The Response of the Water Surface Layer to Internal Turbulence and Surface Forcing

• Main Authors: Mohammad Barzegar, Darek Bogucki, Brian K. Haus, Mingming Shao
• Format: Article
• Language: English
• Published: MDPI AG 2021-02-01
• Series: Journal of Marine Science and Engineering
• Subjects: turbulence; non-breaking wave; water surface layer; convection
• Online Access: https://www.mdpi.com/2077-1312/9/2/217

We have carried out an experimental study of the turbulence kinetic energy dissipation rate (<inline-formula><math display="inline"><semantics><mi>ϵ</mi></semantics></math></inline-formula>), temperature dissipation rate (<inline-formula><math display="inline"><semantics><mi>χ</mi></semantics></math></inline-formula>), and turbulent heat flux (THF) within the water surface layer in the presence of non-breaking wave, surface convection, and horizontal heat and eddy fluxes that play a prominent role in the front. We noted that the non-breaking wave dominates <inline-formula><math display="inline"><semantics><mi>ϵ</mi></semantics></math></inline-formula> values within the surface layer. While analyzing the vertical <inline-formula><math display="inline"><semantics><mi>ϵ</mi></semantics></math></inline-formula> variability, the presence of a wave-affected layer from the water surface to a depth of <inline-formula><math display="inline"><semantics><mrow><mi>z</mi><mo>≈</mo><mn>1.25</mn><msub><mi>λ</mi><mi mathvariant="normal">w</mi></msub></mrow></semantics></math></inline-formula> is observed, where <inline-formula><math display="inline"><semantics><msub><mi>λ</mi><mi mathvariant="normal">w</mi></msub></semantics></math></inline-formula> is the wavelength. <inline-formula><math display="inline"><semantics><mi>ϵ</mi></semantics></math></inline-formula> associated with non-breaking waves ranged to <inline-formula><math display="inline"><semantics><mrow><mn>4.9</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>6</mn></mrow></msup></mrow></semantics></math></inline-formula>–<inline-formula><math display="inline"><semantics><mrow><mn>7</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>6</mn></mrow></msup></mrow></semantics></math></inline-formula> m²/s³ for the wavelength range of 0.038 m < <inline-formula><math display="inline"><semantics><msub><mi>λ</mi><mi mathvariant="normal">w</mi></msub></semantics></math></inline-formula> < 0.098 m categorized as the gravity and gravity-capillary wave regimes. <inline-formula><math display="inline"><semantics><mi>ϵ</mi></semantics></math></inline-formula> values increase for longer <inline-formula><math display="inline"><semantics><msub><mi>λ</mi><mi mathvariant="normal">w</mi></msub></semantics></math></inline-formula> and non-breaking wave <inline-formula><math display="inline"><semantics><mi>ϵ</mi></semantics></math></inline-formula> values represent their significant contribution to the ocean energy budget and dynamic of surface layer considering that the non-breaking wave covers the large fraction of ocean surface. We also found that the surface mean square slope (MSS) and wave generated <inline-formula><math display="inline"><semantics><mi>ϵ</mi></semantics></math></inline-formula> have the same order of magnitude, i.e., MSS <inline-formula><math display="inline"><semantics><mrow><mo>∼</mo><mi>ϵ</mi></mrow></semantics></math></inline-formula>. Besides, we have documented that the small-scale temperature fluctuation change (i.e., <inline-formula><math display="inline"><semantics><mi>χ</mi></semantics></math></inline-formula>) is consistent with the large-scale temperature gradient change (i.e., <inline-formula><math display="inline"><semantics><mrow><mi>d</mi><mo><</mo><mi>T</mi><mo>></mo><mo>/</mo><mi>d</mi><mi>z</mi></mrow></semantics></math></inline-formula>). The value of the THF is approximately constant within the surface layer. It represents that the measured THF near the water surface can be considered a surface water THF, challenging to measure directly.