Amplitude and frequency modulation in wall turbulence

Abstract

In this study we examine the impact of the strength of the large-scale motions on the amplitude and frequency of the small scales in high-Reynolds-number turbulent boundary layers. Time series of hot-wire data are decomposed into large- and small-scale components, and the impact of the large scale on the amplitude and frequency of the small scales is considered. The amplitude modulation effect is examined by conditionally averaging the small-scale intensity (${ u}_{S}^{2} $) for various values of the large-scale fluctuation (${u}_{L} $). It is shown that ${ u}_{S}^{2} $ increases with increasing value of ${u}_{L} $ in the near-wall region, whereas, farther away from the wall, ${ u}_{S}^{2} $ decreases with increasing ${u}_{L} $. The rate of increase in small-scale intensity with the strength of the large-scale signal is neither symmetric (about ${u}_{L} = 0$) nor linear. The extent of the frequency modulation is examined by counting the number of occurrences of local maxima or minima in the small-scale signal. It is shown that the frequency modulation effect is confined to the near-wall region and its extent diminishes rapidly beyond ${y}^{+ } = 100$. A phase lag between the large- and small-scale fluctuations, in terms of amplitude modulation, has also been identified, which is in agreement with previous studies. The phase lag between large- and small-scale fluctuations for frequency modulation is comparable to that of amplitude modulation in the near-wall region. The combined effect of both amplitude and frequency modulation is also examined by computing conditional spectra of the small-scale signal conditioned on the large scales. In the near-wall region, the results indicate that the peak value of pre-multiplied spectra increases with increasing value of ${u}_{L} $, indicating amplitude modulation, while the frequency at which this peak occurs also increases with increasing value of ${u}_{L} $, revealing frequency modulation. The overall trends observed from the conditional spectra are consistent with the results obtained through statistical analyses. Finally, a physical mechanism that can capture most of the above observations is also presented.

Prospectus: towards the development of high-fidelity models of wall turbulence at large Reynolds number

“…Within this context, the present [20] extends the recent findings of Marusic and co-workers showing that these nonlinear interactions between the large and small scales are associated with amplitude and frequency modulations (e.g. [16,30]). Here they provide a detailed presentation of the underlying spatial structure of the flow, and the associated Reynolds number dependencies.…”

Wave-induced coherent turbulence structures and sediment resuspension in the nearshore of a prototype-scale sandy barrier beach

“…Within a given cluster of turbulence, both stresses and suspensions span a certain range of frequencies, which may hint at a nonlinear modulation of both the amplitude and frequency of such small structures with the larger flow structures near the bed. Such behaviour in wall turbulence has been attributed to local changes in shear but not necessarily the spatial and temporal structure of large flow events (Ganapathisubramani et al, 2012).…”

Concurrent scale interactions in the far-field of a turbulent mixing layer

“…It has been previously shown that although a running mean filter does not have a sharp spectral cut-off, the choice of filter has no qualitative effect on the results observed in the modulation of the small-scale fluctuations by the large-scales, and vice versa. 8 The top trace of Figure 6 shows a typical raw signal of u L 1 (x 1 ) from a low-resolution FOV vector field, the middle trace is the low frequency component of the signal, u Lλ 1 (x 1 ), and the bottom trace is the part that is composed of fluctuations of length scale λ or less, u L0 1 (x 1 ). The low frequency part and the "Λ < λ" part sum to give the original signal, i.e., u L0…”

“…A similar feature is also observed in the amplitude modulation effects of wall bounded flows. 8,9,46 For a LES, the filtered LES equations for an incompressible flow can be written as…”

“…Some recent results, primarily in wall-bounded turbulent shear flows, point to the significance of these interactions. [4][5][6][7][8][9] However, very little information is available on these interactions in other forms of shear flows. In this study, we aim to examine the nature of this interaction between large-and small-scale velocity fluctuations in a turbulent free shear flow.…”