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Inviscid and inviscid-limit behavior of a surface quasigeostrophic flow. (English) Zbl 1185.76841
Summary: The growth of the gradient of a scalar temperature in a quasigeostrophic flow is studied numerically in detail. We use a flow evolving from a simple initial condition which was regarded by Constantin et al. as a candidate for a singularity formation in a finite time. For the inviscid problem, we propose a completely different interpretation of the growth, that is, the temperature gradient can be fitted equally well by a double-exponential function of time rather than an algebraic blowup. It seems impossible to distinguish whether the flow blows up or not on the basis of the inviscid computations at hand. In the viscous case, a comparison is made between a series of computations with different Reynolds numbers. The critical time at which the temperature gradient attains the first local maximum is found to depend double logarithmically on the Reynolds number, which suggests the global regularity of the inviscid flow.

76M25 Other numerical methods (fluid mechanics) (MSC2010)
86A10 Meteorology and atmospheric physics
Full Text: DOI
[1] DOI: 10.1063/1.868050 · Zbl 0826.76014 · doi:10.1063/1.868050
[2] DOI: 10.1088/0951-7715/7/6/001 · Zbl 0809.35057 · doi:10.1088/0951-7715/7/6/001
[3] DOI: 10.1175/1520-0469(1978)035<0774:UPVFPI>2.0.CO;2 · doi:10.1175/1520-0469(1978)035<0774:UPVFPI>2.0.CO;2
[4] DOI: 10.1017/S0022112095000012 · Zbl 0832.76012 · doi:10.1017/S0022112095000012
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[6] DOI: 10.1007/BF01212349 · Zbl 0573.76029 · doi:10.1007/BF01212349
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[8] DOI: 10.1137/1036004 · Zbl 0803.35106 · doi:10.1137/1036004
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[10] DOI: 10.1017/S0022112088003015 · doi:10.1017/S0022112088003015
[11] DOI: 10.1063/1.1692443 · Zbl 0217.25801 · doi:10.1063/1.1692443
[12] DOI: 10.1063/1.1762301 · doi:10.1063/1.1762301
[13] DOI: 10.1063/1.1691968 · doi:10.1063/1.1691968
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[15] DOI: 10.1063/1.866137 · Zbl 0629.76067 · doi:10.1063/1.866137
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