive and the spectra of the correlation functions Roo('2')» R (^ cannot be negative anywhere. Since the spectrum of a product of pp YY functions with non-negative spectra has itself a non-negative spectrum, and since the integral of the even function e R q('C)R CC* ) gives the value at the origin of its Fovirier transform, none of the integrals can be negative.
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To quickly assess the difficulty of the text, read a short excerpt:
U. Consequences of the quasi-normality hypothesis It may be seen very simply that the quasi-normality hypothesis (3. 11) is incon- sistent with the conservation properties of the nonlinear interaction. Consider any three modes q, q^, q such that f, f„, f vanish. They could be magnetic modes or velocity modes in the inertial or dissipation ranges. Substituting the integral expression (2. 20) for q in (3. 7), one finds for the mean rate of transfer of energy to mode q through the three-mode inter...action with a y V * 9 - (U. L) -/I ^ - 2 A - y; a, f e "^ T . „ ('D)d^ 'o Y^ 11, X anX J '0 If the hypothesis (3. 11) is asserted, (U. L) may be rewritten*^" where the relations (2. 18), (3. 9) have been used.
It may now be noted that the integrals on the right side of (U. 2) are all positive quantities. This follows from the fact that the spectrum of e is everywhere positive and the spectra of the correlation functions Roo('2')» R (^ cannot be negative anywhere. Since the spectrum of a product of pp YY functions with non-negative spectra has itself a non-negative spectrum, and since the integral of the even function e R q('C)R CC* ) gives the value at the origin of its Fovirier transform, none of the integrals can be negative.
What to read after Relation of Fourth to Second Moments in Stationary Homogeneous Hydromagnetic Tur?
You can find similar books in the "Read Also" column, or choose other free books by R H Kraichnan to read onlineMoreLess
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