1. Introduction
Turbulence within the stable boundary layer (SBL) remains a ubiquitous feature of many geophysical flows, especially over glaciers and ice-sheets. Although numerous studies have investigated various aspects of the boundary layer motions during stable atmospheric conditions, a unified picture of turbulent transport within the SBL does not exist [
1]. Classical descriptions and parameterisations of the SBL [
2,
3,
4] appear acceptable under weakly stable conditions (e.g., when the flux-based Richardson number is well below 0.2) but fail during strong atmospheric stratifications [
5]. In its simplest form, the SBL structure is determined by complex interactions between static stability of the air and processes that govern the mechanical generation of turbulence. Over glaciers and ice-sheets, a number of additional processes complicate the structure of turbulence within the SBL, including mesoscale and sub-meso motions such as drainage flows, meandering and waves. These processes interact in a nonlinear manner with turbulence, and influence heat, mass, and momentum turbulent fluxes that are often weak and intermittent and difficult to correctly accommodate in SBL parameterisations [
6].
In a strongly stratified SBL, turbulence generation is frequently associated with interactions with sub-meso motions that are often a combination of gravity waves (GWs) and horizontal modes, sometimes referred to as pancake vortices [
7,
8]. These quasi-two-dimensional structures arise because buoyancy disproportionately suppresses turbulence in the vertical direction. However, redistribution terms can enhance horizontal mixing of momentum and scalars even when turbulence (and its mixing properties) is suppressed in the vertical. Non-stationary sub-meso modes are also characterised by time scales that are often not too large with respect to the adjustment timescale of turbulence. As a consequence, turbulence cannot maintain its equilibrium with the constantly changing mean flow and becomes globally intermittent [
1] and produces strong non-stationarity that can alter the reliability of the measured turbulence parameters [
9]. It is this issue that frames the compass of the work presented here.
Wavelike motions are a fundamental feature of the SBL dynamics over a wide variety of scales. Typical periods of GWs range from a few minutes to approximately one hour, whereas the wavelengths vary from about hundreds of meters to several kilometres [
10]. GWs may be generated by several mechanisms, including topographic forcing, dynamical instabilities (
i.e., shear instability, microfronts or mesoscale fronts) and wave-wave interactions [
11,
12,
13,
14,
15].
The influence of GWs on the atmospheric dynamics from synoptic to micrometeorological scales is now recognised in a plethora of applications requiring mass, momentum and energy transport. GWs transport energy away from the disturbances that generate them and distribute this energy horizontally and vertically throughout the atmosphere [
16]. The energy and momentum transported by GWs can be transferred to the mean flow, influencing local meteorology and global atmospheric circulations [
10]. Moreover, instability and breaking of waves can produce clear air turbulence in the troposphere and can generate turbulence in the SBL that enhances the intermittent characteristics of turbulent transport of momentum, mass and energy [
17]. The latter influences chemical mixing of aerosols, biogenic and anthropogenic gases. Hence, it is evident that the statistical properties of such wavelike disturbances and their interaction with turbulence are needed to guide future parameterisation schemes aimed at improving weather forecasting and pollution dispersion models within the SBL.
While some progress has been made in the GW parameterisation within global models, description and parameterisation of the turbulence-wave interaction remain an open question, especially near the ground [
17,
18,
19,
20]. The discrimination between waves and turbulence is a focal point needed to make progress as these two motions have different properties with regards to heat, moisture and pollutant transport. Unfiltered GWs can cause significant differences and ambiguities in the determination of turbulence statistics and fluxes [
12,
14].
A number of studies have been concentrated on “clean” linear GWs with nearly constant amplitude and period. However, the existence of such “monochromatic” waves are rare in the SBL as most of the observed waves occur in local packets and consist of only a few cycles with changing amplitude and period. These non-stationary atmospheric wavelike disturbances, often called “dirty” waves, frequently degrade and lead to the generation of intermittent turbulence [
1,
17]. They are often superimposed on turbulent fluctuations and are not always clearly distinguishable from them. In those cases, separation of waves and turbulent fluctuations from time series is problematic due to the frequent absence of a defined spectral gap between the two types of motions [
18,
19,
21].
In a recent study, Sun
et al. [
17] proposed an interesting interpretation of the wave-turbulence interaction that depended on both background flow and wave disturbance. Large coherent eddies can be generated by bulk shear instability triggered by the enhanced wind speed at the wave crests. The consequent increase in the turbulent mixing vertically redistributes momentum and heat and modifies the original wavy oscillations, producing apparent waves at the upper level of the mixing depth. These turbulence-forced oscillations coherently transport momentum and heat and can produce counter-gradient fluxes. Finally, GWs can generate weak turbulent mixing by enhancing the local shear instability above the wave speed troughs. The mechanisms described by Sun
et al. [
17] may explain the commonly observed variations in amplitude and periods of GWs and may highlight the potential role of waves in the induction of global intermittent turbulence in the SBL.
Different methods have been proposed to filter GWs in turbulence time series. In the cases of rare linear and monochromatic waves in which a spectral gap or phase relation between variables is clearly defined, the discrimination between waves and turbulence becomes possible by using wave phase averaging or band-passed filters in Fourier space [
22,
23,
24]. However, in the frequent cases of “dirty waves”, these techniques are not effective and different methods based on multiresolution decomposition or wavelet analysis have been proposed for their localisation properties [
17,
25,
26,
27,
28].
Data collected on the Nansen Ice Sheet (NIS), Antarctica, in the middle of a wide and homogeneous gently sloping area were analysed using these decompositions. Antarctica is an ideal location for exploring the characteristics of the SBL and the GWs because of persistent conditions of strong atmospheric stability in the lower troposphere. Because of their influence on tropospheric and stratospheric circulations and chemistry in the Polar region, Antarctic GWs have been the subject of several studies. These studies suggest that the GW waves are often excited by topography and by katabatic winds that flow down from the glaciers originating from the Antarctic plateau towards the coast [
11,
26,
29,
30,
31,
32,
33,
34].
The goal here is to investigate the characteristics of GWs detected on the NIS during an austral summer and to explore their impact on turbulence statistics and fluxes. A brief description of the experimental site is presented in
Section 2; the methods used to identify and filter the GWs from time series are described in
Section 3; and the obtained results are presented and discussed in
Section 4 and
Section 5.
4. Results
To address the study objectives, the presence of wavy structures in each 30-min time series of velocity components and scalars was identified visually. In this first step, data sampled at the highest level (10 m) was used for guidance because the wavy patterns appeared more definite at this level when compared with the two lower levels (4.5 m and 2 m). This is consistent with the observations of Sun
et al. [
17] and it is due to the decreasing influence of turbulence mixing on GWs with height [
17,
46]. Wavelike motion was observed on most of the 55 days analysed within the SBL. However, only some 80 runs exhibited a discernable wavy pattern as identified and confirmed by the spectral and cospectral analyses.
Table 1 summarises the number and percentage of detected events classified on the basis of the wind direction sectors defined in
Section 3.1. It is evident that the wavy events appear to be associated with winds originating from inland (in particular from Sectors 1 and 3). These waves are probably “excited” by orography or by katabatic winds blowing from the Antarctic Plateau towards the coast as previously reported in other studies [
11,
26,
29,
30,
31,
32,
33,
34]. Moreover, the detected waves were observed during moderate or low wind conditions where the mean velocity (U) at a 10-m height did not exceed 4 m·s
−1.
Table 1.
Classification of the selected 30-min time series based on different wind direction sectors (see
Figure 1). N refers to the number of runs exhibiting a wavelike pattern; (%)
TOT and (%)
GW refer to the percentage of runs exhibiting a wavy pattern relative to the total number of runs in each sector and relative to the total cases of GW, respectively; U represents the average mean wind associated with the wavy selected events for each sector at z = 10 m.
Table 1.
Classification of the selected 30-min time series based on different wind direction sectors (see Figure 1). N refers to the number of runs exhibiting a wavelike pattern; (%)TOT and (%)GW refer to the percentage of runs exhibiting a wavy pattern relative to the total number of runs in each sector and relative to the total cases of GW, respectively; U represents the average mean wind associated with the wavy selected events for each sector at z = 10 m.
Sectors | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|
Wind direction (°) | 330–10 | 10–35 | 45–60 | 60–150 | 150–210 | 210–260 | 260–330 |
N | 19 | 13 | 19 | 5 | 11 | 1 | 12 |
(%)TOT | 8.0 | 9.0 | 6.8 | 1.8 | 3.2 | 0.9 | 4.9 |
(%)GW | 23.8 | 16.2 | 23.8 | 6.2 | 13.8 | 1.2 | 15.0 |
U (m·s−1) | 2.3 ± 1.6 | 3.0 ± 0.9 | 2.2 ± 1.1 | 2.1 ± 1.7 | 2.4 ± 1.7 | 2.3 | 2.2 ± 1.5 |
The detected wavelike structures were rarely monochromatic (with constant amplitude and period), but appeared as multiple events that persisted only for a few cycles with variable amplitudes and periods as observed elsewhere [
1,
17,
20]. Often, the propagation of these “dirty” waves produced non-stationarity and strong global intermittency in turbulent fluctuations.
Figure 2.
Time series of longitudinal (
a) and vertical velocity components (
b), sonic anemometer air temperature (
c) and fluctuations in water vapour concentration (
d) for a selected but uncommon case of a “cleaner” wave (Wave 1). The time series were collected on the 24 November 1993 at 18:00 (local time) and were associated with a drainage wind from the Priestley glacier (Sector 1). The different colours refer to the different levels of measurement: red (10 m), green (4.5 m), blue (2 m). The black dashed lines refer to the mean values. Note that in
Figure 2a,b, the time series relative to the lowest levels (green and blue lines) have been artificially shifted for better visualisation purposes.
Figure 2.
Time series of longitudinal (
a) and vertical velocity components (
b), sonic anemometer air temperature (
c) and fluctuations in water vapour concentration (
d) for a selected but uncommon case of a “cleaner” wave (Wave 1). The time series were collected on the 24 November 1993 at 18:00 (local time) and were associated with a drainage wind from the Priestley glacier (Sector 1). The different colours refer to the different levels of measurement: red (10 m), green (4.5 m), blue (2 m). The black dashed lines refer to the mean values. Note that in
Figure 2a,b, the time series relative to the lowest levels (green and blue lines) have been artificially shifted for better visualisation purposes.
Figure 2 and
Figure 3 feature two examples of wavy events in the records.
Figure 2 displays a case of a roughly “clean” wave characterised by a period of about 6–7 minutes (hereafter Wave 1). It is associated with a decelerating phase of a moderate drainage wind from the Priestley glacier (Sector 1). The stationarity indices based on different stationarity tests (RN: [
47]; NR: [
48]; I
C: [
9]) were computed at the highest level for sensible heat flux (RN = 28, NR = 0.9, I
C = 1) and latent heat flux (RN = 8, NR = 0.9, I
C = 1), indicating stationarity of the corresponding time series. The period and amplitude of the wave changed slightly during the analysed episode. Moreover, the wave period did not differ at the three measurement heights even if the amplitude tended to be attenuated closer to the ice sheet surface. This is mainly true for the vertical velocity component that is characterised by smaller wave amplitude superimposed onto increasing levels of turbulence activity near the ground. Spectral and cospectral analyses (
Figure 4 and
Figure 5) further highlight the presence of a well-defined spectral gap between the turbulence and the wave frequency range. In fact, the spectra of the wind components and the scalars exhibited a secondary maximum at
f~0.0025 Hz, corresponding to the same wave period observed in the time series (6–7 minutes). This low frequency maximum is well separated from the turbulence frequency range by a gap at
f~0.01 Hz. At the frequency of the wave maximum quadspectra, the phase spectrum approaches −90° for
w-T cross-spectrum and +90° for the
w-q cross-spectrum, indicating the small diffusive characteristic of this detected wave.
Figure 3.
As per
Figure 2 but for a selected case of a “dirty” wave (Wave 2). The time series were collected on 28 December 1993 at 00:30 (local time) and were associated with a drainage wind originating from the Browning pass (Sector 3).
Figure 3.
As per
Figure 2 but for a selected case of a “dirty” wave (Wave 2). The time series were collected on 28 December 1993 at 00:30 (local time) and were associated with a drainage wind originating from the Browning pass (Sector 3).
Figure 3 displays an example of a “dirty” wave characterised by variable amplitude and period and by an evident interaction with turbulent flow, highlighted by localised gustiness in turbulent fluctuations (hereafter Wave 2). This event occurred during a light drainage wind originating from the Browning pass (Sector 3). For this wavy episode, the stationarity indices at the highest level for sensible heat flux were RN = 41, NR = 1.7, I
C = 0.87, and for latent heat flux were RN = 31, NR = 1.7, I
C = 0.91 indicating a weaker stationarity of the corresponding time series with respect to the case shown in
Figure 2 (Wave 1).
Figure 4.
Spectra (in pre-multiplied form) computed for the longitudinal and lateral wind velocity components (
a), for vertical wind component (
b) and for temperature and water vapour (
c)
versus the natural frequency (
f) relative to the time series shown in
Figure 2 and sampled at the highest level (10 m).
Figure 4.
Spectra (in pre-multiplied form) computed for the longitudinal and lateral wind velocity components (
a), for vertical wind component (
b) and for temperature and water vapour (
c)
versus the natural frequency (
f) relative to the time series shown in
Figure 2 and sampled at the highest level (10 m).
Figure 5.
Cospectra (black lines) and quadrature spectra (grey lines) for the
w-T cross-spectrum (
a) and the
w-q cross-spectrum (
b); phase spectra for the
w-T cross-spectrum (
c) and the
w-q cross-spectrum (
d)
versus the natural frequency (
f) relative to the time series shown in
Figure 2 and sampled at the highest level (10 m).
Figure 5.
Cospectra (black lines) and quadrature spectra (grey lines) for the
w-T cross-spectrum (
a) and the
w-q cross-spectrum (
b); phase spectra for the
w-T cross-spectrum (
c) and the
w-q cross-spectrum (
d)
versus the natural frequency (
f) relative to the time series shown in
Figure 2 and sampled at the highest level (10 m).
Again, the wavy pattern and amplitude appear attenuated closer to the surface, but more accentuated than in the previous example shown in
Figure 2. Spectral and cospectral analyses (
Figure 6 and
Figure 7) suggest a “quasi-chaotic” behaviour of the analysed wavy episode. In fact, in the wave frequency range [0.003 ÷ 0.02], both spectra and the quadrature spectra exhibit multiple peaks and the scalar cospectra display an erratic behaviour with flux fluctuations of varying signs (signature of counter-gradient fluxes). Despite this behaviour, a spectral gap between wave and turbulent motions can be identified at
f~0.1 Hz.
Figure 8.
Triple decomposition of longitudinal (
a) and vertical wind velocity components (
b), sonic anemometer temperature (
c) and water vapour concentration (
d) relative to the case of the “cleaner” gravity wave shown in
Figure 2 (Wave 1) and sampled at the highest level (10 m). The time series were filtered using the MR decomposition technique based on the Haar wavelet. The threshold frequency used to separate wavy and turbulent components (
f~0.01 Hz) was selected on the basis of the spectral analyses shown in
Figure 4 and
Figure 5. The red lines represent the original fluctuations
, the black lines represent the filtered wavy components
, and the grey lines represent the wave-corrected fluctuations
. Note that red lines have been artificially shifted for better visualisation purposes.
Figure 8.
Triple decomposition of longitudinal (
a) and vertical wind velocity components (
b), sonic anemometer temperature (
c) and water vapour concentration (
d) relative to the case of the “cleaner” gravity wave shown in
Figure 2 (Wave 1) and sampled at the highest level (10 m). The time series were filtered using the MR decomposition technique based on the Haar wavelet. The threshold frequency used to separate wavy and turbulent components (
f~0.01 Hz) was selected on the basis of the spectral analyses shown in
Figure 4 and
Figure 5. The red lines represent the original fluctuations
, the black lines represent the filtered wavy components
, and the grey lines represent the wave-corrected fluctuations
. Note that red lines have been artificially shifted for better visualisation purposes.
Spectral and cospectral analyses were applied to the 80 selected runs to detect the frequency ranges of the wavy structures and the associated spectral gaps. Next, the time series of the wind components and scalars were filtered out by using the MR decomposition based on the Haar wavelet to separate waves from turbulent fluctuations.
Figure 8 and
Figure 9 show the triple decomposition of the measured time series obtained as a result of the MR filtering methodology applied to the wavy events shown in
Figure 2 and
Figure 3. It is evident that the wave passage coincides with the production of large and intermittent turbulent fluctuations, in particular in the case of Wave 2 (
Figure 9).
Figure 9.
As per
Figure 8, but for the case of the “dirty” wave shown in
Figure 3 (Wave 2). The threshold frequency used to separate the wavy and turbulent components (
f~0.1 Hz) was chosen on the basis of the spectral analyses shown in
Figure 6 and
Figure 7.
Figure 9.
As per
Figure 8, but for the case of the “dirty” wave shown in
Figure 3 (Wave 2). The threshold frequency used to separate the wavy and turbulent components (
f~0.1 Hz) was chosen on the basis of the spectral analyses shown in
Figure 6 and
Figure 7.
Figure 10.
Scatter plot of unfiltered turbulent statistics versus the same statistics corrected for the wave effect: standard deviation of the longitudinal (a), lateral (b) and vertical wind velocity component (c), and friction velocity (d). The different colours and symbols refer to the different levels of measurement: red stars (10 m), green points (4.5 m), blue diamonds (2 m). Coloured dotted lines represent the linear best-fit regression lines whereas the black dotted line represents the 1:1 line.
Figure 10.
Scatter plot of unfiltered turbulent statistics versus the same statistics corrected for the wave effect: standard deviation of the longitudinal (a), lateral (b) and vertical wind velocity component (c), and friction velocity (d). The different colours and symbols refer to the different levels of measurement: red stars (10 m), green points (4.5 m), blue diamonds (2 m). Coloured dotted lines represent the linear best-fit regression lines whereas the black dotted line represents the 1:1 line.
The obtained triple decomposition was used to compare the turbulent statistics and fluxes computed using the original fluctuations
and the turbulence fluctuations after the wave effects were filtered out
(
Figure 10 and
Figure 11).
Table 2 and
Table 3 contain the result of the linear regression analysis reported in
Figure 10 and
Figure 11, respectively. Unsurprisingly, these results suggest that the inclusion of wavy oscillations produce an overestimate of the variances associated with turbulence. The impact of waves appears to be similar at all the measurement heights even if the fractional contribution changes for the different turbulent statistics. As observed elsewhere [
18], one of the statistics more impacted by the waves is the turbulent kinetic energy (TKE) and, in particular, the longitudinal and lateral contributions. In fact, the wave filtering produced a reduction of more than 60% in
σu and
σv with respect to the unfiltered values (
Figure 10a,b). On the other hand,
σw slightly decreased after the wave filtering (less than 10%) (
Figure 10c), suggesting that the pancake nature of eddies in a highly stratified SBL flow may be linked to some wave effects. A large wave impact was also observed in the standard deviations of the scalars that appear to be reduced by about 50%–60% (
Figure 11a,b), commensurate with
σu and
σv.
Figure 11.
Same as
Figure 10 but for the standard deviation of air temperature (
a) and water vapour (
b), sensible heat flux (
c), and latent heat flux (
d).
Figure 11.
Same as
Figure 10 but for the standard deviation of air temperature (
a) and water vapour (
b), sensible heat flux (
c), and latent heat flux (
d).
The effect of wave activity on momentum and scalar fluxes is more complex compared with the variances (the presence of waves always increases the overall variance). In fact, waves can produce large errors in sign and magnitude of the computed turbulent fluxes [
14] or they themselves can contribute to intermittent turbulent mixing [
17].
As an example,
Table 4 displays the different contributions of the wavy and turbulent fluctuations to the total fluxes of momentum and sensible heat relative to the time series shown in
Figure 2 and
Figure 3. In both episodes, waves can produce counter-gradient fluxes, which was also reported by Sun
et al. [
17]. However in the case of Wave 1 experiencing larger mean wind speed and bulk shear, the wave resulted in strong mixing and produced down-gradient fluxes at the lower levels comparable to those associated with small-scale turbulent fluctuations. On the other hand, Wave 2 was associated with a lower wind speed and a larger non-stationarity; as a consequence, counter-gradient fluxes were also measured at the lowest level, and wave contributions appeared to dominate the total transport due the low levels of small-scale turbulence. These patterns are consistent with the cospectra shown in
Figure 5 and
Figure 7
Table 2.
Linear regression analysis of turbulent statistics and fluxes computed by using the original fluctuations and corrected for the wave effect shown in
Figure 10. The subscribed numbers refer to different levels of measurements (1 → 10 m; 2 → 4.5 m; 3 → 2 m). R
2 is the coefficient of determination associated with the regression analysis.
Table 2.
Linear regression analysis of turbulent statistics and fluxes computed by using the original fluctuations and corrected for the wave effect shown in Figure 10. The subscribed numbers refer to different levels of measurements (1 → 10 m; 2 → 4.5 m; 3 → 2 m). R2 is the coefficient of determination associated with the regression analysis.
Linear Fit | R2 |
---|
σu1f = 0.34 σu1 + 0.01 | 0.75 |
σu2f = 0.36 σu2 + 0.00 | 0.75 |
σu3f = 0.38 σu3 + 0.00 | 0.73 |
σv1f = 0.29 σv1 + 0.02 | 0.64 |
σv2f = 0.32 σv2 + 0.01 | 0.75 |
σv3f = 0.30 σv3 + 0.02 | 0.71 |
σw1f = 0.92 σw1 - 0.01 | 0.98 |
σw2f = 0.95 σw2 + 0.00 | 0.99 |
σw3f = 0.93 σw3 + 0.00 | 0.98 |
u*1f = 0.75 u*1 + 0.00 | 0.64 |
u*2f = 0.75 u*2 + 0.00 | 0.63 |
u*3f = 0.73 u*3 + 0.00 | 0.80 |
Table 3.
Same as
Table 2 but for turbulent statistics and fluxes computed using the original fluctuations and corrected for the wave effect, shown in
Figure 11.
Table 3.
Same as Table 2 but for turbulent statistics and fluxes computed using the original fluctuations and corrected for the wave effect, shown in Figure 11.
Linear Fit | R2 |
---|
σT1f = 0.49 σT1 − 0.01 | 0.92 |
σT2f = 0.50 σT2 + 0.00 | 0.87 |
σT3f = 0.48 σT3 + 0.01 | 0.85 |
σq1f = 0.42 σq1 + 0.00 | 0.85 |
σq2f = 0.40 σq2 + 0.00 | 0.92 |
σq3f = 0.44 σq3 + 0.00 | 0.88 |
H1f = 0.47 H1 − 0.76 | 0.67 |
H2f = 0.66 H2 − 0.67 | 0.68 |
H3f = 0.69 H3 − 1.53 | 0.78 |
Le1f = 0.35 Le1 + 0.60 | 0.45 |
Le2f = 0.41 Le2 + 0.80 | 0.53 |
Le3f = 0.48 Le3 + 0.38 | 0.46 |
The effect of wave filtering on momentum and scalar fluxes in all the selected episodes is reported in
Figure 11c,d. As already observed elsewhere (
i.e., [
14]), the friction velocity
u* appears reduced after the wave filtering (by about 25%). The waves have a larger impact on the turbulent fluxes of scalars.
Figure 11 confirms that waves often produce counter-gradient positive values of sensible heat flux (
H). In reality, the surface
H should be negative in a stably stratified boundary layer experiencing wavy motion. The wave filtering corrects the turbulent
H sign (that becomes negative), but the magnitude is reduced (also as expected for weak turbulence conditions). On the other hand, in the negative quadrant (
H < 0 and
Hf < 0) where both unfiltered and filtered fluxes are negative, the filtered flux appears less negative than the uncorrected total flux. The percentage of sensible heat flux magnitude reduction due to filtering apparently increased with increasing measurement height (from 30% at 2 m to 50% at 10 m), as reported in
Table 3.
Table 4.
Wind speed (U) and contributions of the wavy and turbulent fluctuations to the total fluxes of momentum (
) and sensible heat (
H) relative to the time series shown in
Figure 2 (Wave 1) and
Figure 3 (Wave 2) at the three measurement heights. Values in bold and underlined characters indicate counter-gradient fluxes.
Table 4.
Wind speed (U) and contributions of the wavy and turbulent fluctuations to the total fluxes of momentum () and sensible heat (H) relative to the time series shown in Figure 2 (Wave 1) and Figure 3 (Wave 2) at the three measurement heights. Values in bold and underlined characters indicate counter-gradient fluxes.
Wave 1 |
Height | 10 | 4.5 | 2 |
U (m·s−1) | 3.2 | 2.5 | 2.3 |
(m·s−1)2 | | | |
total wave turbulence | −0.7 × 10−3 +3.6 × 10−3 −4.3 × 10−3 | −12.0 × 10−3 −7.0 × 10−3 −7.0 × 10−3 | −16.0 × 10−3 −8.0 × 10−3 −8.0 × 10−3 |
H (W·m−2) | | | |
total wave turbulence | −1.0 +0.5 −1.5 | −6.7 −3.3 −3.4 | −1.5 −0.7 −0.7 |
|
Wave 2 |
Height | 10 | 4.5 | 2 |
U (m·s−1) | 1.9 | 1.5 | 1.1 |
(m·s−1)2 | | | |
total wave turbulence | −6.3 × 10−4 −5.9 × 10−4 −0.4 × 10−4 | −6.7 × 10−4 −5.0 × 10−4 −1.7 × 10−4 | +8.0 × 10−4 +9.7 × 10−4 −1.7 × 10−4 |
H (W·m−2) | | | |
total wave turbulence | +1.6 +1.7 −0.1 | −8.6 −7.7 −0.9 | +3.9 +4.7 −0.8 |
In addition, the latent heat flux appears to be attenuated by the filtering processes (
Figure 11d). In these cases, the turbulent component of the latent heat flux assumes low values commonly associated with large random errors that de-correlate the water vapour fluctuations from vertical velocity fluctuations.
Finally,
Figure 12 shows the wavelength of the detected waves
versus the atmospheric stability parameter (
z/L, where
z is the measurement height and
L is the Obukhov length), measured at the highest level and computed after wave filtering. Different colours and symbols refer to data belonging to different wind direction sectors. The highest values of GW wavelength correspond to weak stable stratification (
z/L <1) and are of the order of a few kilometres (~1000–2000 m) as frequently observed in Antarctic coastal areas [
33]. When stability increases, the wavelengths rapidly decrease and can assume extremely small values (~100 m) for strong stability conditions. For reference, exponential and power regression fits were computed and are reported in
Figure 12, even if they are probably dependent on the site and topographic characteristics.
Figure 12.
Wavelength of detected waves (GW) versus the atmospheric stability parameter (z/L, where z is the measurement height and L is the Obukhov length), measured at the highest level (=10 m) and computed after the wave-filtering process. Different colours and symbols refer to data belonging to different wind direction sectors. The continuous black line refers to the exponential regression: y = 1287 e(−0.56x) (R2 = 0.64); the dashed and dotted black lines refer to the power-law regressions: y = 592 x−0.47 (R2 = 0.47) and y = 5687 x−0.06 − 5018 (R2 = 0.62), respectively.
Figure 12.
Wavelength of detected waves (GW) versus the atmospheric stability parameter (z/L, where z is the measurement height and L is the Obukhov length), measured at the highest level (=10 m) and computed after the wave-filtering process. Different colours and symbols refer to data belonging to different wind direction sectors. The continuous black line refers to the exponential regression: y = 1287 e(−0.56x) (R2 = 0.64); the dashed and dotted black lines refer to the power-law regressions: y = 592 x−0.47 (R2 = 0.47) and y = 5687 x−0.06 − 5018 (R2 = 0.62), respectively.