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Laboratory Experiments on Turbulent Lengthscales and Diffusivities in Stratified Fluids of Different Prandtl Number

机译:不同普朗特数分层流体中湍流尺度和扩散率的室内实验

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Linearly salt stratified fluids of different Prandtl number were subjected to turbulent stirring by a horizontally oscillating vertical grid in a closed laboratory system. The experimental setup allowed the independent measurement of an rms turbulent lengthscale L_t, turbulent diffusivity for mass K_ρ, rate of dissipation of turbulent kinetic energy ε, stratification strength N and viscosity ν, for a wide range of turbulence intensities, ε/νN~2. The behaviour of both L_t and K_ρ was characterised in terms of this turbulence intensity and two regimes were identified. In the more energetic of these regimes (Regime E, where 300 < ε/νN~2 < 10~5), quantitative expressions for both L_t and K_ρ were identified. In this regime, L_t was found to be a function of only ν, κ and N, whilst K_ρ was a function of ν, κ and (ε/νN~2)~(1/3). Prom these expressions for L_t and K_ρ, a scaling relation for the root mean square turbulent velocity, U_t, was derived. This scaling relation showed good agreement with other data sets. In the weaker turbulence regime (Regime W, where 10 < ε/νN~2 < 300) a quantitative relationship was found for K_ρ as a function of ν, κ and ε/νN~2. Comparison was made between our expressions for K_ρ and the model of Osborn (1980). For 10 < ε/νN~2 < 1000, the model of Osborn (1980) differs from our experimental results by approximately a factor of 2. For higher turbulence intensities the model and experimental results diverge, such that at ε/νN~2 ≈ 10~4, there is approximately an order of magnitude discrepancy between the model and our measurements.
机译:在封闭的实验室系统中,通过水平振荡的垂直网格对不同Prandtl数的线性盐分层流体进行湍流搅拌。实验设置允许独立测量均方根湍流尺度L_t,质量K_ρ的湍流扩散率,湍动能ε的耗散率,分层强度N和粘度ν,以及广泛的湍流强度ε/νN〜2。 L_t和K_ρ的行为都根据这种湍流强度进行了表征,并确定了两种状态。在这些机制中,如果能量更高(Region E,其中300 <ε/νN〜2 <10〜5),则可以确定L_t和K_ρ的定量表达。在这种情况下,L_t仅是ν,κ和N的函数,而K_ρ是ν,κ和(ε/νN〜2)〜(1/3)的函数。对L_t和K_ρ的这些表达式进行推论,得出了均方根湍流速度U_t的比例关系。这种比例关系与其他数据集显示出良好的一致性。在较弱的湍流状态下(Region W,其中10 <ε/νN〜2 <300),发现K_ρ与ν,κ和ε/νN〜2呈函数关系。我们比较了K_ρ的表达式和Osborn(1980)的模型。对于10 <ε/νN〜2 <1000,Osborn(1980)的模型与我们的实验结果相差大约2倍。对于更高的湍流强度,模型和实验结果会发生分歧,从而在ε/νN〜2≈在10〜4之间,模型与我们的测量值之间存在大约一个数量级的差异。

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