Experimental study of upstream influence in the two‐dimensional flow of a stratified fluid over an obstacle†

Wei, Shuang N.; Kao, Timothy W.; Pao, Hsien‐Ping

doi:10.1080/03091927509365802

Cited by 23 publications

(11 citation statements)

References 12 publications

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“…In ocean science, the classically defined Froude number is based on the first‐mode internal wave speed ( c o ) (e.g., F o = U/c o = πU/NH , where c o =NH/π ). If F o > 1, linear internal waves do not propagate upstream, while if F o < 1 it is possible that the first wave mode (at least) may propagate upstream as a shear front or columnar disturbance mode [e.g., Wei et al ., ; Baines , ]. It is also utilized for flow descriptions in the hydraulic sense.…”

Section: Discussionmentioning

confidence: 99%

Observations on stratified flow over a bank at low Froude numbers

et al. 2014

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In June 2011, a 9 day oceanographic survey was conducted over the East Flower Garden Bank, a coral reef, located on the outer shelf in the northwestern Gulf of Mexico. Current, temperature, conductivity, and microstructure measurements were collected to characterize flow evolution, turbulence, and mixing over the bank. During the experiment, the flow was highly stratified, subcritical (Froude number below 0.4), hydrostatic, and nonlinear with rotational effects being important. Observations showed that flow structure, turbulence, and mixing were highly dependent on the direction and strength of the current; thus, they varied spatially and temporarily. Responses resulting from interactions between the free-stream flow and the obstacle were significantly different on the upstream and downstream sides of the bank. Blocking and diverging of the flow just below the bank height was observed on the upstream side. On the downstream side, a wake with imbedded vortices developed. Moreover, turbulence was amplified over the bank top and on its downstream side. Turbulent dissipation rates were as high as 10 26 W kg 21 and resulted in measured rates of energy dissipation and mixing by turbulence per unit width as high as 40 W m 21 . Mixing on the downstream side was elevated with eddy diffusivities reaching 10 23 m 2 s 21 , well above a typical value of 10 25 m 2 s 21 commonly found in the ocean thermocline and over shelves with flat topography. On the upstream side, estimated eddy diffusivities were close to that for the ocean thermocline, i.e., they were generally less than 0.5310 24 m 2 s 21 .

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Section: Discussionmentioning

confidence: 99%

Observations on stratified flow over a bank at low Froude numbers

et al. 2014

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“…For this flow, two non-dimensional numbers are relevant: k d (=Nd/U) (or its inverse, the Froude number, F d (=U/Nd) and K(=NH/πU) (or the blockage ratio, d/H). k d is defined with the characteristic length of an object while F d is defined in terms of the finite depth, H. According to linear theory, discrete vertical modes exist for the internal gravity wave that arises in stratified flow of finite depth, and the vertical modes depend on the strength of the density stratification [8,17]. The dispersion relation for the nth vertical mode (wavelength in the vertical direction = 2 H/n) can be expressed as:…”

Section: Internal Gravity Waves In Stratified Flows Of Finite Depthmentioning

confidence: 99%

“…When the stratification becomes sufficiently high, blocking occurs and upstream wakes emerge [6,7]. Furthermore, in a highly stratified fluid of finite depth, columnar disturbances emerge and propagate upstream of an object [8,9]. Boyer et al [7] investigated the near-wake flows of a circular cylinder for Reynolds numbers less than 4000 and over a wide range of stratification.…”

Section: Introductionmentioning

confidence: 99%

Near Wake of a Horizontal Circular Cylinder in Stably Stratified Flows

Ohya¹,

Uchida²,

Nagai³

2013

OJFD

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The near wake of a circular cylinder in linearly stratified flows of finite depth was experimentally investigated by means of flow visualization and measurements of vortex shedding frequencies, at Reynolds numbers 3.5 × 10 3-1.2 × 10 4 and stratification parameters k d 0-2.0. The non-dimensional parameter k d is defined as k d = Nd/U, where N is the Brunt-Väisälä frequency, d, the diameter of the cylinder, and U, the approaching flow velocity. The study demonstrates that as k d increases from zero, the vortex shedding from a circular cylinder progressively strengthens, while the Strouhal number gradually becomes lower than that for homogeneous flow. This phenomenon can be explained by the effect of the increasingly stable stratification which enhances the two-dimensionality of the near-wake flow of the circular cylinder; the enhanced two-dimensionality of the flow strengthens the roll-up of the separated shear layer. Above a certain value of k d , however, vortex formation and shedding are strongly suppressed and the Strouhal number rises sharply. This observation is attributable to the development of stationary lee waves downstream of the circular cylinder because the lee waves strongly suppress vertical fluid motions.

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“…Baines and Grimshow suggested that the hypothesis is applicable when the obstacle is small and Froude number with respect to the obstacle height is sufficiently large. Wei et al (1975) showed in a water channel experiment that the change of flow velocity upstream of a cylinder is less than 10 percents under moderate stratification condition. By these results, we can consider that the Long's hypothesis is sufficiently The constants *m are determined so that the function *0 be a good approximation of the flow over a barrier under the non-stratified condition.…”

Section: Conditionmentioning

confidence: 99%

On the Stagnant Zone Upstream of an Obstacle within a Stably Stratified Flow in the Atmosphere

Kitabayashi¹

1981

Journal of the Meteorological Society of Japan

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Stably stratified airflows over a hill or mountain are studied by a wind tunnel and also by a theoretical model with special forcus on the upstream stagnant zone. The wind tunnel experiment shows that a stagnant zone is formed upstream of an obstacle when the Froude number is less than some critical value. The critical Froude number is found to vary with the obstacle height. In the stagnant zone, the airflow is negligible or reverse and the thickness of the zone decreases gradually with the distance from the obstacle.

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Experimental study of upstream influence in the two‐dimensional flow of a stratified fluid over an obstacle†

Cited by 23 publications

References 12 publications

Observations on stratified flow over a bank at low Froude numbers

Observations on stratified flow over a bank at low Froude numbers

Near Wake of a Horizontal Circular Cylinder in Stably Stratified Flows

On the Stagnant Zone Upstream of an Obstacle within a Stably Stratified Flow in the Atmosphere

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