The transport of the energy and other scalar quantities in turbulence can be controlled by scalar-based volume forces, e.g., the buoyancy in the turbulent thermal convection or the electric body force in the electrokinetic (EK) turbulence, and expressed as ∇ⁿA, with A being a control scalar. This paper presents a unified theoretical framework for the transport of the energy and other scalar quantities in the turbulence driven by scalar-based volume forces. Several isolated results that have previously been reported in relation to the turbulent thermal convection (related to n = 0 ) and the EK turbulence (related to n = 1) are unified in this theoretical framework. With the theory, the following interesting results are predicted: (1) When n < 2 / 3 , the transport of the kinetic energy is dominated by the Kolmogorov scale η and another small scale l_A . When n > 2 / 3 , the transport of the kinetic energy is controlled by three characteristic small scales: l_K , l_ηK and l_A . (2) The scaling law range can be divided into an inertial subrange and a volume-force-dominated subrange. (3) In the latter case, the exponents of the power spectra of the velocity and the relevant scalar quantity are η_u = (4n-11)/5, η_A = -(2n+7)/5 , respectively. (4) In the equilibrium state, n cannot exceed 4. (5) The positive exponent of \({l_A} \sim 0.024Ra_{A.{l_0}}^{0.107 \pm 0.016}\) is confirmed in the turbulent thermal convection.

湍流中能量和其他标量的传输可以通过基于标量的体积力来控制，例如，湍流热对流中的浮力或电动 (EK) 湍流中的电体力，并表示为 ∇ ⁿ A，A是控制标量。本文提出了一个统一的理论框架，用于在基于标量的体积力驱动的湍流中传输能量和其他标量。先前已报道的与湍流热对流（与n = 0 相关）和 EK 湍流（与n相关）的几个孤立结果= 1) 统一在这个理论框架中。利用该理论，预测了以下有趣的结果： (1) 当n < 2 / 3 时，动能的传输以 Kolmogorov 尺度η和另一个小尺度l _A为主。当n > 2 / 3 时，动能的传输由三个特征小尺度控制：l _K、l _ηK和l _A。(2) 比例律范围可分为惯性子范围和体积力支配子范围。(3) 在后一种情况下，速度的功率谱和相关标量的指数为η _u= (4 n -11)/5, η _A = -(2 n +7)/5 ，分别。(4) 在平衡状态下，n 不能超过 4。 (5) \({l_A} \sim 0.024Ra_{A.{l_0}}^{0.107 \pm 0.016}\)的正指数在湍流中得到确认热对流。